From f34e2382fa79211b7f03e4a7c0b80cdc9825389e Mon Sep 17 00:00:00 2001 From: Tomas Susanka Date: Fri, 20 Mar 2020 10:24:04 +0000 Subject: [PATCH 01/24] tests: add segwit attack test for mixed inputs --- tests/device_tests/test_msg_signtx_segwit.py | 122 +++++++++++++++++++ tests/ui_tests/fixtures.json | 1 + 2 files changed, 123 insertions(+) diff --git a/tests/device_tests/test_msg_signtx_segwit.py b/tests/device_tests/test_msg_signtx_segwit.py index 18ad6d01c6..7c1bccdc91 100644 --- a/tests/device_tests/test_msg_signtx_segwit.py +++ b/tests/device_tests/test_msg_signtx_segwit.py @@ -32,6 +32,34 @@ TXHASH_20912f = bytes.fromhex( TXHASH_9c3192 = bytes.fromhex( "9c31922be756c06d02167656465c8dc83bb553bf386a3f478ae65b5c021002be" ) +TXHASH_e5040e = bytes.fromhex( + "e5040e1bc1ae7667ffb9e5248e90b2fb93cd9150234151ce90e14ab2f5933bcd" +) + + +def request_input(n, tx_hash=None): + return proto.TxRequest( + request_type=proto.RequestType.TXINPUT, + details=proto.TxRequestDetailsType(request_index=n, tx_hash=tx_hash), + ) + + +def request_output(n, tx_hash=None): + return proto.TxRequest( + request_type=proto.RequestType.TXOUTPUT, + details=proto.TxRequestDetailsType(request_index=n, tx_hash=tx_hash), + ) + + +def request_meta(tx_hash): + return proto.TxRequest( + request_type=proto.RequestType.TXMETA, + details=proto.TxRequestDetailsType(tx_hash=tx_hash), + ) + + +def request_finished(): + return proto.TxRequest(request_type=proto.RequestType.TXFINISHED) class TestMsgSigntxSegwit: @@ -305,3 +333,97 @@ class TestMsgSigntxSegwit: assert exc.value.message.endswith( "Transaction has changed during signing" ) + + def test_attack_mixed_inputs(self, client): + TRUE_AMOUNT = 12345678 + FAKE_AMOUNT = 123 + + inp1 = proto.TxInputType( + address_n=parse_path("44'/1'/0'/0/0"), + amount=31000000, + prev_hash=TXHASH_e5040e, + prev_index=0, + script_type=proto.InputScriptType.SPENDADDRESS, + sequence=0xFFFFFFFD, + ) + inp2 = proto.TxInputType( + address_n=parse_path("49'/1'/0'/1/0"), + amount=TRUE_AMOUNT, + prev_hash=TXHASH_20912f, + prev_index=0, + script_type=proto.InputScriptType.SPENDP2SHWITNESS, + sequence=0xFFFFFFFD, + ) + out1 = proto.TxOutputType( + address="mhRx1CeVfaayqRwq5zgRQmD7W5aWBfD5mC", + amount=30998000, + script_type=proto.OutputScriptType.PAYTOADDRESS, + ) + + expected_responses = [ + request_input(0), + request_meta(TXHASH_e5040e), + request_input(0, TXHASH_e5040e), + request_output(0, TXHASH_e5040e), + request_output(1, TXHASH_e5040e), + request_input(1), + request_output(0), + proto.ButtonRequest(code=proto.ButtonRequestType.ConfirmOutput), + proto.ButtonRequest(code=proto.ButtonRequestType.FeeOverThreshold), + proto.ButtonRequest(code=proto.ButtonRequestType.SignTx), + request_input(0), + request_input(1), + request_output(0), + request_input(1), + request_output(0), + request_input(1), + ] + + if client.features.model == "1": + # T1 asks for first input for witness again + expected_responses.insert(-1, request_input(0)) + pass + + with client: + # Sign unmodified transaction. + # "Fee over threshold" warning is displayed - fee is the whole TRUE_AMOUNT + client.set_expected_responses(expected_responses + [request_finished()]) + btc.sign_tx( + client, "Testnet", [inp1, inp2], [out1], prev_txes=TX_API, + ) + + # In Phase 1 make the user confirm a lower value of the segwit input. + inp2.amount = FAKE_AMOUNT + + ctr = 3 + + def attack(msg): + nonlocal ctr + + if msg.tx.inputs and msg.tx.inputs[0] == inp2: + ctr -= 1 + if ctr <= 0: + # after Phase 1 is done and input 1 is signed, let Trezor sign + # the true amount in Phase 2 + msg.tx.inputs[0].amount = TRUE_AMOUNT + + return msg + + # Sign with attacker. + with pytest.raises(TrezorFailure) as e, client: + # "Fee over threshold" is NOT displayed, because the calculated fee + # in phase 1 is small. + assert expected_responses[8] == proto.ButtonRequest( + code=proto.ButtonRequestType.FeeOverThreshold + ) + del expected_responses[8] + + client.set_filter(proto.TxAck, attack) + client.set_expected_responses(expected_responses + [proto.Failure()]) + btc.sign_tx( + client, "Testnet", [inp1, inp2], [out1], prev_txes=TX_API, + ) + + assert e.value.failure.message.endswith( + "Transaction has changed during signing" + ) diff --git a/tests/ui_tests/fixtures.json b/tests/ui_tests/fixtures.json index 48ecf0061f..9cdad56f91 100644 --- a/tests/ui_tests/fixtures.json +++ b/tests/ui_tests/fixtures.json @@ -273,6 +273,7 @@ "test_msg_signtx_komodo.py-test_one_one_rewards_claim": "e53f221fda81469027e39e21877a81a8fafbffbece0a45aeda12aae8873b0464", "test_msg_signtx_peercoin.py::test_timestamp_included": "825b9bdf5238c5c6415a254a6bae4b2bd9df8fc5cb31f66f0c20145cb4e60bbb", "test_msg_signtx_segwit.py-test_attack_change_input_address": "5ae71202c062ef7942626a80a4ceeb8d8c4ea5065a97f0de6a97505e9cb82c2c", +"test_msg_signtx_segwit.py-test_attack_mixed_inputs": "5bc10a7cc5fab955f0e9003cf1eea603b5a55917e344ced106870bb3d5bb0306", "test_msg_signtx_segwit.py-test_send_multisig_1": "958a0741070e057dcb889b2000e5487d391bc513e4a5d86193a355261c5f361b", "test_msg_signtx_segwit.py-test_send_p2sh": "ca593e31e919b9e920289b13e4c70b9607f34b93d06ace69835e3d08ecf046c8", "test_msg_signtx_segwit.py-test_send_p2sh_change": "562c7ee5a2e264c9f93387dd165403dab32bb305a4c3a6143a902c4a4c9e5950", From 20dd1ddc60085f991a8b79bec38107221ffc2340 Mon Sep 17 00:00:00 2001 From: Andrew Kozlik Date: Tue, 14 Apr 2020 15:22:02 +0200 Subject: [PATCH 02/24] crypto: Fix buffer overflow in b58tobin. --- crypto/base58.c | 23 ++++++++++++----------- 1 file changed, 12 insertions(+), 11 deletions(-) diff --git a/crypto/base58.c b/crypto/base58.c index d95ac9a9d3..faa7635018 100644 --- a/crypto/base58.c +++ b/crypto/base58.c @@ -46,6 +46,9 @@ typedef uint32_t b58_almostmaxint_t; static const b58_almostmaxint_t b58_almostmaxint_mask = ((((b58_maxint_t)1) << b58_almostmaxint_bits) - 1); +// Decodes a null-terminated Base58 string `b58` to binary and writes the result +// at the end of the buffer `bin` of size `*binszp`. On success `*binszp` is set +// to the number of valid bytes at the end of the buffer. bool b58tobin(void *bin, size_t *binszp, const char *b58) { size_t binsz = *binszp; @@ -108,20 +111,18 @@ bool b58tobin(void *bin, size_t *binszp, const char *b58) { } } - // Count canonical base58 byte count + // locate the most significant byte binu = bin; for (i = 0; i < binsz; ++i) { - if (binu[i]) { - if (zerocount > i) { - /* result too large */ - return false; - } - - break; - } - --*binszp; + if (binu[i]) break; } - *binszp += zerocount; + + // prepend the correct number of null-bytes + if (zerocount > i) { + /* result too large */ + return false; + } + *binszp = binsz - i + zerocount; return true; } From 3843f917e9873b80ff2a68bde38be93708a92d76 Mon Sep 17 00:00:00 2001 From: Andrew Kozlik Date: Tue, 14 Apr 2020 17:03:40 +0200 Subject: [PATCH 03/24] crypto: Check for invalid characters in Monero Base58 decode. --- crypto/monero/base58.c | 2 ++ 1 file changed, 2 insertions(+) diff --git a/crypto/monero/base58.c b/crypto/monero/base58.c index 44da376e9a..ec6c4d779f 100644 --- a/crypto/monero/base58.c +++ b/crypto/monero/base58.c @@ -102,6 +102,8 @@ bool decode_block(const char* block, size_t size, char* res) uint64_t order = 1; for (size_t i = size - 1; i < size; --i) { + if (block[i] & 0x80) + return false; // Invalid symbol int digit = reverse_alphabet(block[i]); if (digit < 0) return false; // Invalid symbol From d80468055200bd07cebffd877255d98ae7300d0d Mon Sep 17 00:00:00 2001 From: matejcik Date: Wed, 25 Mar 2020 15:34:21 +0100 Subject: [PATCH 04/24] tests: simplify code of test_msg_signtx Instead of a function generating the expected_responses, introduce shortcuts (request_input, request_output...) so that the static expected_responses are more readable. Also introduce the possibility to include conditional responses (e.g., seen only on trezor-core) WIP --- tests/device_tests/test_msg_signtx.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/tests/device_tests/test_msg_signtx.py b/tests/device_tests/test_msg_signtx.py index 1322125752..7cb2545e2e 100644 --- a/tests/device_tests/test_msg_signtx.py +++ b/tests/device_tests/test_msg_signtx.py @@ -1167,5 +1167,5 @@ class TestMsgSigntx: TrezorFailure, match="Multisig field provided but not expected." ): btc.sign_tx( - client, "Testnet", [inp1], [out1, out2], prev_txes=TxCache("Testnet") + client, "Testnet", [inp1], [out1, out2], prev_txes=TX_CACHE_TESTNET ) From 7a3637d5b0b3162ee4bc93cd837c2b94126df1f5 Mon Sep 17 00:00:00 2001 From: matejcik Date: Fri, 27 Mar 2020 10:31:29 +0100 Subject: [PATCH 05/24] core/sign_tx: add checks for version_group_id and branch_id fields --- core/src/apps/bitcoin/sign_tx/helpers.py | 14 +++++++++++ tests/device_tests/test_msg_signtx.py | 13 ++++++++-- tests/device_tests/test_msg_signtx_zcash.py | 27 +++++++++++++++++++++ 3 files changed, 52 insertions(+), 2 deletions(-) diff --git a/core/src/apps/bitcoin/sign_tx/helpers.py b/core/src/apps/bitcoin/sign_tx/helpers.py index 57981711ac..09a10b2bf6 100644 --- a/core/src/apps/bitcoin/sign_tx/helpers.py +++ b/core/src/apps/bitcoin/sign_tx/helpers.py @@ -199,6 +199,13 @@ def sanitize_sign_tx(tx: SignTx, coin: CoinInfo) -> SignTx: raise wire.DataError("Timestamp must be set.") elif not coin.timestamp and tx.timestamp: raise wire.DataError("Timestamp not enabled on this coin.") + if coin.overwintered and tx.version_group_id is None: + raise wire.DataError("Version group ID must be set.") + elif not coin.overwintered: + if tx.version_group_id is not None: + raise wire.DataError("Version group ID not enabled on this coin.") + if tx.branch_id is not None: + raise wire.DataError("Branch ID not enabled on this coin.") return tx @@ -219,6 +226,13 @@ def sanitize_tx_meta(tx: TransactionType, coin: CoinInfo) -> TransactionType: raise wire.DataError("Timestamp must be set.") elif not coin.timestamp and tx.timestamp: raise wire.DataError("Timestamp not enabled on this coin.") + if coin.overwintered and tx.version_group_id is None: + raise wire.DataError("Version group ID must be set.") + elif not coin.overwintered: + if tx.version_group_id is not None: + raise wire.DataError("Version group ID not enabled on this coin.") + if tx.branch_id is not None: + raise wire.DataError("Branch ID not enabled on this coin.") return tx diff --git a/tests/device_tests/test_msg_signtx.py b/tests/device_tests/test_msg_signtx.py index 7cb2545e2e..2bbd9f6be2 100644 --- a/tests/device_tests/test_msg_signtx.py +++ b/tests/device_tests/test_msg_signtx.py @@ -1022,7 +1022,13 @@ class TestMsgSigntx: @pytest.mark.parametrize( "field, value", - (("extra_data", b"hello world"), ("expiry", 9), ("timestamp", 42)), + ( + ("extra_data", b"hello world"), + ("expiry", 9), + ("timestamp", 42), + ("version_group_id", 69), + ("branch_id", 13), + ), ) @pytest.mark.skip_ui def test_prevtx_forbidden_fields(self, client, field, value): @@ -1045,7 +1051,10 @@ class TestMsgSigntx: client, "Bitcoin", [inp0], [out1], prev_txes={TXHASH_157041: prev_tx} ) - @pytest.mark.parametrize("field, value", (("expiry", 9), ("timestamp", 42))) + @pytest.mark.parametrize( + "field, value", + (("expiry", 9), ("timestamp", 42), ("version_group_id", 69), ("branch_id", 13)), + ) @pytest.mark.skip_ui def test_signtx_forbidden_fields(self, client, field, value): inp0 = proto.TxInputType( diff --git a/tests/device_tests/test_msg_signtx_zcash.py b/tests/device_tests/test_msg_signtx_zcash.py index 7df4e1197f..103f820fed 100644 --- a/tests/device_tests/test_msg_signtx_zcash.py +++ b/tests/device_tests/test_msg_signtx_zcash.py @@ -17,6 +17,7 @@ import pytest from trezorlib import btc, messages as proto +from trezorlib.exceptions import TrezorFailure from trezorlib.tools import parse_path from ..tx_cache import TxCache @@ -133,3 +134,29 @@ class TestMsgSigntxZcash: serialized_tx.hex() == "0400008085202f890168039326c180fa7b1e999392e25a3ec6a8aec83c11b787ddb1746922020682e3000000006b483045022100f28298891f48706697a6f898ac18e39ce2c7cebe547b585d51cc22d80b1b21a602201a807b8a18544832d95d1e3ada82c0617bc6d97d3f24d1fb4801ac396647aa880121030e669acac1f280d1ddf441cd2ba5e97417bf2689e4bbec86df4f831bf9f7ffd0ffffffff016c9be111000000001976a9145b157a678a10021243307e4bb58f36375aa80e1088ac00000000000000000000000000000000000000" ) + + @pytest.mark.skip_ui + def test_version_group_id_missing(self, client): + inp1 = proto.TxInputType( + # tmQoJ3PTXgQLaRRZZYT6xk8XtjRbr2kCqwu + address_n=parse_path("m/44h/1h/0h/0/0"), + amount=300000000, + prev_hash=TXHASH_e38206, + prev_index=0, + ) + out1 = proto.TxOutputType( + address="tmJ1xYxP8XNTtCoDgvdmQPSrxh5qZJgy65Z", + amount=300000000 - 1940, + script_type=proto.OutputScriptType.PAYTOADDRESS, + ) + + details = proto.SignTx(version=4) + with pytest.raises(TrezorFailure, match="Version group ID must be set."): + btc.sign_tx( + client, + "Zcash Testnet", + [inp1], + [out1], + details=details, + prev_txes=TX_API, + ) From 396a509725402fefd340e46cdb494825d91cc4c1 Mon Sep 17 00:00:00 2001 From: matejcik Date: Fri, 27 Mar 2020 09:54:11 +0100 Subject: [PATCH 06/24] tests: update bgold test with actual transactions --- tests/device_tests/test_msg_signtx_bgold.py | 96 ++++++++++----------- 1 file changed, 45 insertions(+), 51 deletions(-) diff --git a/tests/device_tests/test_msg_signtx_bgold.py b/tests/device_tests/test_msg_signtx_bgold.py index 59acf1326a..8a620b31d5 100644 --- a/tests/device_tests/test_msg_signtx_bgold.py +++ b/tests/device_tests/test_msg_signtx_bgold.py @@ -18,7 +18,7 @@ import pytest from trezorlib import btc, messages as proto from trezorlib.exceptions import TrezorFailure -from trezorlib.tools import H_, parse_path +from trezorlib.tools import H_, btc_hash, parse_path from ..tx_cache import TxCache from .signtx import request_finished, request_input, request_output @@ -32,12 +32,6 @@ TXHASH_25526b = bytes.fromhex( TXHASH_db77c2 = bytes.fromhex( "db77c2461b840e6edbe7f9280043184a98e020d9795c1b65cb7cef2551a8fb18" ) -TXHASH_e5040e = bytes.fromhex( - "e5040e1bc1ae7667ffb9e5248e90b2fb93cd9150234151ce90e14ab2f5933bcd" -) -TXHASH_65b811 = bytes.fromhex( - "65b811d3eca0fe6915d9f2d77c86c5a7f19bf66b1b1253c2c51cb4ae5f0c017b" -) # All data taken from T1 @@ -46,7 +40,7 @@ class TestMsgSigntxBitcoinGold: def test_send_bitcoin_gold_change(self, client): inp1 = proto.TxInputType( address_n=parse_path("44'/156'/0'/0/0"), - amount=1995344, + amount=1252382934, prev_hash=TXHASH_25526b, prev_index=0, script_type=proto.InputScriptType.SPENDADDRESS, @@ -58,7 +52,7 @@ class TestMsgSigntxBitcoinGold: ) out2 = proto.TxOutputType( address="GfDB1tvjfm3bukeoBTtfNqrJVFohS2kCTe", - amount=73452, + amount=1252382934 - 1896050 - 1000, script_type=proto.OutputScriptType.PAYTOADDRESS, ) with client: @@ -80,14 +74,14 @@ class TestMsgSigntxBitcoinGold: ) assert ( - serialized_tx.hex() - == "010000000185c9dd4ae1071affd77d90b9d03c1b5fdd7c62cf30a9bb8230ad766cf06b5225000000006b483045022100963904da0731b71ce468afd45366dd80fbff566ec0d39c1161ab85d17459c7ca02202f5c24a7a7272d98b14a3f5bc000c7cde8ac0eb773f20f4c3131518186cc98854121023bd0ec4022d12d0106c5b7308a25572953ba1951f576f691354a7b147ee0cc1fffffffff0272ee1c00000000001976a9141c82b9c11f193ad82413caadc0955730572b50ae88acec1e0100000000001976a914ea5f904d195079a350b534db4446433b3cec222e88ac00000000" + btc_hash(serialized_tx)[::-1].hex() + == "39a0716c361610724c7c40916baa20808cbdd7538b6c38689ce80cb73e7f51d1" ) def test_send_bitcoin_gold_nochange(self, client): inp1 = proto.TxInputType( address_n=parse_path("44'/156'/0'/1/0"), - amount=1896050, + amount=1252382934, prev_hash=TXHASH_25526b, prev_index=0, script_type=proto.InputScriptType.SPENDADDRESS, @@ -95,14 +89,14 @@ class TestMsgSigntxBitcoinGold: inp2 = proto.TxInputType( address_n=parse_path("44'/156'/0'/0/1"), # 1LRspCZNFJcbuNKQkXgHMDucctFRQya5a3 - amount=73452, + amount=38448607, prev_hash=TXHASH_db77c2, - prev_index=1, + prev_index=0, script_type=proto.InputScriptType.SPENDADDRESS, ) out1 = proto.TxOutputType( address="GfDB1tvjfm3bukeoBTtfNqrJVFohS2kCTe", - amount=1934960, + amount=1252382934 + 38448607 - 1000, script_type=proto.OutputScriptType.PAYTOADDRESS, ) with client: @@ -124,14 +118,14 @@ class TestMsgSigntxBitcoinGold: ) assert ( - serialized_tx.hex() - == "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" + btc_hash(serialized_tx)[::-1].hex() + == "ac9d452b900eb747d3137e1f3044bb0f46efaeb6e0fc8c27b02d1d08d238a904" ) def test_attack_change_input(self, client): inp1 = proto.TxInputType( address_n=parse_path("44'/156'/11'/0/0"), - amount=1995344, + amount=1252382934, prev_hash=TXHASH_25526b, prev_index=0, script_type=proto.InputScriptType.SPENDADDRESS, @@ -143,7 +137,7 @@ class TestMsgSigntxBitcoinGold: ) out2 = proto.TxOutputType( address="GfDB1tvjfm3bukeoBTtfNqrJVFohS2kCTe", - amount=73452, + amount=1252382934 - 1896050 - 1000, script_type=proto.OutputScriptType.PAYTOADDRESS, ) @@ -194,7 +188,7 @@ class TestMsgSigntxBitcoinGold: address_n=parse_path("48'/156'/3'/0/0"), multisig=getmultisig(0, 0), # 33Ju286QvonBz5N1V754ZekQv4GLJqcc5R - amount=48490, + amount=1252382934, prev_hash=TXHASH_25526b, prev_index=0, script_type=proto.InputScriptType.SPENDMULTISIG, @@ -208,7 +202,7 @@ class TestMsgSigntxBitcoinGold: address_n=parse_path("48'/156'/3'/1/0"), multisig=getmultisig(1, 0), script_type=proto.OutputScriptType.PAYTOMULTISIG, - amount=24000, + amount=1252382934 - 24000 - 1000, ) with client: client.set_expected_responses( @@ -230,13 +224,13 @@ class TestMsgSigntxBitcoinGold: assert ( signatures[0].hex() - == "3045022100d954f341ddd3ec96e4bc6cdb90f2df9b2032723f85e4a0187346dd743130bfca0220105ce08b795c70dc09a55569d7874bff684a877219ec2fc37c88cdffe12f332c" + == "30440220271c46ef3d7c37bd499804128623da3aa0014f3b4447dd39c4573b23c4537f6902205329167b9eb48427af62b04bf5138295f4c38613f6ba955934d15c499bff0d8a" ) inp1 = proto.TxInputType( address_n=parse_path("48'/156'/1'/0/0"), multisig=getmultisig(0, 0, [b"", b"", signatures[0]]), - amount=48490, + amount=1252382934, prev_hash=TXHASH_25526b, prev_index=0, script_type=proto.InputScriptType.SPENDMULTISIG, @@ -263,17 +257,17 @@ class TestMsgSigntxBitcoinGold: assert ( signatures[0].hex() - == "30440220614f9a18695365a2edba0d930404a77cae970d3430ad86c5b5239a96fd54bf84022030bc76a322e3b2b1c987622b5eb6da23ac1e6c905ee9b3b6405a4e4edd5bbb87" + == "3045022100bdf8c4bd14217c183612c7e8f79691f6479bcb35aa403f77d70182f58633ac6e02205b10a79b7894bb40248a120c8fcb7096a46950593e4c5b48a20bc5ebe53d85fa" ) assert ( - serialized_tx.hex() - == "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" + btc_hash(serialized_tx)[::-1].hex() + == "b45ba21b69e1e1c6ad79f5408fe70d92fb861742d239cb6a952213f60c253e40" ) def test_send_p2sh(self, client): inp1 = proto.TxInputType( address_n=parse_path("49'/156'/0'/1/0"), - amount=123456789, + amount=1252382934, prev_hash=TXHASH_25526b, prev_index=0, script_type=proto.InputScriptType.SPENDP2SHWITNESS, @@ -286,7 +280,7 @@ class TestMsgSigntxBitcoinGold: out2 = proto.TxOutputType( address="GZFLExxrvWFuFT1xRzhfwQWSE2bPDedBfn", script_type=proto.OutputScriptType.PAYTOADDRESS, - amount=123456789 - 11000 - 12300000, + amount=1252382934 - 11000 - 12300000, ) with client: client.set_expected_responses( @@ -309,14 +303,14 @@ class TestMsgSigntxBitcoinGold: ) assert ( - serialized_tx.hex() - == "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" + btc_hash(serialized_tx)[::-1].hex() + == "d5732fc8a594ae3b7ba695d7b276b2186f8572b0eb157120e0ba35d3511c6060" ) def test_send_p2sh_witness_change(self, client): inp1 = proto.TxInputType( address_n=parse_path("49'/156'/0'/1/0"), - amount=123456789, + amount=1252382934, prev_hash=TXHASH_25526b, prev_index=0, script_type=proto.InputScriptType.SPENDP2SHWITNESS, @@ -329,7 +323,7 @@ class TestMsgSigntxBitcoinGold: out2 = proto.TxOutputType( address_n=parse_path("49'/156'/0'/1/0"), script_type=proto.OutputScriptType.PAYTOP2SHWITNESS, - amount=123456789 - 11000 - 12300000, + amount=1252382934 - 11000 - 12300000, ) with client: client.set_expected_responses( @@ -351,8 +345,8 @@ class TestMsgSigntxBitcoinGold: ) assert ( - serialized_tx.hex() - == "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" + btc_hash(serialized_tx)[::-1].hex() + == "eed4ef86a408602e35ae416591f349847db38cdaddef1429a9bb0e39520d100d" ) @pytest.mark.multisig @@ -370,15 +364,15 @@ class TestMsgSigntxBitcoinGold: inp1 = proto.TxInputType( address_n=parse_path("49'/156'/1'/1/0"), prev_hash=TXHASH_25526b, - prev_index=1, + prev_index=0, script_type=proto.InputScriptType.SPENDP2SHWITNESS, multisig=multisig, - amount=1610436, + amount=1252382934, ) out1 = proto.TxOutputType( address="GfDB1tvjfm3bukeoBTtfNqrJVFohS2kCTe", - amount=1605000, + amount=1252382934 - 1000, script_type=proto.OutputScriptType.PAYTOADDRESS, ) @@ -419,30 +413,30 @@ class TestMsgSigntxBitcoinGold: ) assert ( - serialized_tx.hex() - == "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" + btc_hash(serialized_tx)[::-1].hex() + == "efa5b21916ac7ea5316c38b2d7d5520d80cbe563c58304f956ea6ddb241001d1" ) def test_send_mixed_inputs(self, client): # First is non-segwit, second is segwit. inp1 = proto.TxInputType( - address_n=parse_path("44'/156'/0'/0/0"), - amount=31000000, - prev_hash=TXHASH_e5040e, + address_n=parse_path("44'/156'/11'/0/0"), + amount=38448607, + prev_hash=TXHASH_db77c2, prev_index=0, + script_type=proto.InputScriptType.SPENDADDRESS, ) - inp2 = proto.TxInputType( - address_n=parse_path("84'/156'/0'/1/0"), - amount=7289000, - prev_hash=TXHASH_65b811, - prev_index=1, - script_type=proto.InputScriptType.SPENDWITNESS, + address_n=parse_path("49'/156'/0'/1/0"), + amount=1252382934, + prev_hash=TXHASH_25526b, + prev_index=0, + script_type=proto.InputScriptType.SPENDP2SHWITNESS, ) out1 = proto.TxOutputType( address="GfDB1tvjfm3bukeoBTtfNqrJVFohS2kCTe", - amount=31000000 + 7289000 - 1000, + amount=38448607 + 1252382934 - 1000, script_type=proto.OutputScriptType.PAYTOADDRESS, ) @@ -452,6 +446,6 @@ class TestMsgSigntxBitcoinGold: ) assert ( - serialized_tx.hex() - == "01000000000102cd3b93f5b24ae190ce5141235091cd93fbb2908e24e5b9ff6776aec11b0e04e5000000006a473044022061e94392fa4c0a4bf510bf713c23a37c6c5f6f4dbe5c116e86cff23a93c578e9022026661d2ffb1102d07b7c1631270152441fa171d91108b75a7b9a2cc36ca7db6c4121023bd0ec4022d12d0106c5b7308a25572953ba1951f576f691354a7b147ee0cc1fffffffff7b010c5faeb41cc5c253121b6bf69bf1a7c5867cd7f2d91569fea0ecd311b8650100000000ffffffff01803a4802000000001976a914ea5f904d195079a350b534db4446433b3cec222e88ac0002483045022100e39d9bff8350b9ba20cb2ed88e82d7568a83184616acdc16bd1adb4005c5a471022066ff36084e896a69a91a0fad01721f20f2bb42b41e20be35e72fc3729ac7ace74121030b75ccac9add5f82a4c61fe34e791a2f2eda61b544bce4f6fa3d403bb0de748400000000" + btc_hash(serialized_tx)[::-1].hex() + == "2c64109fba890657e37f0782efda29bbc277dfd521658f185d302ddffcacffd2" ) From 4bc0289601e06ba6f6d57acbc79c540c737839aa Mon Sep 17 00:00:00 2001 From: matejcik Date: Fri, 27 Mar 2020 12:11:35 +0100 Subject: [PATCH 07/24] tests: update komodo test with optional message feature --- tests/device_tests/test_msg_signtx_komodo.py | 61 ++++++++++---------- 1 file changed, 29 insertions(+), 32 deletions(-) diff --git a/tests/device_tests/test_msg_signtx_komodo.py b/tests/device_tests/test_msg_signtx_komodo.py index 917b8d37da..0897d09b8b 100644 --- a/tests/device_tests/test_msg_signtx_komodo.py +++ b/tests/device_tests/test_msg_signtx_komodo.py @@ -54,22 +54,20 @@ class TestMsgSigntxKomodo: script_type=proto.OutputScriptType.PAYTOADDRESS, ) + trezor_core = client.features.model != "1" with client: - er = [ - request_input(0), - request_output(0), - proto.ButtonRequest(code=B.ConfirmOutput), - ] - if client.features.model != "1": # extra screen for lock_time - er += [proto.ButtonRequest(code=B.SignTx)] - er += [ - proto.ButtonRequest(code=B.SignTx), - request_input(0), - request_output(0), - request_finished(), - ] - - client.set_expected_responses(er) + client.set_expected_responses( + [ + request_input(0), + request_output(0), + proto.ButtonRequest(code=B.ConfirmOutput), + (trezor_core, proto.ButtonRequest(code=B.SignTx)), + proto.ButtonRequest(code=B.SignTx), + request_input(0), + request_output(0), + request_finished(), + ] + ) details = proto.SignTx( version=4, @@ -112,24 +110,23 @@ class TestMsgSigntxKomodo: script_type=proto.OutputScriptType.PAYTOADDRESS, ) + trezor_core = client.features.model != "1" with client: - er = [ - request_input(0), - request_output(0), - proto.ButtonRequest(code=B.ConfirmOutput), - request_output(1), - proto.ButtonRequest(code=B.ConfirmOutput), - ] - if client.features.model != "1": # extra screen for lock_time - er += [proto.ButtonRequest(code=B.SignTx)] - er += [ - proto.ButtonRequest(code=B.SignTx), - request_input(0), - request_output(0), - request_output(1), - request_finished(), - ] - client.set_expected_responses(er) + client.set_expected_responses( + [ + request_input(0), + request_output(0), + proto.ButtonRequest(code=B.ConfirmOutput), + request_output(1), + proto.ButtonRequest(code=B.ConfirmOutput), + (trezor_core, proto.ButtonRequest(code=B.SignTx)), + proto.ButtonRequest(code=B.SignTx), + request_input(0), + request_output(0), + request_output(1), + request_finished(), + ] + ) details = proto.SignTx( version=4, From 72ef86d79a1619f81f4dfcff0e91f5a27458db27 Mon Sep 17 00:00:00 2001 From: matejcik Date: Fri, 27 Mar 2020 12:39:34 +0100 Subject: [PATCH 08/24] all: enable extra_data for komodo --- common/defs/bitcoin/komodo.json | 2 +- core/src/apps/common/coininfo.py | 2 +- 2 files changed, 2 insertions(+), 2 deletions(-) diff --git a/common/defs/bitcoin/komodo.json b/common/defs/bitcoin/komodo.json index 8e821e80d3..2e16d42b6d 100644 --- a/common/defs/bitcoin/komodo.json +++ b/common/defs/bitcoin/komodo.json @@ -44,7 +44,7 @@ "3": 1537743641, "4": 1991772603 }, - "extra_data": false, + "extra_data": true, "timestamp": false, "confidential_assets": null } diff --git a/core/src/apps/common/coininfo.py b/core/src/apps/common/coininfo.py index 1851e434d7..0ae6003a79 100644 --- a/core/src/apps/common/coininfo.py +++ b/core/src/apps/common/coininfo.py @@ -940,7 +940,7 @@ def by_name(name: str) -> CoinInfo: decred=False, negative_fee=True, curve_name='secp256k1', - extra_data=False, + extra_data=True, timestamp=False, overwintered=True, confidential_assets=None, From d4390f78a4797f67b8431091cbe3853dfe3bda35 Mon Sep 17 00:00:00 2001 From: matejcik Date: Thu, 26 Mar 2020 16:07:04 +0100 Subject: [PATCH 09/24] tests: add request_meta queries (needed for transaction streaming) --- tests/device_tests/test_msg_signtx_bcash.py | 109 ++++++------------ tests/device_tests/test_msg_signtx_bgold.py | 42 ++++++- tests/device_tests/test_msg_signtx_grs.py | 29 ++++- tests/device_tests/test_msg_signtx_komodo.py | 16 ++- tests/device_tests/test_msg_signtx_segwit.py | 39 ++++++- .../test_msg_signtx_segwit_native.py | 59 +++++++++- tests/device_tests/test_msg_signtx_zcash.py | 19 ++- tests/device_tests/test_multisig.py | 10 +- ...1ab0c63321b1be7a8cad7bf5c5c216fcf062c.json | 22 ++++ ...b484fc32b96f89c3c39f98d86f90db16076a0.json | 18 +++ ...f752a3977d7e5337915071bb4151e6b711a78.json | 18 +++ ...a6856c6edcbf4d05ebef3486510ae1c293d5f.json | 22 ++++ ...27cdd5f1b3cd0b9907dd7ff1a07e14addc985.json | 22 ++++ ...3184a98e020d9795c1b65cb7cef2551a8fb18.json | 24 ++++ ...2d0891855e8acfe5334f9ebd72b9ad2de60cf.json | 22 ++++ ...0be865a387446e32fc876d086203f483f61d1.json | 22 ++++ ...4c8b4ce1d7724905f8ebef8dca26b0c8e0f1d.json | 21 ++++ ...70165818a829bbf4477cd1afe5149dbcd34b1.json | 21 ++++ ...0e3684e948709c5cdcaf12da3bb079c99448a.json | 22 ++++ ...c8cb4fc301961c5988cba56902d8ffb61c337.json | 22 ++++ ...5bad0b561ad1dfc047d0a7fbb8814668f91e5.json | 18 +++ ...6c5a7f19bf66b1b1253c2c51cb4ae5f0c017b.json | 22 ++++ ...c8dc83bb553bf386a3f478ae65b5c021002be.json | 22 ++++ ...aa77e8161a65009dc009489b48aa6587ce348.json | 18 +++ ...06b0398646b91acf314da028c3f03dd0179fc.json | 18 +++ ...4cb40896d9bb459951bdf590ca6a495293a02.json | 9 ++ ...aa665125464547db5c7a6cd28f21639fe1228.json | 18 +++ ...5efb8ad839953376ae5eceaf92774102c6e39.json | 22 ++++ ...e4cf1539c5172684721e38e69f4ef634d75dc.json | 25 ++++ ...8aea8c63e5ae29293991e7bfa80c126930368.json | 31 +++++ 30 files changed, 693 insertions(+), 89 deletions(-) create mode 100644 tests/txcache/bcash/502e8577b237b0152843a416f8f1ab0c63321b1be7a8cad7bf5c5c216fcf062c.json create mode 100644 tests/txcache/bcash/8b6db9b8ba24235d86b053ea2ccb484fc32b96f89c3c39f98d86f90db16076a0.json create mode 100644 tests/txcache/bcash/bc37c28dfb467d2ecb50261387bf752a3977d7e5337915071bb4151e6b711a78.json create mode 100644 tests/txcache/bcash/f68caf10df12d5b07a34601d88fa6856c6edcbf4d05ebef3486510ae1c293d5f.json create mode 100644 tests/txcache/bgold/25526bf06c76ad3082bba930cf627cdd5f1b3cd0b9907dd7ff1a07e14addc985.json create mode 100644 tests/txcache/bgold/db77c2461b840e6edbe7f9280043184a98e020d9795c1b65cb7cef2551a8fb18.json create mode 100644 tests/txcache/groestlcoin_testnet/09a48bce2f9d5c6e4f0cb9ea1b32d0891855e8acfe5334f9ebd72b9ad2de60cf.json create mode 100644 tests/txcache/groestlcoin_testnet/4f2f857f39ed1afe05542d058fb0be865a387446e32fc876d086203f483f61d1.json create mode 100644 tests/txcache/komodo/2807c5b126ec8e2b078cab0f12e4c8b4ce1d7724905f8ebef8dca26b0c8e0f1d.json create mode 100644 tests/txcache/komodo/7b28bd91119e9776f0d4ebd80e570165818a829bbf4477cd1afe5149dbcd34b1.json create mode 100644 tests/txcache/testnet/09144602765ce3dd8f4329445b20e3684e948709c5cdcaf12da3bb079c99448a.json create mode 100644 tests/txcache/testnet/20912f98ea3ed849042efed0fdac8cb4fc301961c5988cba56902d8ffb61c337.json create mode 100644 tests/txcache/testnet/31bc1c88ce6ae337a6b3057a16d5bad0b561ad1dfc047d0a7fbb8814668f91e5.json create mode 100644 tests/txcache/testnet/65b811d3eca0fe6915d9f2d77c86c5a7f19bf66b1b1253c2c51cb4ae5f0c017b.json create mode 100644 tests/txcache/testnet/9c31922be756c06d02167656465c8dc83bb553bf386a3f478ae65b5c021002be.json create mode 100644 tests/txcache/testnet/a345b85759b385c6446055e4c3baa77e8161a65009dc009489b48aa6587ce348.json create mode 100644 tests/txcache/testnet/c9348040bbc2024e12dcb4a0b4806b0398646b91acf314da028c3f03dd0179fc.json create mode 100644 tests/txcache/testnet/dee13c469e7ab28108a1ce470d74cb40896d9bb459951bdf590ca6a495293a02.json create mode 100644 tests/txcache/testnet/f41cbedd8becee05a830f418d13aa665125464547db5c7a6cd28f21639fe1228.json create mode 100644 tests/txcache/testnet/fbbff7f3c85f8067453d7c062bd5efb8ad839953376ae5eceaf92774102c6e39.json create mode 100644 tests/txcache/zcash_testnet/aaf51e4606c264e47e5c42c958fe4cf1539c5172684721e38e69f4ef634d75dc.json create mode 100644 tests/txcache/zcash_testnet/e3820602226974b1dd87b7113cc8aea8c63e5ae29293991e7bfa80c126930368.json diff --git a/tests/device_tests/test_msg_signtx_bcash.py b/tests/device_tests/test_msg_signtx_bcash.py index 9b20be92e9..ea46a0be6c 100644 --- a/tests/device_tests/test_msg_signtx_bcash.py +++ b/tests/device_tests/test_msg_signtx_bcash.py @@ -21,7 +21,7 @@ from trezorlib.exceptions import TrezorFailure from trezorlib.tools import H_, parse_path from ..tx_cache import TxCache -from .signtx import request_finished, request_input, request_output +from .signtx import request_finished, request_input, request_meta, request_output B = proto.ButtonRequestType TX_API = TxCache("Bcash") @@ -65,6 +65,9 @@ class TestMsgSigntxBch: client.set_expected_responses( [ request_input(0), + request_meta(TXHASH_bc37c2), + request_input(0, TXHASH_bc37c2), + request_output(0, TXHASH_bc37c2), request_output(0), request_output(1), proto.ButtonRequest(code=B.ConfirmOutput), @@ -110,7 +113,15 @@ class TestMsgSigntxBch: client.set_expected_responses( [ request_input(0), + request_meta(TXHASH_502e85), + request_input(0, TXHASH_502e85), + request_output(0, TXHASH_502e85), + request_output(1, TXHASH_502e85), request_input(1), + request_meta(TXHASH_502e85), + request_input(0, TXHASH_502e85), + request_output(0, TXHASH_502e85), + request_output(1, TXHASH_502e85), request_output(0), proto.ButtonRequest(code=B.ConfirmOutput), proto.ButtonRequest(code=B.SignTx), @@ -155,7 +166,15 @@ class TestMsgSigntxBch: client.set_expected_responses( [ request_input(0), + request_meta(TXHASH_502e85), + request_input(0, TXHASH_502e85), + request_output(0, TXHASH_502e85), + request_output(1, TXHASH_502e85), request_input(1), + request_meta(TXHASH_502e85), + request_input(0, TXHASH_502e85), + request_output(0, TXHASH_502e85), + request_output(1, TXHASH_502e85), request_output(0), proto.ButtonRequest(code=B.ConfirmOutput), proto.ButtonRequest(code=B.SignTx), @@ -174,81 +193,6 @@ class TestMsgSigntxBch: == "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" ) - def test_attack_amount(self, client): - inp1 = proto.TxInputType( - address_n=parse_path("44'/145'/0'/1/0"), - # bitcoincash:qzc5q87w069lzg7g3gzx0c8dz83mn7l02scej5aluw - amount=300, - prev_hash=TXHASH_502e85, - prev_index=0, - script_type=proto.InputScriptType.SPENDADDRESS, - ) - inp2 = proto.TxInputType( - address_n=parse_path("44'/145'/0'/0/1"), - # bitcoincash:qr23ajjfd9wd73l87j642puf8cad20lfmqdgwvpat4 - amount=70, - prev_hash=TXHASH_502e85, - prev_index=1, - script_type=proto.InputScriptType.SPENDADDRESS, - ) - out1 = proto.TxOutputType( - address="bitcoincash:qq6wnnkrz7ykaqvxrx4hmjvayvzjzml54uyk76arx4", - amount=200, - script_type=proto.OutputScriptType.PAYTOADDRESS, - ) - - # test if passes without modifications - with client: - client.set_expected_responses( - [ - request_input(0), - request_input(1), - request_output(0), - proto.ButtonRequest(code=B.ConfirmOutput), - proto.ButtonRequest(code=B.SignTx), - request_input(0), - request_input(1), - request_output(0), - request_finished(), - ] - ) - btc.sign_tx(client, "Bcash", [inp1, inp2], [out1], prev_txes=TX_API) - - run_attack = True - - def attack_processor(msg): - nonlocal run_attack - - if run_attack and msg.tx.inputs and msg.tx.inputs[0] == inp1: - # 300 is lowered to 280 at the first run - # the user confirms 280 but the transaction - # is spending 300 => larger fee without the user knowing - msg.tx.inputs[0].amount = 280 - run_attack = False - - return msg - - # now fails - client.set_filter(proto.TxAck, attack_processor) - with client: - client.set_expected_responses( - [ - request_input(0), - request_input(1), - request_output(0), - proto.ButtonRequest(code=B.ConfirmOutput), - proto.ButtonRequest(code=B.SignTx), - request_input(0), - request_input(1), - proto.Failure(), - ] - ) - - with pytest.raises( - TrezorFailure, match="Transaction has changed during signing" - ): - btc.sign_tx(client, "Bcash", [inp1, inp2], [out1], prev_txes=TX_API) - def test_attack_change_input(self, client): inp1 = proto.TxInputType( address_n=parse_path("44'/145'/10'/0/0"), @@ -287,6 +231,9 @@ class TestMsgSigntxBch: client.set_expected_responses( [ request_input(0), + request_meta(TXHASH_bc37c2), + request_input(0, TXHASH_bc37c2), + request_output(0, TXHASH_bc37c2), request_output(0), request_output(1), proto.ButtonRequest(code=B.ConfirmOutput), @@ -353,6 +300,10 @@ class TestMsgSigntxBch: client.set_expected_responses( [ request_input(0), + request_meta(TXHASH_f68caf), + request_input(0, TXHASH_f68caf), + request_output(0, TXHASH_f68caf), + request_output(1, TXHASH_f68caf), request_output(0), proto.ButtonRequest(code=B.ConfirmOutput), proto.ButtonRequest(code=B.SignTx), @@ -410,6 +361,9 @@ class TestMsgSigntxBch: client.set_expected_responses( [ request_input(0), + request_meta(TXHASH_8b6db9), + request_input(0, TXHASH_8b6db9), + request_output(0, TXHASH_8b6db9), request_output(0), proto.ButtonRequest(code=B.ConfirmOutput), request_output(1), @@ -444,6 +398,9 @@ class TestMsgSigntxBch: client.set_expected_responses( [ request_input(0), + request_meta(TXHASH_8b6db9), + request_input(0, TXHASH_8b6db9), + request_output(0, TXHASH_8b6db9), request_output(0), proto.ButtonRequest(code=B.ConfirmOutput), request_output(1), diff --git a/tests/device_tests/test_msg_signtx_bgold.py b/tests/device_tests/test_msg_signtx_bgold.py index 8a620b31d5..cb783a1865 100644 --- a/tests/device_tests/test_msg_signtx_bgold.py +++ b/tests/device_tests/test_msg_signtx_bgold.py @@ -21,7 +21,7 @@ from trezorlib.exceptions import TrezorFailure from trezorlib.tools import H_, btc_hash, parse_path from ..tx_cache import TxCache -from .signtx import request_finished, request_input, request_output +from .signtx import request_finished, request_input, request_meta, request_output B = proto.ButtonRequestType TX_API = TxCache("Bgold") @@ -59,6 +59,10 @@ class TestMsgSigntxBitcoinGold: client.set_expected_responses( [ request_input(0), + request_meta(TXHASH_25526b), + request_input(0, TXHASH_25526b), + request_output(0, TXHASH_25526b), + request_output(1, TXHASH_25526b), request_output(0), request_output(1), proto.ButtonRequest(code=B.ConfirmOutput), @@ -103,7 +107,15 @@ class TestMsgSigntxBitcoinGold: client.set_expected_responses( [ request_input(0), + request_meta(TXHASH_25526b), + request_input(0, TXHASH_25526b), + request_output(0, TXHASH_25526b), + request_output(1, TXHASH_25526b), request_input(1), + request_meta(TXHASH_db77c2), + request_input(0, TXHASH_db77c2), + request_input(1, TXHASH_db77c2), + request_output(0, TXHASH_db77c2), request_output(0), proto.ButtonRequest(code=B.ConfirmOutput), proto.ButtonRequest(code=B.SignTx), @@ -159,6 +171,10 @@ class TestMsgSigntxBitcoinGold: client.set_expected_responses( [ request_input(0), + request_meta(TXHASH_25526b), + request_input(0, TXHASH_25526b), + request_output(0, TXHASH_25526b), + request_output(1, TXHASH_25526b), request_output(0), request_output(1), proto.ButtonRequest(code=B.ConfirmOutput), @@ -208,6 +224,10 @@ class TestMsgSigntxBitcoinGold: client.set_expected_responses( [ request_input(0), + request_meta(TXHASH_25526b), + request_input(0, TXHASH_25526b), + request_output(0, TXHASH_25526b), + request_output(1, TXHASH_25526b), request_output(0), proto.ButtonRequest(code=B.ConfirmOutput), request_output(1), @@ -241,6 +261,10 @@ class TestMsgSigntxBitcoinGold: client.set_expected_responses( [ request_input(0), + request_meta(TXHASH_25526b), + request_input(0, TXHASH_25526b), + request_output(0, TXHASH_25526b), + request_output(1, TXHASH_25526b), request_output(0), proto.ButtonRequest(code=B.ConfirmOutput), request_output(1), @@ -286,6 +310,10 @@ class TestMsgSigntxBitcoinGold: client.set_expected_responses( [ request_input(0), + request_meta(TXHASH_25526b), + request_input(0, TXHASH_25526b), + request_output(0, TXHASH_25526b), + request_output(1, TXHASH_25526b), request_output(0), proto.ButtonRequest(code=B.ConfirmOutput), request_output(1), @@ -329,6 +357,10 @@ class TestMsgSigntxBitcoinGold: client.set_expected_responses( [ request_input(0), + request_meta(TXHASH_25526b), + request_input(0, TXHASH_25526b), + request_output(0, TXHASH_25526b), + request_output(1, TXHASH_25526b), request_output(0), proto.ButtonRequest(code=B.ConfirmOutput), request_output(1), @@ -380,6 +412,10 @@ class TestMsgSigntxBitcoinGold: client.set_expected_responses( [ request_input(0), + request_meta(TXHASH_25526b), + request_input(0, TXHASH_25526b), + request_output(0, TXHASH_25526b), + request_output(1, TXHASH_25526b), request_output(0), proto.ButtonRequest(code=B.ConfirmOutput), proto.ButtonRequest(code=B.SignTx), @@ -399,6 +435,10 @@ class TestMsgSigntxBitcoinGold: client.set_expected_responses( [ request_input(0), + request_meta(TXHASH_25526b), + request_input(0, TXHASH_25526b), + request_output(0, TXHASH_25526b), + request_output(1, TXHASH_25526b), request_output(0), proto.ButtonRequest(code=B.ConfirmOutput), proto.ButtonRequest(code=B.SignTx), diff --git a/tests/device_tests/test_msg_signtx_grs.py b/tests/device_tests/test_msg_signtx_grs.py index 0ac3b9dcec..27e75d44c6 100644 --- a/tests/device_tests/test_msg_signtx_grs.py +++ b/tests/device_tests/test_msg_signtx_grs.py @@ -23,6 +23,7 @@ from ..tx_cache import TxCache B = proto.ButtonRequestType TX_API = TxCache("Groestlcoin") +TX_API_TESTNET = TxCache("Groestlcoin Testnet") TXHASH_cb74c8 = bytes.fromhex( "cb74c8478c5814742c87cffdb4a21231869888f8042fb07a90e015a9db1f9d4a" @@ -101,7 +102,12 @@ class TestMsgSigntxGRS: ) details = proto.SignTx(lock_time=650756) _, serialized_tx = btc.sign_tx( - client, "Groestlcoin Testnet", [inp1], [out1, out2], details=details + client, + "Groestlcoin Testnet", + [inp1], + [out1, out2], + details=details, + prev_txes=TX_API_TESTNET, ) assert ( serialized_tx.hex() @@ -130,7 +136,12 @@ class TestMsgSigntxGRS: ) details = proto.SignTx(lock_time=650756) _, serialized_tx = btc.sign_tx( - client, "Groestlcoin Testnet", [inp1], [out1, out2], details=details + client, + "Groestlcoin Testnet", + [inp1], + [out1, out2], + details=details, + prev_txes=TX_API_TESTNET, ) assert ( serialized_tx.hex() @@ -158,7 +169,12 @@ class TestMsgSigntxGRS: ) details = proto.SignTx(lock_time=650713) _, serialized_tx = btc.sign_tx( - client, "Groestlcoin Testnet", [inp1], [out1, out2], details=details + client, + "Groestlcoin Testnet", + [inp1], + [out1, out2], + details=details, + prev_txes=TX_API_TESTNET, ) assert ( serialized_tx.hex() @@ -186,7 +202,12 @@ class TestMsgSigntxGRS: ) details = proto.SignTx(lock_time=650713) _, serialized_tx = btc.sign_tx( - client, "Groestlcoin Testnet", [inp1], [out1, out2], details=details + client, + "Groestlcoin Testnet", + [inp1], + [out1, out2], + details=details, + prev_txes=TX_API_TESTNET, ) assert ( serialized_tx.hex() diff --git a/tests/device_tests/test_msg_signtx_komodo.py b/tests/device_tests/test_msg_signtx_komodo.py index 0897d09b8b..aa086d9c82 100644 --- a/tests/device_tests/test_msg_signtx_komodo.py +++ b/tests/device_tests/test_msg_signtx_komodo.py @@ -20,7 +20,13 @@ from trezorlib import btc, messages as proto from trezorlib.tools import parse_path from ..tx_cache import TxCache -from .signtx import request_finished, request_input, request_output +from .signtx import ( + request_extra_data, + request_finished, + request_input, + request_meta, + request_output, +) B = proto.ButtonRequestType TX_API = TxCache("Komodo") @@ -59,6 +65,10 @@ class TestMsgSigntxKomodo: client.set_expected_responses( [ request_input(0), + request_meta(TXHASH_2807c), + request_input(0, TXHASH_2807c), + request_output(0, TXHASH_2807c), + request_extra_data(0, 11, TXHASH_2807c), request_output(0), proto.ButtonRequest(code=B.ConfirmOutput), (trezor_core, proto.ButtonRequest(code=B.SignTx)), @@ -115,6 +125,10 @@ class TestMsgSigntxKomodo: client.set_expected_responses( [ request_input(0), + request_meta(TXHASH_7b28bd), + request_input(0, TXHASH_7b28bd), + request_output(0, TXHASH_7b28bd), + request_extra_data(0, 11, TXHASH_7b28bd), request_output(0), proto.ButtonRequest(code=B.ConfirmOutput), request_output(1), diff --git a/tests/device_tests/test_msg_signtx_segwit.py b/tests/device_tests/test_msg_signtx_segwit.py index 7c1bccdc91..67b8dce7a1 100644 --- a/tests/device_tests/test_msg_signtx_segwit.py +++ b/tests/device_tests/test_msg_signtx_segwit.py @@ -21,7 +21,7 @@ from trezorlib.exceptions import TrezorFailure from trezorlib.tools import H_, parse_path from ..tx_cache import TxCache -from .signtx import request_finished, request_input, request_output +from .signtx import request_finished, request_input, request_meta, request_output B = proto.ButtonRequestType TX_API = TxCache("Testnet") @@ -32,6 +32,9 @@ TXHASH_20912f = bytes.fromhex( TXHASH_9c3192 = bytes.fromhex( "9c31922be756c06d02167656465c8dc83bb553bf386a3f478ae65b5c021002be" ) +TXHASH_dee13c = bytes.fromhex( + "dee13c469e7ab28108a1ce470d74cb40896d9bb459951bdf590ca6a495293a02" +) TXHASH_e5040e = bytes.fromhex( "e5040e1bc1ae7667ffb9e5248e90b2fb93cd9150234151ce90e14ab2f5933bcd" ) @@ -86,6 +89,10 @@ class TestMsgSigntxSegwit: client.set_expected_responses( [ request_input(0), + request_meta(TXHASH_20912f), + request_input(0, TXHASH_20912f), + request_output(0, TXHASH_20912f), + request_output(1, TXHASH_20912f), request_output(0), proto.ButtonRequest(code=B.ConfirmOutput), request_output(1), @@ -130,6 +137,10 @@ class TestMsgSigntxSegwit: client.set_expected_responses( [ request_input(0), + request_meta(TXHASH_20912f), + request_input(0, TXHASH_20912f), + request_output(0, TXHASH_20912f), + request_output(1, TXHASH_20912f), request_output(0), proto.ButtonRequest(code=B.ConfirmOutput), request_output(1), @@ -156,7 +167,7 @@ class TestMsgSigntxSegwit: inp1 = proto.TxInputType( address_n=parse_path("m/49'/1'/0'/0/0"), amount=2 ** 32 + 1, - prev_hash=b"\xff" * 32, + prev_hash=TXHASH_dee13c, prev_index=0, script_type=proto.InputScriptType.SPENDP2SHWITNESS, ) @@ -169,6 +180,8 @@ class TestMsgSigntxSegwit: client.set_expected_responses( [ request_input(0), + request_meta(TXHASH_dee13c), + request_output(0, TXHASH_dee13c), request_output(0), proto.ButtonRequest(code=B.ConfirmOutput), proto.ButtonRequest(code=B.SignTx), @@ -178,10 +191,12 @@ class TestMsgSigntxSegwit: request_finished(), ] ) - _, serialized_tx = btc.sign_tx(client, "Testnet", [inp1], [out1]) + _, serialized_tx = btc.sign_tx( + client, "Testnet", [inp1], [out1], prev_txes=TX_API + ) assert ( serialized_tx.hex() - == "01000000000101ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff00000000171600140099a7ecbd938ed1839f5f6bf6d50933c6db9d5cffffffff01010000000100000017a914097c569095163e84475d07aa95a1f736df895b7b8702483045022100cb9d3aa7a8064702e6b61c20c7fb9cb672c69d3786cf5efef8ad6d90136ca7d8022065119ff6c6e6e6960e6508fc5360359bb269bb25ef8d90019decaa0a050cc45a0121033add1f0e8e3c3136f7428dd4a4de1057380bd311f5b0856e2269170b4ffa65bf00000000" + == "01000000000101023a2995a4a60c59df1b9559b49b6d8940cb740d47cea10881b27a9e463ce1de00000000171600140099a7ecbd938ed1839f5f6bf6d50933c6db9d5cffffffff01010000000100000017a914097c569095163e84475d07aa95a1f736df895b7b8702483045022100965aa8897c7cd5f0bff830481ed5259bf662ed0415ab497a6a152a3c335eb0a1022060acbbbada909b6575ac6f19382a6bdf4cab2fa1c5421aa66677806f380ddb870121033add1f0e8e3c3136f7428dd4a4de1057380bd311f5b0856e2269170b4ffa65bf00000000" ) @pytest.mark.multisig @@ -216,6 +231,10 @@ class TestMsgSigntxSegwit: client.set_expected_responses( [ request_input(0), + request_meta(TXHASH_9c3192), + request_input(0, TXHASH_9c3192), + request_output(0, TXHASH_9c3192), + request_output(1, TXHASH_9c3192), request_output(0), proto.ButtonRequest(code=B.ConfirmOutput), proto.ButtonRequest(code=B.SignTx), @@ -235,6 +254,10 @@ class TestMsgSigntxSegwit: client.set_expected_responses( [ request_input(0), + request_meta(TXHASH_9c3192), + request_input(0, TXHASH_9c3192), + request_output(0, TXHASH_9c3192), + request_output(1, TXHASH_9c3192), request_output(0), proto.ButtonRequest(code=B.ConfirmOutput), proto.ButtonRequest(code=B.SignTx), @@ -278,6 +301,10 @@ class TestMsgSigntxSegwit: client.set_expected_responses( [ request_input(0), + request_meta(TXHASH_20912f), + request_input(0, TXHASH_20912f), + request_output(0, TXHASH_20912f), + request_output(1, TXHASH_20912f), request_output(0), proto.ButtonRequest(code=B.ConfirmOutput), request_output(1), @@ -316,6 +343,10 @@ class TestMsgSigntxSegwit: client.set_expected_responses( [ request_input(0), + request_meta(TXHASH_20912f), + request_input(0, TXHASH_20912f), + request_output(0, TXHASH_20912f), + request_output(1, TXHASH_20912f), request_output(0), proto.ButtonRequest(code=B.ConfirmOutput), request_output(1), diff --git a/tests/device_tests/test_msg_signtx_segwit_native.py b/tests/device_tests/test_msg_signtx_segwit_native.py index 1e97149867..47e1e1dedf 100644 --- a/tests/device_tests/test_msg_signtx_segwit_native.py +++ b/tests/device_tests/test_msg_signtx_segwit_native.py @@ -21,7 +21,7 @@ from trezorlib.tools import H_, parse_path from ..bip32 import deserialize from ..tx_cache import TxCache -from .signtx import request_finished, request_input, request_output +from .signtx import request_finished, request_input, request_meta, request_output B = proto.ButtonRequestType TX_API = TxCache("Testnet") @@ -79,6 +79,10 @@ class TestMsgSigntxSegwitNative: client.set_expected_responses( [ request_input(0), + request_meta(TXHASH_20912f), + request_input(0, TXHASH_20912f), + request_output(0, TXHASH_20912f), + request_output(1, TXHASH_20912f), request_output(0), proto.ButtonRequest(code=B.ConfirmOutput), request_output(1), @@ -123,6 +127,10 @@ class TestMsgSigntxSegwitNative: client.set_expected_responses( [ request_input(0), + request_meta(TXHASH_20912f), + request_input(0, TXHASH_20912f), + request_output(0, TXHASH_20912f), + request_output(1, TXHASH_20912f), request_output(0), proto.ButtonRequest(code=B.ConfirmOutput), request_output(1), @@ -165,6 +173,10 @@ class TestMsgSigntxSegwitNative: client.set_expected_responses( [ request_input(0), + request_meta(TXHASH_091446), + request_input(0, TXHASH_091446), + request_output(0, TXHASH_091446), + request_output(1, TXHASH_091446), request_output(0), proto.ButtonRequest(code=B.ConfirmOutput), request_output(1), @@ -208,6 +220,10 @@ class TestMsgSigntxSegwitNative: client.set_expected_responses( [ request_input(0), + request_meta(TXHASH_091446), + request_input(0, TXHASH_091446), + request_output(0, TXHASH_091446), + request_output(1, TXHASH_091446), request_output(0), proto.ButtonRequest(code=B.ConfirmOutput), request_output(1), @@ -266,7 +282,15 @@ class TestMsgSigntxSegwitNative: client.set_expected_responses( [ request_input(0), + request_meta(TXHASH_091446), + request_input(0, TXHASH_091446), + request_output(0, TXHASH_091446), + request_output(1, TXHASH_091446), request_input(1), + request_meta(TXHASH_65b811), + request_input(0, TXHASH_65b811), + request_output(0, TXHASH_65b811), + request_output(1, TXHASH_65b811), request_output(0), proto.ButtonRequest(code=B.ConfirmOutput), request_output(1), @@ -327,6 +351,10 @@ class TestMsgSigntxSegwitNative: client.set_expected_responses( [ request_input(0), + request_meta(TXHASH_9c3192), + request_input(0, TXHASH_9c3192), + request_output(0, TXHASH_9c3192), + request_output(1, TXHASH_9c3192), request_output(0), proto.ButtonRequest(code=B.ConfirmOutput), proto.ButtonRequest(code=B.SignTx), @@ -346,6 +374,10 @@ class TestMsgSigntxSegwitNative: client.set_expected_responses( [ request_input(0), + request_meta(TXHASH_9c3192), + request_input(0, TXHASH_9c3192), + request_output(0, TXHASH_9c3192), + request_output(1, TXHASH_9c3192), request_output(0), proto.ButtonRequest(code=B.ConfirmOutput), proto.ButtonRequest(code=B.SignTx), @@ -398,6 +430,9 @@ class TestMsgSigntxSegwitNative: client.set_expected_responses( [ request_input(0), + request_meta(TXHASH_f41cbe), + request_input(0, TXHASH_f41cbe), + request_output(0, TXHASH_f41cbe), request_output(0), proto.ButtonRequest(code=B.ConfirmOutput), proto.ButtonRequest(code=B.SignTx), @@ -417,6 +452,9 @@ class TestMsgSigntxSegwitNative: client.set_expected_responses( [ request_input(0), + request_meta(TXHASH_f41cbe), + request_input(0, TXHASH_f41cbe), + request_output(0, TXHASH_f41cbe), request_output(0), proto.ButtonRequest(code=B.ConfirmOutput), proto.ButtonRequest(code=B.SignTx), @@ -476,6 +514,9 @@ class TestMsgSigntxSegwitNative: client.set_expected_responses( [ request_input(0), + request_meta(TXHASH_c93480), + request_input(0, TXHASH_c93480), + request_output(0, TXHASH_c93480), request_output(0), proto.ButtonRequest(code=B.SignTx), request_input(0), @@ -495,6 +536,9 @@ class TestMsgSigntxSegwitNative: client.set_expected_responses( [ request_input(0), + request_meta(TXHASH_c93480), + request_input(0, TXHASH_c93480), + request_output(0, TXHASH_c93480), request_output(0), proto.ButtonRequest(code=B.SignTx), request_input(0), @@ -553,6 +597,9 @@ class TestMsgSigntxSegwitNative: client.set_expected_responses( [ request_input(0), + request_meta(TXHASH_31bc1c), + request_input(0, TXHASH_31bc1c), + request_output(0, TXHASH_31bc1c), request_output(0), proto.ButtonRequest(code=B.SignTx), request_input(0), @@ -572,6 +619,9 @@ class TestMsgSigntxSegwitNative: client.set_expected_responses( [ request_input(0), + request_meta(TXHASH_31bc1c), + request_input(0, TXHASH_31bc1c), + request_output(0, TXHASH_31bc1c), request_output(0), proto.ButtonRequest(code=B.SignTx), request_input(0), @@ -645,7 +695,14 @@ class TestMsgSigntxSegwitNative: client.set_expected_responses( [ request_input(0), + request_meta(TXHASH_091446), + request_input(0, TXHASH_091446), + request_output(0, TXHASH_091446), + request_output(1, TXHASH_091446), request_input(1), + request_meta(TXHASH_a345b8), + request_input(0, TXHASH_a345b8), + request_output(0, TXHASH_a345b8), request_output(0), proto.ButtonRequest(code=B.ConfirmOutput), request_output(1), diff --git a/tests/device_tests/test_msg_signtx_zcash.py b/tests/device_tests/test_msg_signtx_zcash.py index 103f820fed..c02e75da97 100644 --- a/tests/device_tests/test_msg_signtx_zcash.py +++ b/tests/device_tests/test_msg_signtx_zcash.py @@ -21,7 +21,13 @@ from trezorlib.exceptions import TrezorFailure from trezorlib.tools import parse_path from ..tx_cache import TxCache -from .signtx import request_finished, request_input, request_output +from .signtx import ( + request_extra_data, + request_finished, + request_input, + request_meta, + request_output, +) B = proto.ButtonRequestType TX_API = TxCache("Zcash Testnet") @@ -59,6 +65,11 @@ class TestMsgSigntxZcash: client.set_expected_responses( [ request_input(0), + request_meta(TXHASH_aaf51e), + request_input(0, TXHASH_aaf51e), + request_output(0, TXHASH_aaf51e), + request_output(1, TXHASH_aaf51e), + request_extra_data(0, 1, TXHASH_aaf51e), request_output(0), proto.ButtonRequest(code=B.ConfirmOutput), proto.ButtonRequest(code=B.SignTx), @@ -108,6 +119,12 @@ class TestMsgSigntxZcash: client.set_expected_responses( [ request_input(0), + request_meta(TXHASH_e38206), + request_input(0, TXHASH_e38206), + request_input(1, TXHASH_e38206), + request_output(0, TXHASH_e38206), + request_output(1, TXHASH_e38206), + request_extra_data(0, 1, TXHASH_e38206), request_output(0), proto.ButtonRequest(code=B.ConfirmOutput), proto.ButtonRequest(code=B.SignTx), diff --git a/tests/device_tests/test_multisig.py b/tests/device_tests/test_multisig.py index d534aee85c..4f186edd02 100644 --- a/tests/device_tests/test_multisig.py +++ b/tests/device_tests/test_multisig.py @@ -293,6 +293,10 @@ class TestMultisig: client.set_expected_responses( [ request_input(0), + request_meta(TXHASH_fbbff7), + request_input(0, TXHASH_fbbff7), + request_output(0, TXHASH_fbbff7), + request_output(1, TXHASH_fbbff7), request_output(0), proto.ButtonRequest(code=B.ConfirmOutput), request_output(1), @@ -307,7 +311,11 @@ class TestMultisig: with pytest.raises(TrezorFailure) as exc: btc.sign_tx( - client, "Testnet", [input_real], [output_payee, output_change] + client, + "Testnet", + [input_real], + [output_payee, output_change], + prev_txes=TxCache("Testnet"), ) # must not produce this tx: # 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 diff --git a/tests/txcache/bcash/502e8577b237b0152843a416f8f1ab0c63321b1be7a8cad7bf5c5c216fcf062c.json b/tests/txcache/bcash/502e8577b237b0152843a416f8f1ab0c63321b1be7a8cad7bf5c5c216fcf062c.json new file mode 100644 index 0000000000..299ae1009c --- /dev/null +++ b/tests/txcache/bcash/502e8577b237b0152843a416f8f1ab0c63321b1be7a8cad7bf5c5c216fcf062c.json @@ -0,0 +1,22 @@ +{ + "bin_outputs": [ + { + "amount": 1896050, + "script_pubkey": "76a914b1401fce7e8bf123c88a0467e0ed11e3b9fbef5488ac" + }, + { + "amount": 73452, + "script_pubkey": "76a914d51eca49695cdf47e7f4b55507893e3ad53fe9d888ac" + } + ], + "inputs": [ + { + "prev_hash": "bc37c28dfb467d2ecb50261387bf752a3977d7e5337915071bb4151e6b711a78", + "prev_index": 0, + "script_sig": "473044022061aee4f17abe044d5df8c52c9ffd3b84e5a29743517e488b20ecf1ae0b3e4d3a02206bb84c55e407f3b684ff8d9bea0a3409cfd865795a19d10b3d3c31f12795c34a412103a020b36130021a0f037c1d1a02042e325c0cb666d6478c1afdcd9d913b9ef080", + "sequence": 4294967295 + } + ], + "lock_time": 0, + "version": 1 +} diff --git a/tests/txcache/bcash/8b6db9b8ba24235d86b053ea2ccb484fc32b96f89c3c39f98d86f90db16076a0.json b/tests/txcache/bcash/8b6db9b8ba24235d86b053ea2ccb484fc32b96f89c3c39f98d86f90db16076a0.json new file mode 100644 index 0000000000..f80dbd426f --- /dev/null +++ b/tests/txcache/bcash/8b6db9b8ba24235d86b053ea2ccb484fc32b96f89c3c39f98d86f90db16076a0.json @@ -0,0 +1,18 @@ +{ + "bin_outputs": [ + { + "amount": 48490, + "script_pubkey": "a91411c1566006ab2b8e8c8d981055b090ecdefa977187" + } + ], + "inputs": [ + { + "prev_hash": "5f72ec264d961dfdd460a9cc22743c795127b129d40be8087244d93b3f7eee11", + "prev_index": 0, + "script_sig": "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", + "sequence": 4294967294 + } + ], + "lock_time": 0, + "version": 1 +} diff --git a/tests/txcache/bcash/bc37c28dfb467d2ecb50261387bf752a3977d7e5337915071bb4151e6b711a78.json b/tests/txcache/bcash/bc37c28dfb467d2ecb50261387bf752a3977d7e5337915071bb4151e6b711a78.json new file mode 100644 index 0000000000..e4b271a6ec --- /dev/null +++ b/tests/txcache/bcash/bc37c28dfb467d2ecb50261387bf752a3977d7e5337915071bb4151e6b711a78.json @@ -0,0 +1,18 @@ +{ + "bin_outputs": [ + { + "amount": 1995344, + "script_pubkey": "76a914de701ce12e576395c863e9377c76dd7efe0c55c188ac" + } + ], + "inputs": [ + { + "prev_hash": "8d566ad80d5f1d3887d3acddb35b980641919e6efa7c3a3a78413e56f95ea516", + "prev_index": 1, + "script_sig": "483045022100860b4c43649f86ee603c13791646af4736c50b532e1fc905c53d73ddd3754f3902206a301113f27b0d10622b333eb914751eed8af7f5534e0e4ee01176668674f259412102e227a30cc2aa732090af6667086b1665cbe6dbde71aab95ada5a518a4c2fdb6e", + "sequence": 4294967295 + } + ], + "lock_time": 0, + "version": 1 +} diff --git a/tests/txcache/bcash/f68caf10df12d5b07a34601d88fa6856c6edcbf4d05ebef3486510ae1c293d5f.json b/tests/txcache/bcash/f68caf10df12d5b07a34601d88fa6856c6edcbf4d05ebef3486510ae1c293d5f.json new file mode 100644 index 0000000000..e27a61cd9d --- /dev/null +++ b/tests/txcache/bcash/f68caf10df12d5b07a34601d88fa6856c6edcbf4d05ebef3486510ae1c293d5f.json @@ -0,0 +1,22 @@ +{ + "bin_outputs": [ + { + "amount": 24000, + "script_pubkey": "76a91400741952f6a6eab5394f366db5cc5a54b0c2429f88ac" + }, + { + "amount": 24000, + "script_pubkey": "a914756c06d7e77de3950a6124f026d8e1a2464b3ecf87" + } + ], + "inputs": [ + { + "prev_hash": "8b6db9b8ba24235d86b053ea2ccb484fc32b96f89c3c39f98d86f90db16076a0", + "prev_index": 0, + "script_sig": "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", + "sequence": 4294967295 + } + ], + "lock_time": 0, + "version": 1 +} diff --git a/tests/txcache/bgold/25526bf06c76ad3082bba930cf627cdd5f1b3cd0b9907dd7ff1a07e14addc985.json b/tests/txcache/bgold/25526bf06c76ad3082bba930cf627cdd5f1b3cd0b9907dd7ff1a07e14addc985.json new file mode 100644 index 0000000000..73635e9690 --- /dev/null +++ b/tests/txcache/bgold/25526bf06c76ad3082bba930cf627cdd5f1b3cd0b9907dd7ff1a07e14addc985.json @@ -0,0 +1,22 @@ +{ + "bin_outputs": [ + { + "amount": 1252382934, + "script_pubkey": "76a9140cb60a52559620e5de9a297612d49f55f7fd14ea88ac" + }, + { + "amount": 0, + "script_pubkey": "6a24aa21a9eddb3ac2bba12721c8db157ba6b522196093d3a27a8083591a2b785a230a1d254f" + } + ], + "inputs": [ + { + "prev_hash": "0000000000000000000000000000000000000000000000000000000000000000", + "prev_index": 4294967295, + "script_sig": "03b4e407005a2d4e4f4d50212068747470733a2f2f6769746875622e636f6d2f6a6f7368756179616275742f7a2d6e6f6d70", + "sequence": 4294967295 + } + ], + "lock_time": 0, + "version": 1 +} diff --git a/tests/txcache/bgold/db77c2461b840e6edbe7f9280043184a98e020d9795c1b65cb7cef2551a8fb18.json b/tests/txcache/bgold/db77c2461b840e6edbe7f9280043184a98e020d9795c1b65cb7cef2551a8fb18.json new file mode 100644 index 0000000000..1bb1a0e3a8 --- /dev/null +++ b/tests/txcache/bgold/db77c2461b840e6edbe7f9280043184a98e020d9795c1b65cb7cef2551a8fb18.json @@ -0,0 +1,24 @@ +{ + "bin_outputs": [ + { + "amount": 38448607, + "script_pubkey": "76a914b79bbff2766286a99129642d70912c6a4223c62b88ac" + } + ], + "inputs": [ + { + "prev_hash": "52fb172f86926a89a16edf55bc9baec3929149b7cd2d2389be3c7d08d744d300", + "prev_index": 1, + "script_sig": "4830450221008bff524a092086372a19b924f41fa7fa2a5523bf42a4801b9503fcdfff2094e8022000f223a032bd0d7fee31d5663cd5cf86b82533bda6871366d519a68deae1042341210222c6760cc54de6fd7f2a40207a13137d497c7cdb472376523700d8ea88275a96", + "sequence": 4294967295 + }, + { + "prev_hash": "371eb4feaa4085b378bb825f3c1b457867c24211ee838584b1adac226bba654b", + "prev_index": 0, + "script_sig": "47304402206aee1d853479782029755dd3c360dbd963e6390da12ddf2c2c38314692510385022040c9c01253a77bc33ac11ce0e8c187ab4f2d78346c0b222a87b1f00fea6b212941210222c6760cc54de6fd7f2a40207a13137d497c7cdb472376523700d8ea88275a96", + "sequence": 4294967295 + } + ], + "lock_time": 0, + "version": 1 +} diff --git a/tests/txcache/groestlcoin_testnet/09a48bce2f9d5c6e4f0cb9ea1b32d0891855e8acfe5334f9ebd72b9ad2de60cf.json b/tests/txcache/groestlcoin_testnet/09a48bce2f9d5c6e4f0cb9ea1b32d0891855e8acfe5334f9ebd72b9ad2de60cf.json new file mode 100644 index 0000000000..eb7ad9b549 --- /dev/null +++ b/tests/txcache/groestlcoin_testnet/09a48bce2f9d5c6e4f0cb9ea1b32d0891855e8acfe5334f9ebd72b9ad2de60cf.json @@ -0,0 +1,22 @@ +{ + "bin_outputs": [ + { + "amount": 123456789, + "script_pubkey": "a91458b53ea7f832e8f096e896b8713a8c6df0e892ca87" + }, + { + "amount": 9764242764, + "script_pubkey": "76a91435528b20e9a793cf2c3a1cf9cff1f2127ad377da88ac" + } + ], + "inputs": [ + { + "prev_hash": "4f2f857f39ed1afe05542d058fb0be865a387446e32fc876d086203f483f61d1", + "prev_index": 1, + "script_sig": "47304402201f8f57f708144c3a11da322546cb37bd385aa825d940c37e8016f0efd6ec3e9402202a41bc02c29e4f3f13efd4bededbcd4308a6393279111d614ee1f7635cf3e65701210371546a36bdf6bc82087301b3f6e759736dc8790150673d2e7e2715d2ad72f3a4", + "sequence": 4294967294 + } + ], + "lock_time": 650749, + "version": 1 +} diff --git a/tests/txcache/groestlcoin_testnet/4f2f857f39ed1afe05542d058fb0be865a387446e32fc876d086203f483f61d1.json b/tests/txcache/groestlcoin_testnet/4f2f857f39ed1afe05542d058fb0be865a387446e32fc876d086203f483f61d1.json new file mode 100644 index 0000000000..ab29fbe3f5 --- /dev/null +++ b/tests/txcache/groestlcoin_testnet/4f2f857f39ed1afe05542d058fb0be865a387446e32fc876d086203f483f61d1.json @@ -0,0 +1,22 @@ +{ + "bin_outputs": [ + { + "amount": 12300000, + "script_pubkey": "0014b31dc2a236505a6cb9201fa0411ca38a254a7bf1" + }, + { + "amount": 9887699777, + "script_pubkey": "76a91438cc090e4a4b2e458c33fe35af1c5c0094699ac288ac" + } + ], + "inputs": [ + { + "prev_hash": "1c92508b38239e5c10b23fb46dcf765ee2f3a95b835edbf0943ec21b21711160", + "prev_index": 1, + "script_sig": "483045022100d9615361c044e91f6dd7bb4455f3ad686cd5a663d7800bb74c448b2706500ccb022026bed24b81a501e8398411c5a9a793741d9bfe39617d51c363dde0a84f44f4f9012102659a6eefcc72d6f2eff92e57095388b17db0b06034946ecd44120e5e7a830ff4", + "sequence": 4294967293 + } + ], + "lock_time": 650645, + "version": 1 +} diff --git a/tests/txcache/komodo/2807c5b126ec8e2b078cab0f12e4c8b4ce1d7724905f8ebef8dca26b0c8e0f1d.json b/tests/txcache/komodo/2807c5b126ec8e2b078cab0f12e4c8b4ce1d7724905f8ebef8dca26b0c8e0f1d.json new file mode 100644 index 0000000000..3b8cfb2f9d --- /dev/null +++ b/tests/txcache/komodo/2807c5b126ec8e2b078cab0f12e4c8b4ce1d7724905f8ebef8dca26b0c8e0f1d.json @@ -0,0 +1,21 @@ +{ + "bin_outputs": [ + { + "amount": 1099980000, + "script_pubkey": "76a91400178fa0b6fc253a3a402ee2cadd8a7bfec08f6388ac" + } + ], + "branch_id": 1991772603, + "inputs": [ + { + "prev_hash": "340d478f0c5750057d5f5028db8c10993578849e63f5cf8500e33ddefcd5334f", + "prev_index": 0, + "script_sig": "483045022100d29433faed373d23883ace59acda117a67d6e8e3e99bc767b96a183a840b4aec0220258baef0d63360324f2a455299b2695ae2fa727a5969a25a604c22086e36c6e9012102a87aef7b1a8f676e452d6240767699719cd58b0261c822472c25df146938bca5", + "sequence": 4294967295 + } + ], + "extra_data": "0000000000000000000000", + "lock_time": 0, + "version": 4, + "version_group_id": 2301567109 +} diff --git a/tests/txcache/komodo/7b28bd91119e9776f0d4ebd80e570165818a829bbf4477cd1afe5149dbcd34b1.json b/tests/txcache/komodo/7b28bd91119e9776f0d4ebd80e570165818a829bbf4477cd1afe5149dbcd34b1.json new file mode 100644 index 0000000000..8d34ffb0c9 --- /dev/null +++ b/tests/txcache/komodo/7b28bd91119e9776f0d4ebd80e570165818a829bbf4477cd1afe5149dbcd34b1.json @@ -0,0 +1,21 @@ +{ + "bin_outputs": [ + { + "amount": 1099970000, + "script_pubkey": "76a91400178fa0b6fc253a3a402ee2cadd8a7bfec08f6388ac" + } + ], + "branch_id": 1991772603, + "inputs": [ + { + "prev_hash": "2807c5b126ec8e2b078cab0f12e4c8b4ce1d7724905f8ebef8dca26b0c8e0f1d", + "prev_index": 0, + "script_sig": "4730440220158c970ca2fc6bcc33026eb5366f0342f63b35d178f7efb334b1df78fe90b67202207bc4ff69f67cf843b08564a5adc77bf5593e28ab4d5104911824ac13fe885d8f012102a87aef7b1a8f676e452d6240767699719cd58b0261c822472c25df146938bca5", + "sequence": 4294967295 + } + ], + "extra_data": "0000000000000000000000", + "lock_time": 1563046072, + "version": 4, + "version_group_id": 2301567109 +} diff --git a/tests/txcache/testnet/09144602765ce3dd8f4329445b20e3684e948709c5cdcaf12da3bb079c99448a.json b/tests/txcache/testnet/09144602765ce3dd8f4329445b20e3684e948709c5cdcaf12da3bb079c99448a.json new file mode 100644 index 0000000000..34731eb2a9 --- /dev/null +++ b/tests/txcache/testnet/09144602765ce3dd8f4329445b20e3684e948709c5cdcaf12da3bb079c99448a.json @@ -0,0 +1,22 @@ +{ + "bin_outputs": [ + { + "amount": 12300000, + "script_pubkey": "00140099a7ecbd938ed1839f5f6bf6d50933c6db9d5c" + }, + { + "amount": 111145789, + "script_pubkey": "a91458b53ea7f832e8f096e896b8713a8c6df0e892ca87" + } + ], + "inputs": [ + { + "prev_hash": "20912f98ea3ed849042efed0fdac8cb4fc301961c5988cba56902d8ffb61c337", + "prev_index": 0, + "script_sig": "160014d16b8c0680c61fc6ed2e407455715055e41052f5", + "sequence": 4294967295 + } + ], + "lock_time": 0, + "version": 1 +} diff --git a/tests/txcache/testnet/20912f98ea3ed849042efed0fdac8cb4fc301961c5988cba56902d8ffb61c337.json b/tests/txcache/testnet/20912f98ea3ed849042efed0fdac8cb4fc301961c5988cba56902d8ffb61c337.json new file mode 100644 index 0000000000..4ca9d24cd3 --- /dev/null +++ b/tests/txcache/testnet/20912f98ea3ed849042efed0fdac8cb4fc301961c5988cba56902d8ffb61c337.json @@ -0,0 +1,22 @@ +{ + "bin_outputs": [ + { + "amount": 123456789, + "script_pubkey": "a91458b53ea7f832e8f096e896b8713a8c6df0e892ca87" + }, + { + "amount": 865519308, + "script_pubkey": "76a914b84bacdcd8f4cc59274a5bfb73f804ca10f7fd1488ac" + } + ], + "inputs": [ + { + "prev_hash": "802cabf0843b945eabe136d7fc7c89f41021658abf56cba000acbce88c41143a", + "prev_index": 0, + "script_sig": "4730440220548e087d0426b20b8a571b03b9e05829f7558b80c53c12143e342f56ab29e51d02205b68cb7fb223981d4c999725ac1485a982c4259c4f50b8280f137878c232998a012102794a25b254a268e59a5869da57fbae2fadc6727cb3309321dab409b12b2fa17c", + "sequence": 4294967295 + } + ], + "lock_time": 0, + "version": 1 +} diff --git a/tests/txcache/testnet/31bc1c88ce6ae337a6b3057a16d5bad0b561ad1dfc047d0a7fbb8814668f91e5.json b/tests/txcache/testnet/31bc1c88ce6ae337a6b3057a16d5bad0b561ad1dfc047d0a7fbb8814668f91e5.json new file mode 100644 index 0000000000..0530ad4a98 --- /dev/null +++ b/tests/txcache/testnet/31bc1c88ce6ae337a6b3057a16d5bad0b561ad1dfc047d0a7fbb8814668f91e5.json @@ -0,0 +1,18 @@ +{ + "bin_outputs": [ + { + "amount": 1603000, + "script_pubkey": "a914a8655acf68f785125561158b0f4db9b5d004404787" + } + ], + "inputs": [ + { + "prev_hash": "c9348040bbc2024e12dcb4a0b4806b0398646b91acf314da028c3f03dd0179fc", + "prev_index": 0, + "script_sig": "", + "sequence": 4294967295 + } + ], + "lock_time": 0, + "version": 1 +} diff --git a/tests/txcache/testnet/65b811d3eca0fe6915d9f2d77c86c5a7f19bf66b1b1253c2c51cb4ae5f0c017b.json b/tests/txcache/testnet/65b811d3eca0fe6915d9f2d77c86c5a7f19bf66b1b1253c2c51cb4ae5f0c017b.json new file mode 100644 index 0000000000..a6d82b759a --- /dev/null +++ b/tests/txcache/testnet/65b811d3eca0fe6915d9f2d77c86c5a7f19bf66b1b1253c2c51cb4ae5f0c017b.json @@ -0,0 +1,22 @@ +{ + "bin_outputs": [ + { + "amount": 5000000, + "script_pubkey": "a9147a55d61848e77ca266e79a39bfc85c580a6426c987" + }, + { + "amount": 7289000, + "script_pubkey": "0014d16b8c0680c61fc6ed2e407455715055e41052f5" + } + ], + "inputs": [ + { + "prev_hash": "09144602765ce3dd8f4329445b20e3684e948709c5cdcaf12da3bb079c99448a", + "prev_index": 0, + "script_sig": "", + "sequence": 4294967295 + } + ], + "lock_time": 0, + "version": 1 +} diff --git a/tests/txcache/testnet/9c31922be756c06d02167656465c8dc83bb553bf386a3f478ae65b5c021002be.json b/tests/txcache/testnet/9c31922be756c06d02167656465c8dc83bb553bf386a3f478ae65b5c021002be.json new file mode 100644 index 0000000000..ce6c36afcc --- /dev/null +++ b/tests/txcache/testnet/9c31922be756c06d02167656465c8dc83bb553bf386a3f478ae65b5c021002be.json @@ -0,0 +1,22 @@ +{ + "bin_outputs": [ + { + "amount": 11924164, + "script_pubkey": "76a914b6fc54e2f7c490ba20c686f532bfb02230656dbf88ac" + }, + { + "amount": 1610436, + "script_pubkey": "a91463ff81a0110ab929bd1d44befa32b081839bbece87" + } + ], + "inputs": [ + { + "prev_hash": "fbbf0824193fc4e4bb410276345cc235d530563d0da63ecc8d0fecf483c01e5e", + "prev_index": 1, + "script_sig": "47304402206d881393370f90ed0d74121b840794c62701a3fb98f2b14c45cbdc3869f7085802201a884b10eb1a5af026635d266e9b4514a9639b78d0a25cf7ebc579bca254fc7301210307c080981397c49589f3a8eb61e58d654ed1c2aa2fe049149c9757e4ba2a6ba8", + "sequence": 4294967295 + } + ], + "lock_time": 0, + "version": 1 +} diff --git a/tests/txcache/testnet/a345b85759b385c6446055e4c3baa77e8161a65009dc009489b48aa6587ce348.json b/tests/txcache/testnet/a345b85759b385c6446055e4c3baa77e8161a65009dc009489b48aa6587ce348.json new file mode 100644 index 0000000000..96b81e66ac --- /dev/null +++ b/tests/txcache/testnet/a345b85759b385c6446055e4c3baa77e8161a65009dc009489b48aa6587ce348.json @@ -0,0 +1,18 @@ +{ + "bin_outputs": [ + { + "amount": 100, + "script_pubkey": "002008b681071cd896cd879102bce735080758ad48ad45a05505939e55f115391991" + } + ], + "inputs": [ + { + "prev_hash": "5a67c3318c1636e192924c30ca849dec057892acdce5931b504dc453248d681e", + "prev_index": 0, + "script_sig": "", + "sequence": 4294967293 + } + ], + "lock_time": 1583125, + "version": 2 +} diff --git a/tests/txcache/testnet/c9348040bbc2024e12dcb4a0b4806b0398646b91acf314da028c3f03dd0179fc.json b/tests/txcache/testnet/c9348040bbc2024e12dcb4a0b4806b0398646b91acf314da028c3f03dd0179fc.json new file mode 100644 index 0000000000..c847c31b39 --- /dev/null +++ b/tests/txcache/testnet/c9348040bbc2024e12dcb4a0b4806b0398646b91acf314da028c3f03dd0179fc.json @@ -0,0 +1,18 @@ +{ + "bin_outputs": [ + { + "amount": 1604000, + "script_pubkey": "00201e8dda334f11171190b3da72e526d441491464769679a319a2f011da5ad312a1" + } + ], + "inputs": [ + { + "prev_hash": "f41cbedd8becee05a830f418d13aa665125464547db5c7a6cd28f21639fe1228", + "prev_index": 0, + "script_sig": "", + "sequence": 4294967295 + } + ], + "lock_time": 0, + "version": 1 +} diff --git a/tests/txcache/testnet/dee13c469e7ab28108a1ce470d74cb40896d9bb459951bdf590ca6a495293a02.json b/tests/txcache/testnet/dee13c469e7ab28108a1ce470d74cb40896d9bb459951bdf590ca6a495293a02.json new file mode 100644 index 0000000000..582d0d6c60 --- /dev/null +++ b/tests/txcache/testnet/dee13c469e7ab28108a1ce470d74cb40896d9bb459951bdf590ca6a495293a02.json @@ -0,0 +1,9 @@ +{ + "bin_outputs": [ + { + "amount": 4294967297, + "script_pubkey": "4d7920686f76657263726166742069732066756c6c206f662065656c732e" + } + ], + "version": 1 +} diff --git a/tests/txcache/testnet/f41cbedd8becee05a830f418d13aa665125464547db5c7a6cd28f21639fe1228.json b/tests/txcache/testnet/f41cbedd8becee05a830f418d13aa665125464547db5c7a6cd28f21639fe1228.json new file mode 100644 index 0000000000..6e70f9f3cd --- /dev/null +++ b/tests/txcache/testnet/f41cbedd8becee05a830f418d13aa665125464547db5c7a6cd28f21639fe1228.json @@ -0,0 +1,18 @@ +{ + "bin_outputs": [ + { + "amount": 1605000, + "script_pubkey": "0020c5f4a0a4ea7c0392efe0a9670a73264cffa90b19107cd8a8e9750ff93c77fdfb" + } + ], + "inputs": [ + { + "prev_hash": "9c31922be756c06d02167656465c8dc83bb553bf386a3f478ae65b5c021002be", + "prev_index": 1, + "script_sig": "2200201e8dda334f11171190b3da72e526d441491464769679a319a2f011da5ad312a1", + "sequence": 4294967295 + } + ], + "lock_time": 0, + "version": 1 +} diff --git a/tests/txcache/testnet/fbbff7f3c85f8067453d7c062bd5efb8ad839953376ae5eceaf92774102c6e39.json b/tests/txcache/testnet/fbbff7f3c85f8067453d7c062bd5efb8ad839953376ae5eceaf92774102c6e39.json new file mode 100644 index 0000000000..4dfff45596 --- /dev/null +++ b/tests/txcache/testnet/fbbff7f3c85f8067453d7c062bd5efb8ad839953376ae5eceaf92774102c6e39.json @@ -0,0 +1,22 @@ +{ + "bin_outputs": [ + { + "amount": 3199834, + "script_pubkey": "a9146794cf0b05c69d8e1942a8f9eeaf59a0847dafda87" + }, + { + "amount": 1000000, + "script_pubkey": "a914bbc6a47c8984cf60fd1f0eb753291458b5b42aa687" + } + ], + "inputs": [ + { + "prev_hash": "0e4194441d68c26d3bbc3646d7ad7bc0435cc7c85ac7f39d22587cb4f6959a69", + "prev_index": 15, + "script_sig": "160014e09c199e2cbcd552f0e58acfb933b3f4f426781f", + "sequence": 4294967294 + } + ], + "lock_time": 1667005, + "version": 2 +} diff --git a/tests/txcache/zcash_testnet/aaf51e4606c264e47e5c42c958fe4cf1539c5172684721e38e69f4ef634d75dc.json b/tests/txcache/zcash_testnet/aaf51e4606c264e47e5c42c958fe4cf1539c5172684721e38e69f4ef634d75dc.json new file mode 100644 index 0000000000..02227bb5e8 --- /dev/null +++ b/tests/txcache/zcash_testnet/aaf51e4606c264e47e5c42c958fe4cf1539c5172684721e38e69f4ef634d75dc.json @@ -0,0 +1,25 @@ +{ + "bin_outputs": [ + { + "amount": 417937001, + "script_pubkey": "76a914f5ea91f798002a6520f19da514f354b1c37b30d188ac" + }, + { + "amount": 300000000, + "script_pubkey": "76a914a579388225827d9f2fe9014add644487808c695d88ac" + } + ], + "inputs": [ + { + "prev_hash": "01d175a5421206439525542f83d168577e92d59e8283e8862e236a1461d5938a", + "prev_index": 2, + "script_sig": "473044022053a63f730e449f2d6c687ac53e9be627c4241614c041f458da2c4f91143179c802206ade1de030fc5fc77c4a88ccc79daedd28a79bfaf9e24533727a6fb81cbe4bd801210201d494a45f36f545443bafd1a9050b02f448dd236bb4ce2602f83978980b98f2", + "sequence": 4294967294 + } + ], + "expiry": 234352, + "extra_data": "00", + "lock_time": 234321, + "version": 3, + "version_group_id": 63210096 +} diff --git a/tests/txcache/zcash_testnet/e3820602226974b1dd87b7113cc8aea8c63e5ae29293991e7bfa80c126930368.json b/tests/txcache/zcash_testnet/e3820602226974b1dd87b7113cc8aea8c63e5ae29293991e7bfa80c126930368.json new file mode 100644 index 0000000000..d467d2fde8 --- /dev/null +++ b/tests/txcache/zcash_testnet/e3820602226974b1dd87b7113cc8aea8c63e5ae29293991e7bfa80c126930368.json @@ -0,0 +1,31 @@ +{ + "bin_outputs": [ + { + "amount": 300000000, + "script_pubkey": "76a914a579388225827d9f2fe9014add644487808c695d88ac" + }, + { + "amount": 1251648, + "script_pubkey": "76a91474374446b18916decd3292384ea73006ebd268ba88ac" + } + ], + "inputs": [ + { + "prev_hash": "4e8e8c5a5524cb8b20d05aefd5b1fd004d6c8c584e3e314876f13edb5ba0eead", + "prev_index": 0, + "script_sig": "473044022064e1e5f957308fcc91f7b174113c8e3cb8060b1404ae823ab3f77f313d5b557b02204b2afcde9ef8b61f5e85192c38fb82307d077ec91d2c8249aa69e19967df8c0c01210201d494a45f36f545443bafd1a9050b02f448dd236bb4ce2602f83978980b98f2", + "sequence": 4294967294 + }, + { + "prev_hash": "7afab9216fee6763ffbd6a412d46d68c480220af093c9becee6f79d41b954b13", + "prev_index": 0, + "script_sig": "47304402207f63a484ee75900ce2b0e2a5f0d52f2cfb5d1475588576f645c20ecf5e04659a02205c9b614ca846b0cb9ff4a72ca8482c9aed542282b9ee8eaa70a5f472408f3f04012103e974b89ace172f24bb25f8137d19c4205c5cf6bb6505454230ea172f54152d08", + "sequence": 4294967294 + } + ], + "expiry": 261318, + "extra_data": "00", + "lock_time": 261287, + "version": 3, + "version_group_id": 63210096 +} From cbc0ceff06be5bad9b7370b216d460e617cc5bd1 Mon Sep 17 00:00:00 2001 From: matejcik Date: Fri, 27 Mar 2020 13:05:19 +0100 Subject: [PATCH 10/24] tests: use valid prev_hash in attack test --- tests/device_tests/test_msg_signtx_prevhash.py | 8 ++++---- 1 file changed, 4 insertions(+), 4 deletions(-) diff --git a/tests/device_tests/test_msg_signtx_prevhash.py b/tests/device_tests/test_msg_signtx_prevhash.py index 22957a254e..ecbe63abcf 100644 --- a/tests/device_tests/test_msg_signtx_prevhash.py +++ b/tests/device_tests/test_msg_signtx_prevhash.py @@ -100,13 +100,13 @@ def test_invalid_prev_hash_attack(client, prev_hash): # prepare input with a valid prev-hash inp1 = messages.TxInputType( address_n=tools.parse_path("m/44h/0h/0h/0/0"), - amount=123456789, - prev_hash=b"\x00" * 32, + amount=100000000, + prev_hash=TXHASH_157041, prev_index=0, script_type=messages.InputScriptType.SPENDP2SHWITNESS, ) out1 = messages.TxOutputType( - address="mhRx1CeVfaayqRwq5zgRQmD7W5aWBfD5mC", + address="1MJ2tj2ThBE62zXbBYA5ZaN3fdve5CPAz1", amount=12300000, script_type=messages.OutputScriptType.PAYTOADDRESS, ) @@ -130,7 +130,7 @@ def test_invalid_prev_hash_attack(client, prev_hash): with client, pytest.raises(TrezorFailure) as e: client.set_filter(messages.TxAck, attack_filter) - btc.sign_tx(client, "Testnet", [inp1], [out1]) + btc.sign_tx(client, "Bitcoin", [inp1], [out1], prev_txes=TxCache("Bitcoin")) # check that injection was performed assert counter == 0 From 5aea566eb55089930b9a36a2e508631f8c1fce37 Mon Sep 17 00:00:00 2001 From: Andrew Kozlik Date: Wed, 25 Mar 2020 18:23:12 +0100 Subject: [PATCH 11/24] legacy/signing: validate prevout amount in all cases --- legacy/firmware/signing.c | 50 +++++++++------------------------------ 1 file changed, 11 insertions(+), 39 deletions(-) diff --git a/legacy/firmware/signing.c b/legacy/firmware/signing.c index 6e09739c8a..3907bab64b 100644 --- a/legacy/firmware/signing.c +++ b/legacy/firmware/signing.c @@ -68,7 +68,7 @@ static uint8_t hash_prevouts[32], hash_sequence[32], hash_outputs[32]; static uint8_t decred_hash_prefix[32]; #endif static uint8_t hash_check[32]; -static uint64_t to_spend, authorized_bip143_in, spending, change_spend; +static uint64_t to_spend, spending, change_spend; static uint32_t version = 1; static uint32_t lock_time = 0; static uint32_t expiry = 0; @@ -529,7 +529,6 @@ void signing_init(const SignTx *msg, const CoinInfo *_coin, to_spend = 0; spending = 0; change_spend = 0; - authorized_bip143_in = 0; memzero(&input, sizeof(TxInputType)); memzero(&resp, sizeof(TxRequest)); @@ -1144,13 +1143,6 @@ static bool signing_sign_segwit_input(TxInputType *txinput) { signing_abort(); return false; } - if (txinput->amount > authorized_bip143_in) { - fsm_sendFailure(FailureType_Failure_DataError, - _("Transaction has changed during signing")); - signing_abort(); - return false; - } - authorized_bip143_in -= txinput->amount; signing_hash_bip143(txinput, hash); @@ -1259,9 +1251,10 @@ void signing_txack(TransactionType *tx) { } #endif + memcpy(&input, tx->inputs, sizeof(TxInputType)); + if (tx->inputs[0].script_type == InputScriptType_SPENDMULTISIG || tx->inputs[0].script_type == InputScriptType_SPENDADDRESS) { - memcpy(&input, tx->inputs, sizeof(TxInputType)); #if !ENABLE_SEGWIT_NONSEGWIT_MIXING // don't mix segwit and non-segwit inputs if (idx1 > 0 && to.is_segwit == true) { @@ -1273,30 +1266,12 @@ void signing_txack(TransactionType *tx) { } #endif -#if !BITCOIN_ONLY - if (coin->force_bip143 || coin->overwintered) { - if (to_spend + tx->inputs[0].amount < to_spend) { - fsm_sendFailure(FailureType_Failure_DataError, _("Value overflow")); - signing_abort(); - return; - } - to_spend += tx->inputs[0].amount; - authorized_bip143_in += tx->inputs[0].amount; - phase1_request_next_input(); - } else -#endif - { + if (!coin->force_bip143 && !coin->overwintered) { // remember the first non-segwit input -- this is the first input // we need to sign during phase2 if (next_nonsegwit_input == 0xffffffff) next_nonsegwit_input = idx1; - send_req_2_prev_meta(); } } else if (is_segwit_input_script_type(&tx->inputs[0])) { - if (to_spend + tx->inputs[0].amount < to_spend) { - fsm_sendFailure(FailureType_Failure_DataError, _("Value overflow")); - signing_abort(); - return; - } if (!to.is_segwit) { tx_weight += TXSIZE_SEGWIT_OVERHEAD + to.inputs_len; } @@ -1314,15 +1289,13 @@ void signing_txack(TransactionType *tx) { #else to.is_segwit = true; #endif - to_spend += tx->inputs[0].amount; - authorized_bip143_in += tx->inputs[0].amount; - phase1_request_next_input(); } else { fsm_sendFailure(FailureType_Failure_DataError, _("Wrong input script type")); signing_abort(); return; } + send_req_2_prev_meta(); return; case STAGE_REQUEST_2_PREV_META: if (tx->outputs_cnt <= input.prev_index) { @@ -1412,6 +1385,12 @@ void signing_txack(TransactionType *tx) { return; } if (idx2 == input.prev_index) { + if (input.has_amount && input.amount != tx->bin_outputs[0].amount) { + fsm_sendFailure(FailureType_Failure_DataError, + _("Invalid amount specified")); + signing_abort(); + return; + } if (to_spend + tx->bin_outputs[0].amount < to_spend) { fsm_sendFailure(FailureType_Failure_DataError, _("Value overflow")); signing_abort(); @@ -1596,13 +1575,6 @@ void signing_txack(TransactionType *tx) { signing_abort(); return; } - if (tx->inputs[0].amount > authorized_bip143_in) { - fsm_sendFailure(FailureType_Failure_DataError, - _("Transaction has changed during signing")); - signing_abort(); - return; - } - authorized_bip143_in -= tx->inputs[0].amount; uint8_t hash[32] = {0}; #if !BITCOIN_ONLY From d34428eeb357fa6a03010220c7fcc209a093a4fa Mon Sep 17 00:00:00 2001 From: Andrew Kozlik Date: Fri, 27 Mar 2020 15:33:43 +0100 Subject: [PATCH 12/24] legacy/signing: add checks for version_group_id and branch_id fields --- legacy/firmware/signing.c | 42 +++++++++++++++++++++++++++++++++++++++ 1 file changed, 42 insertions(+) diff --git a/legacy/firmware/signing.c b/legacy/firmware/signing.c index 3907bab64b..1cfcf4c308 100644 --- a/legacy/firmware/signing.c +++ b/legacy/firmware/signing.c @@ -489,6 +489,28 @@ void signing_init(const SignTx *msg, const CoinInfo *_coin, memcpy(&root, _root, sizeof(HDNode)); version = msg->version; lock_time = msg->lock_time; + + if (coin->overwintered && !msg->has_version_group_id) { + fsm_sendFailure(FailureType_Failure_DataError, + _("Version group ID must be set.")); + signing_abort(); + return; + } + if (!coin->overwintered) { + if (msg->has_version_group_id) { + fsm_sendFailure(FailureType_Failure_DataError, + _("Version group ID not enabled on this coin.")); + signing_abort(); + return; + } + if (msg->has_branch_id) { + fsm_sendFailure(FailureType_Failure_DataError, + _("Branch ID not enabled on this coin.")); + signing_abort(); + return; + } + } + #if !BITCOIN_ONLY expiry = (coin->decred || coin->overwintered) ? msg->expiry : 0; timestamp = coin->timestamp ? msg->timestamp : 0; @@ -1328,6 +1350,26 @@ void signing_txack(TransactionType *tx) { signing_abort(); return; } + if (coin->overwintered && !tx->has_version_group_id) { + fsm_sendFailure(FailureType_Failure_DataError, + _("Version group ID must be set.")); + signing_abort(); + return; + } + if (!coin->overwintered) { + if (tx->has_version_group_id) { + fsm_sendFailure(FailureType_Failure_DataError, + _("Version group ID not enabled on this coin.")); + signing_abort(); + return; + } + if (tx->has_branch_id) { + fsm_sendFailure(FailureType_Failure_DataError, + _("Branch ID not enabled on this coin.")); + signing_abort(); + return; + } + } if (tx->inputs_cnt + tx->outputs_cnt < tx->inputs_cnt) { fsm_sendFailure(FailureType_Failure_DataError, _("Value overflow")); signing_abort(); From 386be6ff09acf5c0104751f1fc9c236c76d78525 Mon Sep 17 00:00:00 2001 From: Andrew Kozlik Date: Fri, 27 Mar 2020 16:42:50 +0100 Subject: [PATCH 13/24] legacy/signing: Check inputs for amount field only when amount is required. --- legacy/firmware/signing.c | 29 ++++++++++++----------------- 1 file changed, 12 insertions(+), 17 deletions(-) diff --git a/legacy/firmware/signing.c b/legacy/firmware/signing.c index 1cfcf4c308..51ab2f70b1 100644 --- a/legacy/firmware/signing.c +++ b/legacy/firmware/signing.c @@ -674,17 +674,6 @@ static bool signing_validate_input(const TxInputType *txinput) { return false; } -#if !BITCOIN_ONLY - if (coin->force_bip143 || coin->overwintered) { - if (!txinput->has_amount) { - fsm_sendFailure(FailureType_Failure_DataError, - _("Expected input with amount")); - signing_abort(); - return false; - } - } -#endif - if (is_segwit_input_script_type(txinput)) { if (!coin->has_segwit) { fsm_sendFailure(FailureType_Failure_DataError, @@ -692,12 +681,6 @@ static bool signing_validate_input(const TxInputType *txinput) { signing_abort(); return false; } - if (!txinput->has_amount) { - fsm_sendFailure(FailureType_Failure_DataError, - _("Segwit input without amount")); - signing_abort(); - return false; - } } return true; @@ -1159,6 +1142,12 @@ static bool signing_sign_segwit_input(TxInputType *txinput) { uint8_t hash[32] = {0}; if (is_segwit_input_script_type(txinput)) { + if (!txinput->has_amount) { + fsm_sendFailure(FailureType_Failure_DataError, + _("Segwit input without amount")); + signing_abort(); + return false; + } if (!compile_input_script_sig(txinput)) { fsm_sendFailure(FailureType_Failure_ProcessError, _("Failed to compile input")); @@ -1617,6 +1606,12 @@ void signing_txack(TransactionType *tx) { signing_abort(); return; } + if (!tx->inputs[0].has_amount) { + fsm_sendFailure(FailureType_Failure_DataError, + _("Expected input with amount")); + signing_abort(); + return; + } uint8_t hash[32] = {0}; #if !BITCOIN_ONLY From e6745bce438506a9f8c0e7e4212e021d4b12c2e5 Mon Sep 17 00:00:00 2001 From: Andrew Kozlik Date: Mon, 30 Mar 2020 11:13:34 +0200 Subject: [PATCH 14/24] legacy/signing: Don't force nJoinSplit to be 0 for prev_tx in overwintered. This was dead code until we started validating prevout amounts. --- legacy/firmware/transaction.c | 3 +-- 1 file changed, 1 insertion(+), 2 deletions(-) diff --git a/legacy/firmware/transaction.c b/legacy/firmware/transaction.c index 28866603fc..e5b68e0e45 100644 --- a/legacy/firmware/transaction.c +++ b/legacy/firmware/transaction.c @@ -711,8 +711,7 @@ uint32_t tx_serialize_footer_hash(TxStruct *tx) { #if !BITCOIN_ONLY if (tx->overwintered) { hasher_Update(&(tx->hasher), (const uint8_t *)&(tx->expiry), 4); - hasher_Update(&(tx->hasher), (const uint8_t *)"\x00", 1); // nJoinSplit - return 9; + return 8; } if (tx->is_decred) { hasher_Update(&(tx->hasher), (const uint8_t *)&(tx->expiry), 4); From 7b94cbee5465b8191706600b39becca4cdb97e3d Mon Sep 17 00:00:00 2001 From: Andrew Kozlik Date: Thu, 14 May 2020 18:03:10 +0200 Subject: [PATCH 15/24] tests: Fix fake amount attack in test_msg_signtx_segwit to account for segwit transaction streaming. --- tests/device_tests/test_msg_signtx_segwit.py | 70 +++++--------------- 1 file changed, 15 insertions(+), 55 deletions(-) diff --git a/tests/device_tests/test_msg_signtx_segwit.py b/tests/device_tests/test_msg_signtx_segwit.py index 67b8dce7a1..db757a1d26 100644 --- a/tests/device_tests/test_msg_signtx_segwit.py +++ b/tests/device_tests/test_msg_signtx_segwit.py @@ -40,31 +40,6 @@ TXHASH_e5040e = bytes.fromhex( ) -def request_input(n, tx_hash=None): - return proto.TxRequest( - request_type=proto.RequestType.TXINPUT, - details=proto.TxRequestDetailsType(request_index=n, tx_hash=tx_hash), - ) - - -def request_output(n, tx_hash=None): - return proto.TxRequest( - request_type=proto.RequestType.TXOUTPUT, - details=proto.TxRequestDetailsType(request_index=n, tx_hash=tx_hash), - ) - - -def request_meta(tx_hash): - return proto.TxRequest( - request_type=proto.RequestType.TXMETA, - details=proto.TxRequestDetailsType(tx_hash=tx_hash), - ) - - -def request_finished(): - return proto.TxRequest(request_type=proto.RequestType.TXFINISHED) - - class TestMsgSigntxSegwit: def test_send_p2sh(self, client): inp1 = proto.TxInputType( @@ -366,7 +341,7 @@ class TestMsgSigntxSegwit: ) def test_attack_mixed_inputs(self, client): - TRUE_AMOUNT = 12345678 + TRUE_AMOUNT = 123456789 FAKE_AMOUNT = 123 inp1 = proto.TxInputType( @@ -398,6 +373,10 @@ class TestMsgSigntxSegwit: request_output(0, TXHASH_e5040e), request_output(1, TXHASH_e5040e), request_input(1), + request_meta(TXHASH_20912f), + request_input(0, TXHASH_20912f), + request_output(0, TXHASH_20912f), + request_output(1, TXHASH_20912f), request_output(0), proto.ButtonRequest(code=proto.ButtonRequestType.ConfirmOutput), proto.ButtonRequest(code=proto.ButtonRequestType.FeeOverThreshold), @@ -408,17 +387,17 @@ class TestMsgSigntxSegwit: request_input(1), request_output(0), request_input(1), + request_finished(), ] if client.features.model == "1": # T1 asks for first input for witness again - expected_responses.insert(-1, request_input(0)) - pass + expected_responses.insert(-2, request_input(0)) with client: # Sign unmodified transaction. # "Fee over threshold" warning is displayed - fee is the whole TRUE_AMOUNT - client.set_expected_responses(expected_responses + [request_finished()]) + client.set_expected_responses(expected_responses) btc.sign_tx( client, "Testnet", [inp1, inp2], [out1], prev_txes=TX_API, ) @@ -426,35 +405,16 @@ class TestMsgSigntxSegwit: # In Phase 1 make the user confirm a lower value of the segwit input. inp2.amount = FAKE_AMOUNT - ctr = 3 + if client.features.model == "1": + # T1 fails as soon as it encounters the fake amount. + expected_responses = expected_responses[:9] + [proto.Failure()] + else: + expected_responses = expected_responses[:10] + [proto.Failure()] - def attack(msg): - nonlocal ctr - - if msg.tx.inputs and msg.tx.inputs[0] == inp2: - ctr -= 1 - if ctr <= 0: - # after Phase 1 is done and input 1 is signed, let Trezor sign - # the true amount in Phase 2 - msg.tx.inputs[0].amount = TRUE_AMOUNT - - return msg - - # Sign with attacker. with pytest.raises(TrezorFailure) as e, client: - # "Fee over threshold" is NOT displayed, because the calculated fee - # in phase 1 is small. - assert expected_responses[8] == proto.ButtonRequest( - code=proto.ButtonRequestType.FeeOverThreshold - ) - del expected_responses[8] - - client.set_filter(proto.TxAck, attack) - client.set_expected_responses(expected_responses + [proto.Failure()]) + client.set_expected_responses(expected_responses) btc.sign_tx( client, "Testnet", [inp1, inp2], [out1], prev_txes=TX_API, ) - assert e.value.failure.message.endswith( - "Transaction has changed during signing" - ) + assert e.value.failure.message.endswith("Invalid amount specified") From 7db3e930d4cc87866fba3bf73c3190f21a21df02 Mon Sep 17 00:00:00 2001 From: Andrew Kozlik Date: Fri, 15 May 2020 15:01:50 +0200 Subject: [PATCH 16/24] core/sign_tx: Add further message sanitization checks. --- core/src/apps/bitcoin/sign_tx/helpers.py | 12 ++++++++++-- 1 file changed, 10 insertions(+), 2 deletions(-) diff --git a/core/src/apps/bitcoin/sign_tx/helpers.py b/core/src/apps/bitcoin/sign_tx/helpers.py index 09a10b2bf6..3f79b099f4 100644 --- a/core/src/apps/bitcoin/sign_tx/helpers.py +++ b/core/src/apps/bitcoin/sign_tx/helpers.py @@ -242,6 +242,8 @@ def sanitize_tx_input(tx: TransactionType, coin: CoinInfo) -> TxInputType: txi.script_type = InputScriptType.SPENDADDRESS if txi.sequence is None: txi.sequence = 0xFFFFFFFF + if txi.prev_index is None: + raise wire.DataError("Missing prev_index field.") if txi.prev_hash is None or len(txi.prev_hash) != TX_HASH_SIZE: raise wire.DataError("Provided prev_hash is invalid.") if txi.multisig and txi.script_type not in MULTISIG_INPUT_SCRIPT_TYPES: @@ -253,8 +255,6 @@ def sanitize_tx_input(tx: TransactionType, coin: CoinInfo) -> TxInputType: if txi.script_type in SEGWIT_INPUT_SCRIPT_TYPES: if not coin.segwit: raise wire.DataError("Segwit not enabled on this coin") - if txi.amount is None: - raise wire.DataError("Segwit input without amount") return txi @@ -264,8 +264,12 @@ def sanitize_tx_output(tx: TransactionType, coin: CoinInfo) -> TxOutputType: raise wire.DataError("Multisig field provided but not expected.") if txo.address_n and txo.script_type not in CHANGE_OUTPUT_SCRIPT_TYPES: raise wire.DataError("Output's address_n provided but not expected.") + if txo.amount is None: + raise wire.DataError("Missing amount field.") if txo.script_type == OutputScriptType.PAYTOOPRETURN: # op_return output + if txo.op_return_data is None: + raise wire.DataError("OP_RETURN output without op_return_data") if txo.amount != 0: raise wire.DataError("OP_RETURN output with non-zero amount") if txo.address or txo.address_n or txo.multisig: @@ -284,4 +288,8 @@ def sanitize_tx_output(tx: TransactionType, coin: CoinInfo) -> TxOutputType: def sanitize_tx_binoutput(tx: TransactionType, coin: CoinInfo) -> TxOutputBinType: txo_bin = tx.bin_outputs[0] + if txo_bin.amount is None: + raise wire.DataError("Missing amount field.") + if txo_bin.script_pubkey is None: + raise wire.DataError("Missing script_pubkey field.") return txo_bin From 42eddf8e04c059832e0205925fd60f0943f3884b Mon Sep 17 00:00:00 2001 From: Andrew Kozlik Date: Fri, 15 May 2020 15:22:34 +0200 Subject: [PATCH 17/24] core/sign_tx: validate prevout amount in all cases --- core/src/apps/bitcoin/sign_tx/bitcoin.py | 29 +++++-------------- core/src/apps/bitcoin/sign_tx/bitcoinlike.py | 22 ++++---------- core/src/apps/bitcoin/sign_tx/zcash.py | 9 +++--- ...ps.bitcoin.segwit.signtx.p2wpkh_in_p2sh.py | 2 +- 4 files changed, 18 insertions(+), 44 deletions(-) diff --git a/core/src/apps/bitcoin/sign_tx/bitcoin.py b/core/src/apps/bitcoin/sign_tx/bitcoin.py index efa6f0c298..240096a1de 100644 --- a/core/src/apps/bitcoin/sign_tx/bitcoin.py +++ b/core/src/apps/bitcoin/sign_tx/bitcoin.py @@ -84,7 +84,6 @@ class Bitcoin: # amounts self.total_in = 0 # sum of input amounts - self.bip143_in = 0 # sum of segwit input amounts self.total_out = 0 # sum of output amounts self.change_out = 0 # change output amount self.weight = tx_weight.TxWeightCalculator(tx.inputs_count, tx.outputs_count) @@ -178,26 +177,15 @@ class Bitcoin: if not addresses.validate_full_path(txi.address_n, self.coin, txi.script_type): await helpers.confirm_foreign_address(txi.address_n) - if input_is_segwit(txi): - await self.process_segwit_input(txi) - elif input_is_nonsegwit(txi): - await self.process_nonsegwit_input(txi) - else: + if txi.script_type not in helpers.INTERNAL_INPUT_SCRIPT_TYPES: raise wire.DataError("Wrong input script type") - async def process_segwit_input(self, txi: TxInputType) -> None: - await self.process_bip143_input(txi) + prev_amount = await self.get_prevtx_output_value(txi.prev_hash, txi.prev_index) - async def process_nonsegwit_input(self, txi: TxInputType) -> None: - self.total_in += await self.get_prevtx_output_value( - txi.prev_hash, txi.prev_index - ) + if txi.amount is not None and prev_amount != txi.amount: + raise wire.DataError("Invalid amount specified") - async def process_bip143_input(self, txi: TxInputType) -> None: - if not txi.amount: - raise wire.DataError("Expected input with amount") - self.bip143_in += txi.amount - self.total_in += txi.amount + self.total_in += prev_amount async def confirm_output(self, txo: TxOutputType, script_pubkey: bytes) -> None: if self.change_out == 0 and self.output_is_change(txo): @@ -229,13 +217,12 @@ class Bitcoin: self.write_tx_input(self.serialized_tx, txi, script_sig) def sign_bip143_input(self, txi: TxInputType) -> Tuple[bytes, bytes]: + if txi.amount is None: + raise wire.DataError("Expected input with amount") + self.wallet_path.check_input(txi) self.multisig_fingerprint.check_input(txi) - if txi.amount > self.bip143_in: - raise wire.ProcessError("Transaction has changed during signing") - self.bip143_in -= txi.amount - node = self.keychain.derive(txi.address_n) public_key = node.public_key() hash143_hash = self.hash143_preimage_hash( diff --git a/core/src/apps/bitcoin/sign_tx/bitcoinlike.py b/core/src/apps/bitcoin/sign_tx/bitcoinlike.py index a37b7509dc..7b57c265af 100644 --- a/core/src/apps/bitcoin/sign_tx/bitcoinlike.py +++ b/core/src/apps/bitcoin/sign_tx/bitcoinlike.py @@ -4,7 +4,6 @@ from micropython import const from trezor import wire from trezor.messages.SignTx import SignTx from trezor.messages.TransactionType import TransactionType -from trezor.messages.TxInputType import TxInputType from apps.common.writers import write_bitcoin_varint @@ -19,17 +18,6 @@ _SIGHASH_FORKID = const(0x40) class Bitcoinlike(Bitcoin): - async def process_segwit_input(self, txi: TxInputType) -> None: - if not self.coin.segwit: - raise wire.DataError("Segwit not enabled on this coin") - await super().process_segwit_input(txi) - - async def process_nonsegwit_input(self, txi: TxInputType) -> None: - if self.coin.force_bip143: - await self.process_bip143_input(txi) - else: - await super().process_nonsegwit_input(txi) - async def sign_nonsegwit_bip143_input(self, i_sign: int) -> None: txi = await helpers.request_tx_input(self.tx_req, i_sign, self.coin) @@ -83,11 +71,11 @@ class Bitcoinlike(Bitcoin): await super().write_prev_tx_footer(w, tx, prev_hash) if self.coin.extra_data: - ofs = 0 - while ofs < tx.extra_data_len: - size = min(1024, tx.extra_data_len - ofs) + offset = 0 + while offset < tx.extra_data_len: + size = min(1024, tx.extra_data_len - offset) data = await helpers.request_tx_extra_data( - self.tx_req, ofs, size, prev_hash + self.tx_req, offset, size, prev_hash ) writers.write_bytes_unchecked(w, data) - ofs += len(data) + offset += len(data) diff --git a/core/src/apps/bitcoin/sign_tx/zcash.py b/core/src/apps/bitcoin/sign_tx/zcash.py index 7483791288..63eecd7dc5 100644 --- a/core/src/apps/bitcoin/sign_tx/zcash.py +++ b/core/src/apps/bitcoin/sign_tx/zcash.py @@ -52,10 +52,8 @@ class Overwintered(Bitcoinlike): self.write_tx_footer(self.serialized_tx, self.tx) if self.tx.version == 3: - write_uint32(self.serialized_tx, self.tx.expiry) # expiryHeight write_bitcoin_varint(self.serialized_tx, 0) # nJoinSplit elif self.tx.version == 4: - write_uint32(self.serialized_tx, self.tx.expiry) # expiryHeight write_uint64(self.serialized_tx, 0) # valueBalance write_bitcoin_varint(self.serialized_tx, 0) # nShieldedSpend write_bitcoin_varint(self.serialized_tx, 0) # nShieldedOutput @@ -65,9 +63,6 @@ class Overwintered(Bitcoinlike): await helpers.request_tx_finish(self.tx_req) - async def process_nonsegwit_input(self, txi: TxInputType) -> None: - await self.process_bip143_input(txi) - async def sign_nonsegwit_input(self, i_sign: int) -> None: await self.sign_nonsegwit_bip143_input(i_sign) @@ -78,6 +73,10 @@ class Overwintered(Bitcoinlike): write_uint32(w, tx.version | OVERWINTERED) write_uint32(w, tx.version_group_id) # nVersionGroupId + def write_tx_footer(self, w: Writer, tx: Union[SignTx, TransactionType]) -> None: + write_uint32(w, tx.lock_time) + write_uint32(w, tx.expiry) # expiryHeight + # ZIP-0143 / ZIP-0243 # === diff --git a/core/tests/test_apps.bitcoin.segwit.signtx.p2wpkh_in_p2sh.py b/core/tests/test_apps.bitcoin.segwit.signtx.p2wpkh_in_p2sh.py index 7f98816727..e3d0de2d15 100644 --- a/core/tests/test_apps.bitcoin.segwit.signtx.p2wpkh_in_p2sh.py +++ b/core/tests/test_apps.bitcoin.segwit.signtx.p2wpkh_in_p2sh.py @@ -343,7 +343,7 @@ class TestSignSegwitTxP2WPKHInP2SH(unittest.TestCase): messages_count = int(len(messages) / 2) for request, response in chunks(messages, 2): if i == messages_count - 1: # last message should throw wire.Error - self.assertRaises(wire.ProcessError, signer.send, request) + self.assertRaises(wire.DataError, signer.send, request) else: self.assertEqual(signer.send(request), response) i += 1 From cb32ae2e4bafc4fdd064323f6a11d5f36f741c90 Mon Sep 17 00:00:00 2001 From: Andrew Kozlik Date: Fri, 15 May 2020 16:55:18 +0200 Subject: [PATCH 18/24] core/tests: add request_meta queries to unit tests (needed for transaction streaming) --- ...pps.bitcoin.segwit.signtx.native_p2wpkh.py | 72 +++++++++- ...bitcoin.segwit.signtx.native_p2wpkh_grs.py | 49 ++++++- ...ps.bitcoin.segwit.signtx.p2wpkh_in_p2sh.py | 125 ++++++++++-------- ...itcoin.segwit.signtx.p2wpkh_in_p2sh_grs.py | 49 ++++++- 4 files changed, 238 insertions(+), 57 deletions(-) diff --git a/core/tests/test_apps.bitcoin.segwit.signtx.native_p2wpkh.py b/core/tests/test_apps.bitcoin.segwit.signtx.native_p2wpkh.py index a20853ef79..14d639cba9 100644 --- a/core/tests/test_apps.bitcoin.segwit.signtx.native_p2wpkh.py +++ b/core/tests/test_apps.bitcoin.segwit.signtx.native_p2wpkh.py @@ -4,11 +4,12 @@ from trezor.utils import chunks from trezor.crypto import bip39 from trezor.messages.SignTx import SignTx from trezor.messages.TxInputType import TxInputType +from trezor.messages.TxOutputBinType import TxOutputBinType from trezor.messages.TxOutputType import TxOutputType from trezor.messages.TxRequest import TxRequest from trezor.messages.TxAck import TxAck from trezor.messages.TransactionType import TransactionType -from trezor.messages.RequestType import TXINPUT, TXOUTPUT, TXFINISHED +from trezor.messages.RequestType import TXINPUT, TXMETA, TXOUTPUT, TXFINISHED from trezor.messages.TxRequestDetailsType import TxRequestDetailsType from trezor.messages.TxRequestSerializedType import TxRequestSerializedType from trezor.messages import InputScriptType @@ -42,6 +43,17 @@ class TestSignSegwitTxNativeP2WPKH(unittest.TestCase): sequence=0xffffffff, multisig=None, ) + ptx1 = TransactionType(version=1, lock_time=0, inputs_cnt=1, outputs_cnt=2, extra_data_len=0) + pinp1 = TxInputType(script_sig=unhexlify('160014d16b8c0680c61fc6ed2e407455715055e41052f5'), + prev_hash=unhexlify('20912f98ea3ed849042efed0fdac8cb4fc301961c5988cba56902d8ffb61c337'), + prev_index=0, + script_type=None, + sequence=4294967295) + pout1 = TxOutputBinType(script_pubkey=unhexlify('00140099a7ecbd938ed1839f5f6bf6d50933c6db9d5c'), + amount=12300000) + pout2 = TxOutputBinType(script_pubkey=unhexlify('a91458b53ea7f832e8f096e896b8713a8c6df0e892ca87'), + amount=111145789) + out1 = TxOutputType( address='2N4Q5FhU2497BryFfUgbqkAJE87aKHUhXMp', amount=5000000, @@ -68,6 +80,18 @@ class TestSignSegwitTxNativeP2WPKH(unittest.TestCase): helpers.UiConfirmForeignAddress(address_n=inp1.address_n), True, + TxRequest(request_type=TXMETA, details=TxRequestDetailsType(request_index=None, tx_hash=inp1.prev_hash), serialized=EMPTY_SERIALIZED), + TxAck(tx=ptx1), + + TxRequest(request_type=TXINPUT, details=TxRequestDetailsType(request_index=0, tx_hash=inp1.prev_hash), serialized=EMPTY_SERIALIZED), + TxAck(tx=TransactionType(inputs=[pinp1])), + + TxRequest(request_type=TXOUTPUT, details=TxRequestDetailsType(request_index=0, tx_hash=inp1.prev_hash), serialized=EMPTY_SERIALIZED), + TxAck(tx=TransactionType(bin_outputs=[pout1])), + + TxRequest(request_type=TXOUTPUT, details=TxRequestDetailsType(request_index=1, tx_hash=inp1.prev_hash), serialized=EMPTY_SERIALIZED), + TxAck(tx=TransactionType(bin_outputs=[pout2])), + TxRequest(request_type=TXOUTPUT, details=TxRequestDetailsType(request_index=0, tx_hash=None), serialized=EMPTY_SERIALIZED), TxAck(tx=TransactionType(outputs=[out1])), @@ -144,6 +168,17 @@ class TestSignSegwitTxNativeP2WPKH(unittest.TestCase): sequence=0xffffffff, multisig=None, ) + ptx1 = TransactionType(version=1, lock_time=0, inputs_cnt=1, outputs_cnt=2, extra_data_len=0) + pinp1 = TxInputType(script_sig=unhexlify('160014d16b8c0680c61fc6ed2e407455715055e41052f5'), + prev_hash=unhexlify('20912f98ea3ed849042efed0fdac8cb4fc301961c5988cba56902d8ffb61c337'), + prev_index=0, + script_type=None, + sequence=4294967295) + pout1 = TxOutputBinType(script_pubkey=unhexlify('00140099a7ecbd938ed1839f5f6bf6d50933c6db9d5c'), + amount=12300000) + pout2 = TxOutputBinType(script_pubkey=unhexlify('a91458b53ea7f832e8f096e896b8713a8c6df0e892ca87'), + amount=111145789) + out1 = TxOutputType( address='2N4Q5FhU2497BryFfUgbqkAJE87aKHUhXMp', amount=5000000, @@ -170,6 +205,18 @@ class TestSignSegwitTxNativeP2WPKH(unittest.TestCase): helpers.UiConfirmForeignAddress(address_n=inp1.address_n), True, + TxRequest(request_type=TXMETA, details=TxRequestDetailsType(request_index=None, tx_hash=inp1.prev_hash), serialized=EMPTY_SERIALIZED), + TxAck(tx=ptx1), + + TxRequest(request_type=TXINPUT, details=TxRequestDetailsType(request_index=0, tx_hash=inp1.prev_hash), serialized=EMPTY_SERIALIZED), + TxAck(tx=TransactionType(inputs=[pinp1])), + + TxRequest(request_type=TXOUTPUT, details=TxRequestDetailsType(request_index=0, tx_hash=inp1.prev_hash), serialized=EMPTY_SERIALIZED), + TxAck(tx=TransactionType(bin_outputs=[pout1])), + + TxRequest(request_type=TXOUTPUT, details=TxRequestDetailsType(request_index=1, tx_hash=inp1.prev_hash), serialized=EMPTY_SERIALIZED), + TxAck(tx=TransactionType(bin_outputs=[pout2])), + TxRequest(request_type=TXOUTPUT, details=TxRequestDetailsType(request_index=0, tx_hash=None), serialized=EMPTY_SERIALIZED), TxAck(tx=TransactionType(outputs=[out1])), @@ -243,6 +290,17 @@ class TestSignSegwitTxNativeP2WPKH(unittest.TestCase): sequence=0xffffffff, multisig=None, ) + ptx1 = TransactionType(version=1, lock_time=0, inputs_cnt=1, outputs_cnt=2, extra_data_len=0) + pinp1 = TxInputType(script_sig=unhexlify('160014d16b8c0680c61fc6ed2e407455715055e41052f5'), + prev_hash=unhexlify('20912f98ea3ed849042efed0fdac8cb4fc301961c5988cba56902d8ffb61c337'), + prev_index=0, + script_type=None, + sequence=4294967295) + pout1 = TxOutputBinType(script_pubkey=unhexlify('00140099a7ecbd938ed1839f5f6bf6d50933c6db9d5c'), + amount=12300000) + pout2 = TxOutputBinType(script_pubkey=unhexlify('a91458b53ea7f832e8f096e896b8713a8c6df0e892ca87'), + amount=111145789) + out1 = TxOutputType( address='TB1Q694CCP5QCC0UDMFWGP692U2S2HJPQ5H407URTU', # Error: should be lower case script_type=OutputScriptType.PAYTOADDRESS, @@ -262,6 +320,18 @@ class TestSignSegwitTxNativeP2WPKH(unittest.TestCase): helpers.UiConfirmForeignAddress(address_n=inp1.address_n), True, + TxRequest(request_type=TXMETA, details=TxRequestDetailsType(request_index=None, tx_hash=inp1.prev_hash), serialized=EMPTY_SERIALIZED), + TxAck(tx=ptx1), + + TxRequest(request_type=TXINPUT, details=TxRequestDetailsType(request_index=0, tx_hash=inp1.prev_hash), serialized=EMPTY_SERIALIZED), + TxAck(tx=TransactionType(inputs=[pinp1])), + + TxRequest(request_type=TXOUTPUT, details=TxRequestDetailsType(request_index=0, tx_hash=inp1.prev_hash), serialized=EMPTY_SERIALIZED), + TxAck(tx=TransactionType(bin_outputs=[pout1])), + + TxRequest(request_type=TXOUTPUT, details=TxRequestDetailsType(request_index=1, tx_hash=inp1.prev_hash), serialized=EMPTY_SERIALIZED), + TxAck(tx=TransactionType(bin_outputs=[pout2])), + TxRequest(request_type=TXOUTPUT, details=TxRequestDetailsType(request_index=0, tx_hash=None), serialized=EMPTY_SERIALIZED), TxAck(tx=TransactionType(outputs=[out1])), None diff --git a/core/tests/test_apps.bitcoin.segwit.signtx.native_p2wpkh_grs.py b/core/tests/test_apps.bitcoin.segwit.signtx.native_p2wpkh_grs.py index e2b0251251..d2a5084da1 100644 --- a/core/tests/test_apps.bitcoin.segwit.signtx.native_p2wpkh_grs.py +++ b/core/tests/test_apps.bitcoin.segwit.signtx.native_p2wpkh_grs.py @@ -4,11 +4,12 @@ from trezor.utils import chunks from trezor.crypto import bip39 from trezor.messages.SignTx import SignTx from trezor.messages.TxInputType import TxInputType +from trezor.messages.TxOutputBinType import TxOutputBinType from trezor.messages.TxOutputType import TxOutputType from trezor.messages.TxRequest import TxRequest from trezor.messages.TxAck import TxAck from trezor.messages.TransactionType import TransactionType -from trezor.messages.RequestType import TXINPUT, TXOUTPUT, TXFINISHED +from trezor.messages.RequestType import TXINPUT, TXMETA, TXOUTPUT, TXFINISHED from trezor.messages.TxRequestDetailsType import TxRequestDetailsType from trezor.messages.TxRequestSerializedType import TxRequestSerializedType from trezor.messages import InputScriptType @@ -43,6 +44,17 @@ class TestSignSegwitTxNativeP2WPKH_GRS(unittest.TestCase): sequence=0xfffffffe, multisig=None, ) + ptx1 = TransactionType(version=1, lock_time=650645, inputs_cnt=1, outputs_cnt=2, extra_data_len=0) + pinp1 = TxInputType(script_sig=unhexlify('483045022100d9615361c044e91f6dd7bb4455f3ad686cd5a663d7800bb74c448b2706500ccb022026bed24b81a501e8398411c5a9a793741d9bfe39617d51c363dde0a84f44f4f9012102659a6eefcc72d6f2eff92e57095388b17db0b06034946ecd44120e5e7a830ff4'), + prev_hash=unhexlify('1c92508b38239e5c10b23fb46dcf765ee2f3a95b835edbf0943ec21b21711160'), + prev_index=1, + script_type=None, + sequence=4294967293) + pout1 = TxOutputBinType(script_pubkey=unhexlify('0014b31dc2a236505a6cb9201fa0411ca38a254a7bf1'), + amount=12300000) + pout2 = TxOutputBinType(script_pubkey=unhexlify('76a91438cc090e4a4b2e458c33fe35af1c5c0094699ac288ac'), + amount=9887699777) + out1 = TxOutputType( address='2N4Q5FhU2497BryFfUgbqkAJE87aKDv3V3e', amount=5000000, @@ -66,6 +78,18 @@ class TestSignSegwitTxNativeP2WPKH_GRS(unittest.TestCase): TxRequest(request_type=TXINPUT, details=TxRequestDetailsType(request_index=0, tx_hash=None), serialized=EMPTY_SERIALIZED), TxAck(tx=TransactionType(inputs=[inp1])), + TxRequest(request_type=TXMETA, details=TxRequestDetailsType(request_index=None, tx_hash=inp1.prev_hash), serialized=EMPTY_SERIALIZED), + TxAck(tx=ptx1), + + TxRequest(request_type=TXINPUT, details=TxRequestDetailsType(request_index=0, tx_hash=inp1.prev_hash), serialized=EMPTY_SERIALIZED), + TxAck(tx=TransactionType(inputs=[pinp1])), + + TxRequest(request_type=TXOUTPUT, details=TxRequestDetailsType(request_index=0, tx_hash=inp1.prev_hash), serialized=EMPTY_SERIALIZED), + TxAck(tx=TransactionType(bin_outputs=[pout1])), + + TxRequest(request_type=TXOUTPUT, details=TxRequestDetailsType(request_index=1, tx_hash=inp1.prev_hash), serialized=EMPTY_SERIALIZED), + TxAck(tx=TransactionType(bin_outputs=[pout2])), + TxRequest(request_type=TXOUTPUT, details=TxRequestDetailsType(request_index=0, tx_hash=None), serialized=EMPTY_SERIALIZED), TxAck(tx=TransactionType(outputs=[out1])), @@ -144,6 +168,17 @@ class TestSignSegwitTxNativeP2WPKH_GRS(unittest.TestCase): sequence=0xfffffffe, multisig=None, ) + ptx1 = TransactionType(version=1, lock_time=650645, inputs_cnt=1, outputs_cnt=2, extra_data_len=0) + pinp1 = TxInputType(script_sig=unhexlify('483045022100d9615361c044e91f6dd7bb4455f3ad686cd5a663d7800bb74c448b2706500ccb022026bed24b81a501e8398411c5a9a793741d9bfe39617d51c363dde0a84f44f4f9012102659a6eefcc72d6f2eff92e57095388b17db0b06034946ecd44120e5e7a830ff4'), + prev_hash=unhexlify('1c92508b38239e5c10b23fb46dcf765ee2f3a95b835edbf0943ec21b21711160'), + prev_index=1, + script_type=None, + sequence=4294967293) + pout1 = TxOutputBinType(script_pubkey=unhexlify('0014b31dc2a236505a6cb9201fa0411ca38a254a7bf1'), + amount=12300000) + pout2 = TxOutputBinType(script_pubkey=unhexlify('76a91438cc090e4a4b2e458c33fe35af1c5c0094699ac288ac'), + amount=9887699777) + out1 = TxOutputType( address='2N4Q5FhU2497BryFfUgbqkAJE87aKDv3V3e', amount=5000000, @@ -167,6 +202,18 @@ class TestSignSegwitTxNativeP2WPKH_GRS(unittest.TestCase): TxRequest(request_type=TXINPUT, details=TxRequestDetailsType(request_index=0, tx_hash=None), serialized=EMPTY_SERIALIZED), TxAck(tx=TransactionType(inputs=[inp1])), + TxRequest(request_type=TXMETA, details=TxRequestDetailsType(request_index=None, tx_hash=inp1.prev_hash), serialized=EMPTY_SERIALIZED), + TxAck(tx=ptx1), + + TxRequest(request_type=TXINPUT, details=TxRequestDetailsType(request_index=0, tx_hash=inp1.prev_hash), serialized=EMPTY_SERIALIZED), + TxAck(tx=TransactionType(inputs=[pinp1])), + + TxRequest(request_type=TXOUTPUT, details=TxRequestDetailsType(request_index=0, tx_hash=inp1.prev_hash), serialized=EMPTY_SERIALIZED), + TxAck(tx=TransactionType(bin_outputs=[pout1])), + + TxRequest(request_type=TXOUTPUT, details=TxRequestDetailsType(request_index=1, tx_hash=inp1.prev_hash), serialized=EMPTY_SERIALIZED), + TxAck(tx=TransactionType(bin_outputs=[pout2])), + TxRequest(request_type=TXOUTPUT, details=TxRequestDetailsType(request_index=0, tx_hash=None), serialized=EMPTY_SERIALIZED), TxAck(tx=TransactionType(outputs=[out1])), diff --git a/core/tests/test_apps.bitcoin.segwit.signtx.p2wpkh_in_p2sh.py b/core/tests/test_apps.bitcoin.segwit.signtx.p2wpkh_in_p2sh.py index e3d0de2d15..6de06fe80c 100644 --- a/core/tests/test_apps.bitcoin.segwit.signtx.p2wpkh_in_p2sh.py +++ b/core/tests/test_apps.bitcoin.segwit.signtx.p2wpkh_in_p2sh.py @@ -5,10 +5,11 @@ from trezor.crypto import bip39 from trezor.messages.SignTx import SignTx from trezor.messages.TxInputType import TxInputType from trezor.messages.TxOutputType import TxOutputType +from trezor.messages.TxOutputBinType import TxOutputBinType from trezor.messages.TxRequest import TxRequest from trezor.messages.TxAck import TxAck from trezor.messages.TransactionType import TransactionType -from trezor.messages.RequestType import TXINPUT, TXOUTPUT, TXFINISHED +from trezor.messages.RequestType import TXINPUT, TXMETA, TXOUTPUT, TXFINISHED from trezor.messages.TxRequestDetailsType import TxRequestDetailsType from trezor.messages.TxRequestSerializedType import TxRequestSerializedType from trezor.messages import InputScriptType @@ -42,6 +43,17 @@ class TestSignSegwitTxP2WPKHInP2SH(unittest.TestCase): sequence=0xffffffff, multisig=None, ) + ptx1 = TransactionType(version=1, lock_time=0, inputs_cnt=1, outputs_cnt=2, extra_data_len=0) + pinp1 = TxInputType(script_sig=unhexlify('4730440220548e087d0426b20b8a571b03b9e05829f7558b80c53c12143e342f56ab29e51d02205b68cb7fb223981d4c999725ac1485a982c4259c4f50b8280f137878c232998a012102794a25b254a268e59a5869da57fbae2fadc6727cb3309321dab409b12b2fa17c'), + prev_hash=unhexlify('802cabf0843b945eabe136d7fc7c89f41021658abf56cba000acbce88c41143a'), + prev_index=0, + script_type=None, + sequence=4294967295) + pout1 = TxOutputBinType(script_pubkey=unhexlify('a91458b53ea7f832e8f096e896b8713a8c6df0e892ca87'), + amount=123456789) + pout2 = TxOutputBinType(script_pubkey=unhexlify('76a914b84bacdcd8f4cc59274a5bfb73f804ca10f7fd1488ac'), + amount=865519308) + out1 = TxOutputType( address='mhRx1CeVfaayqRwq5zgRQmD7W5aWBfD5mC', amount=12300000, @@ -65,6 +77,18 @@ class TestSignSegwitTxP2WPKHInP2SH(unittest.TestCase): TxRequest(request_type=TXINPUT, details=TxRequestDetailsType(request_index=0, tx_hash=None), serialized=EMPTY_SERIALIZED), TxAck(tx=TransactionType(inputs=[inp1])), + TxRequest(request_type=TXMETA, details=TxRequestDetailsType(request_index=None, tx_hash=inp1.prev_hash), serialized=EMPTY_SERIALIZED), + TxAck(tx=ptx1), + + TxRequest(request_type=TXINPUT, details=TxRequestDetailsType(request_index=0, tx_hash=inp1.prev_hash), serialized=EMPTY_SERIALIZED), + TxAck(tx=TransactionType(inputs=[pinp1])), + + TxRequest(request_type=TXOUTPUT, details=TxRequestDetailsType(request_index=0, tx_hash=inp1.prev_hash), serialized=EMPTY_SERIALIZED), + TxAck(tx=TransactionType(bin_outputs=[pout1])), + + TxRequest(request_type=TXOUTPUT, details=TxRequestDetailsType(request_index=1, tx_hash=inp1.prev_hash), serialized=EMPTY_SERIALIZED), + TxAck(tx=TransactionType(bin_outputs=[pout2])), + TxRequest(request_type=TXOUTPUT, details=TxRequestDetailsType(request_index=0, tx_hash=None), serialized=EMPTY_SERIALIZED), TxAck(tx=TransactionType(outputs=[out1])), @@ -140,6 +164,17 @@ class TestSignSegwitTxP2WPKHInP2SH(unittest.TestCase): sequence=0xffffffff, multisig=None, ) + ptx1 = TransactionType(version=1, lock_time=0, inputs_cnt=1, outputs_cnt=2, extra_data_len=0) + pinp1 = TxInputType(script_sig=unhexlify('4730440220548e087d0426b20b8a571b03b9e05829f7558b80c53c12143e342f56ab29e51d02205b68cb7fb223981d4c999725ac1485a982c4259c4f50b8280f137878c232998a012102794a25b254a268e59a5869da57fbae2fadc6727cb3309321dab409b12b2fa17c'), + prev_hash=unhexlify('802cabf0843b945eabe136d7fc7c89f41021658abf56cba000acbce88c41143a'), + prev_index=0, + script_type=None, + sequence=4294967295) + pout1 = TxOutputBinType(script_pubkey=unhexlify('a91458b53ea7f832e8f096e896b8713a8c6df0e892ca87'), + amount=123456789) + pout2 = TxOutputBinType(script_pubkey=unhexlify('76a914b84bacdcd8f4cc59274a5bfb73f804ca10f7fd1488ac'), + amount=865519308) + out1 = TxOutputType( address='mhRx1CeVfaayqRwq5zgRQmD7W5aWBfD5mC', amount=12300000, @@ -163,6 +198,18 @@ class TestSignSegwitTxP2WPKHInP2SH(unittest.TestCase): TxRequest(request_type=TXINPUT, details=TxRequestDetailsType(request_index=0, tx_hash=None), serialized=EMPTY_SERIALIZED), TxAck(tx=TransactionType(inputs=[inp1])), + TxRequest(request_type=TXMETA, details=TxRequestDetailsType(request_index=None, tx_hash=inp1.prev_hash), serialized=EMPTY_SERIALIZED), + TxAck(tx=ptx1), + + TxRequest(request_type=TXINPUT, details=TxRequestDetailsType(request_index=0, tx_hash=inp1.prev_hash), serialized=EMPTY_SERIALIZED), + TxAck(tx=TransactionType(inputs=[pinp1])), + + TxRequest(request_type=TXOUTPUT, details=TxRequestDetailsType(request_index=0, tx_hash=inp1.prev_hash), serialized=EMPTY_SERIALIZED), + TxAck(tx=TransactionType(bin_outputs=[pout1])), + + TxRequest(request_type=TXOUTPUT, details=TxRequestDetailsType(request_index=1, tx_hash=inp1.prev_hash), serialized=EMPTY_SERIALIZED), + TxAck(tx=TransactionType(bin_outputs=[pout2])), + TxRequest(request_type=TXOUTPUT, details=TxRequestDetailsType(request_index=0, tx_hash=None), serialized=EMPTY_SERIALIZED), TxAck(tx=TransactionType(outputs=[out1])), @@ -232,8 +279,6 @@ class TestSignSegwitTxP2WPKHInP2SH(unittest.TestCase): with self.assertRaises(StopIteration): signer.send(None) - # see https://github.com/trezor/trezor-mcu/commit/6b615ce40567cc0da0b3b38ff668916aaae9dd4b#commitcomment-25505919 - # for the rational behind this attack def test_send_p2wpkh_in_p2sh_attack_amount(self): coin = coins.by_name('Testnet') @@ -249,6 +294,17 @@ class TestSignSegwitTxP2WPKHInP2SH(unittest.TestCase): sequence=0xffffffff, multisig=None, ) + ptx1 = TransactionType(version=1, lock_time=0, inputs_cnt=1, outputs_cnt=2, extra_data_len=0) + pinp1 = TxInputType(script_sig=unhexlify('4730440220548e087d0426b20b8a571b03b9e05829f7558b80c53c12143e342f56ab29e51d02205b68cb7fb223981d4c999725ac1485a982c4259c4f50b8280f137878c232998a012102794a25b254a268e59a5869da57fbae2fadc6727cb3309321dab409b12b2fa17c'), + prev_hash=unhexlify('802cabf0843b945eabe136d7fc7c89f41021658abf56cba000acbce88c41143a'), + prev_index=0, + script_type=None, + sequence=4294967295) + pout1 = TxOutputBinType(script_pubkey=unhexlify('a91458b53ea7f832e8f096e896b8713a8c6df0e892ca87'), + amount=123456789) + pout2 = TxOutputBinType(script_pubkey=unhexlify('76a914b84bacdcd8f4cc59274a5bfb73f804ca10f7fd1488ac'), + amount=865519308) + inpattack = TxInputType( # 49'/1'/0'/1/0" - 2N1LGaGg836mqSQqiuUBLfcyGBhyZbremDX address_n=[49 | 0x80000000, 1 | 0x80000000, 0 | 0x80000000, 1, 0], @@ -282,58 +338,19 @@ class TestSignSegwitTxP2WPKHInP2SH(unittest.TestCase): TxRequest(request_type=TXINPUT, details=TxRequestDetailsType(request_index=0, tx_hash=None), serialized=EMPTY_SERIALIZED), TxAck(tx=TransactionType(inputs=[inpattack])), + TxRequest(request_type=TXMETA, details=TxRequestDetailsType(request_index=None, tx_hash=inp1.prev_hash), serialized=EMPTY_SERIALIZED), + TxAck(tx=ptx1), + + TxRequest(request_type=TXINPUT, details=TxRequestDetailsType(request_index=0, tx_hash=inp1.prev_hash), serialized=EMPTY_SERIALIZED), + TxAck(tx=TransactionType(inputs=[pinp1])), + + TxRequest(request_type=TXOUTPUT, details=TxRequestDetailsType(request_index=0, tx_hash=inp1.prev_hash), serialized=EMPTY_SERIALIZED), + TxAck(tx=TransactionType(bin_outputs=[pout1])), + + TxRequest(request_type=TXOUTPUT, details=TxRequestDetailsType(request_index=1, tx_hash=inp1.prev_hash), serialized=EMPTY_SERIALIZED), + TxAck(tx=TransactionType(bin_outputs=[pout2])), + TxRequest(request_type=TXOUTPUT, details=TxRequestDetailsType(request_index=0, tx_hash=None), serialized=EMPTY_SERIALIZED), - TxAck(tx=TransactionType(outputs=[out1])), - - helpers.UiConfirmOutput(out1, coin), - True, - - TxRequest(request_type=TXOUTPUT, details=TxRequestDetailsType(request_index=1, tx_hash=None), serialized=EMPTY_SERIALIZED), - TxAck(tx=TransactionType(outputs=[out2])), - - helpers.UiConfirmTotal(8, 0, coin), - True, - - TxRequest(request_type=TXINPUT, details=TxRequestDetailsType(request_index=0, tx_hash=None), - serialized=TxRequestSerializedType( - # returned serialized header - serialized_tx=unhexlify( - '01000000000101'), - )), - - TxAck(tx=TransactionType(inputs=[inp1])), - - TxRequest(request_type=TXOUTPUT, details=TxRequestDetailsType(request_index=0, tx_hash=None), - serialized=TxRequestSerializedType( - # returned serialized inpattack - serialized_tx=unhexlify( - '37c361fb8f2d9056ba8c98c5611930fcb48cacfdd0fe2e0449d83eea982f91200000000017160014d16b8c0680c61fc6ed2e407455715055e41052f5ffffffff02'), - )), - # the out has to be cloned not to send the same object which was modified - TxAck(tx=TransactionType(outputs=[TxOutputType(**out1.__dict__)])), - - TxRequest(request_type=TXOUTPUT, details=TxRequestDetailsType(request_index=1, tx_hash=None), - serialized=TxRequestSerializedType( - # returned serialized out1 - serialized_tx=unhexlify( - '08000000000000001976a91414fdede0ddc3be652a0ce1afbc1b509a55b6b94888ac'), - signature_index=None, - signature=None, - )), - TxAck(tx=TransactionType(outputs=[TxOutputType(**out2.__dict__)])), - - # segwit - TxRequest(request_type=TXINPUT, details=TxRequestDetailsType(request_index=0, tx_hash=None), - serialized=TxRequestSerializedType( - # returned serialized out2 - serialized_tx=unhexlify( - '010000000000000017a91458b53ea7f832e8f096e896b8713a8c6df0e892ca87'), - signature_index=None, - signature=None, - )), - TxAck(tx=TransactionType(inputs=[inp1])), - - TxRequest(request_type=TXFINISHED, details=TxRequestDetailsType()) ] ns = get_namespaces_for_coin(coin) diff --git a/core/tests/test_apps.bitcoin.segwit.signtx.p2wpkh_in_p2sh_grs.py b/core/tests/test_apps.bitcoin.segwit.signtx.p2wpkh_in_p2sh_grs.py index 8a1e71fb0e..09dd5fe0d9 100644 --- a/core/tests/test_apps.bitcoin.segwit.signtx.p2wpkh_in_p2sh_grs.py +++ b/core/tests/test_apps.bitcoin.segwit.signtx.p2wpkh_in_p2sh_grs.py @@ -4,11 +4,12 @@ from trezor.utils import chunks from trezor.crypto import bip39 from trezor.messages.SignTx import SignTx from trezor.messages.TxInputType import TxInputType +from trezor.messages.TxOutputBinType import TxOutputBinType from trezor.messages.TxOutputType import TxOutputType from trezor.messages.TxRequest import TxRequest from trezor.messages.TxAck import TxAck from trezor.messages.TransactionType import TransactionType -from trezor.messages.RequestType import TXINPUT, TXOUTPUT, TXFINISHED +from trezor.messages.RequestType import TXINPUT, TXMETA, TXOUTPUT, TXFINISHED from trezor.messages.TxRequestDetailsType import TxRequestDetailsType from trezor.messages.TxRequestSerializedType import TxRequestSerializedType from trezor.messages import InputScriptType @@ -43,6 +44,17 @@ class TestSignSegwitTxP2WPKHInP2SH_GRS(unittest.TestCase): sequence=0xfffffffe, multisig=None, ) + ptx1 = TransactionType(version=1, lock_time=650749, inputs_cnt=1, outputs_cnt=2, extra_data_len=0) + pinp1 = TxInputType(script_sig=unhexlify('47304402201f8f57f708144c3a11da322546cb37bd385aa825d940c37e8016f0efd6ec3e9402202a41bc02c29e4f3f13efd4bededbcd4308a6393279111d614ee1f7635cf3e65701210371546a36bdf6bc82087301b3f6e759736dc8790150673d2e7e2715d2ad72f3a4'), + prev_hash=unhexlify('4f2f857f39ed1afe05542d058fb0be865a387446e32fc876d086203f483f61d1'), + prev_index=1, + script_type=None, + sequence=4294967294) + pout1 = TxOutputBinType(script_pubkey=unhexlify('a91458b53ea7f832e8f096e896b8713a8c6df0e892ca87'), + amount=123456789) + pout2 = TxOutputBinType(script_pubkey=unhexlify('76a91435528b20e9a793cf2c3a1cf9cff1f2127ad377da88ac'), + amount=9764242764) + out1 = TxOutputType( address='mvbu1Gdy8SUjTenqerxUaZyYjmvedc787y', amount=12300000, @@ -66,6 +78,18 @@ class TestSignSegwitTxP2WPKHInP2SH_GRS(unittest.TestCase): TxRequest(request_type=TXINPUT, details=TxRequestDetailsType(request_index=0, tx_hash=None), serialized=EMPTY_SERIALIZED), TxAck(tx=TransactionType(inputs=[inp1])), + TxRequest(request_type=TXMETA, details=TxRequestDetailsType(request_index=None, tx_hash=inp1.prev_hash), serialized=EMPTY_SERIALIZED), + TxAck(tx=ptx1), + + TxRequest(request_type=TXINPUT, details=TxRequestDetailsType(request_index=0, tx_hash=inp1.prev_hash), serialized=EMPTY_SERIALIZED), + TxAck(tx=TransactionType(inputs=[pinp1])), + + TxRequest(request_type=TXOUTPUT, details=TxRequestDetailsType(request_index=0, tx_hash=inp1.prev_hash), serialized=EMPTY_SERIALIZED), + TxAck(tx=TransactionType(bin_outputs=[pout1])), + + TxRequest(request_type=TXOUTPUT, details=TxRequestDetailsType(request_index=1, tx_hash=inp1.prev_hash), serialized=EMPTY_SERIALIZED), + TxAck(tx=TransactionType(bin_outputs=[pout2])), + TxRequest(request_type=TXOUTPUT, details=TxRequestDetailsType(request_index=0, tx_hash=None), serialized=EMPTY_SERIALIZED), TxAck(tx=TransactionType(outputs=[out1])), @@ -144,6 +168,17 @@ class TestSignSegwitTxP2WPKHInP2SH_GRS(unittest.TestCase): sequence=0xfffffffe, multisig=None, ) + ptx1 = TransactionType(version=1, lock_time=650749, inputs_cnt=1, outputs_cnt=2, extra_data_len=0) + pinp1 = TxInputType(script_sig=unhexlify('47304402201f8f57f708144c3a11da322546cb37bd385aa825d940c37e8016f0efd6ec3e9402202a41bc02c29e4f3f13efd4bededbcd4308a6393279111d614ee1f7635cf3e65701210371546a36bdf6bc82087301b3f6e759736dc8790150673d2e7e2715d2ad72f3a4'), + prev_hash=unhexlify('4f2f857f39ed1afe05542d058fb0be865a387446e32fc876d086203f483f61d1'), + prev_index=1, + script_type=None, + sequence=4294967294) + pout1 = TxOutputBinType(script_pubkey=unhexlify('a91458b53ea7f832e8f096e896b8713a8c6df0e892ca87'), + amount=123456789) + pout2 = TxOutputBinType(script_pubkey=unhexlify('76a91435528b20e9a793cf2c3a1cf9cff1f2127ad377da88ac'), + amount=9764242764) + out1 = TxOutputType( address='mvbu1Gdy8SUjTenqerxUaZyYjmvedc787y', amount=12300000, @@ -167,6 +202,18 @@ class TestSignSegwitTxP2WPKHInP2SH_GRS(unittest.TestCase): TxRequest(request_type=TXINPUT, details=TxRequestDetailsType(request_index=0, tx_hash=None), serialized=EMPTY_SERIALIZED), TxAck(tx=TransactionType(inputs=[inp1])), + TxRequest(request_type=TXMETA, details=TxRequestDetailsType(request_index=None, tx_hash=inp1.prev_hash), serialized=EMPTY_SERIALIZED), + TxAck(tx=ptx1), + + TxRequest(request_type=TXINPUT, details=TxRequestDetailsType(request_index=0, tx_hash=inp1.prev_hash), serialized=EMPTY_SERIALIZED), + TxAck(tx=TransactionType(inputs=[pinp1])), + + TxRequest(request_type=TXOUTPUT, details=TxRequestDetailsType(request_index=0, tx_hash=inp1.prev_hash), serialized=EMPTY_SERIALIZED), + TxAck(tx=TransactionType(bin_outputs=[pout1])), + + TxRequest(request_type=TXOUTPUT, details=TxRequestDetailsType(request_index=1, tx_hash=inp1.prev_hash), serialized=EMPTY_SERIALIZED), + TxAck(tx=TransactionType(bin_outputs=[pout2])), + TxRequest(request_type=TXOUTPUT, details=TxRequestDetailsType(request_index=0, tx_hash=None), serialized=EMPTY_SERIALIZED), TxAck(tx=TransactionType(outputs=[out1])), From a5eecf7a3c403d067be0107805d598e0a7ac2331 Mon Sep 17 00:00:00 2001 From: Andrew Kozlik Date: Fri, 15 May 2020 17:22:44 +0200 Subject: [PATCH 19/24] tests/ui: update fixtures to account for changed bgold amounts --- tests/ui_tests/fixtures.json | 17 ++++++++--------- 1 file changed, 8 insertions(+), 9 deletions(-) diff --git a/tests/ui_tests/fixtures.json b/tests/ui_tests/fixtures.json index 9cdad56f91..bfbba346d3 100644 --- a/tests/ui_tests/fixtures.json +++ b/tests/ui_tests/fixtures.json @@ -243,20 +243,19 @@ "test_msg_signtx.py-test_testnet_one_two_fee": "cfd5c83510c044c456622298138e222aee135a6df607bb6e5603228535f0762f", "test_msg_signtx.py-test_two_changes": "77ac9a437f9ba258577d17528eca1c0c60791fbc273d9cf046ce193bbd9e5e56", "test_msg_signtx.py-test_two_two": "57707ecbcb77f670148c6076724b3da2e880d27ecf86e29135af4a5aeef6fdbc", -"test_msg_signtx_bcash.py-test_attack_amount": "05cb99d3f9b862c448d07934af46d07f0bc4775c7aef4b113f137932870370bb", "test_msg_signtx_bcash.py-test_attack_change_input": "a03ee0471deeb54d51b73c0fde08795ab0ba8c37daec2d43f5637e705420b435", "test_msg_signtx_bcash.py-test_send_bch_change": "a03ee0471deeb54d51b73c0fde08795ab0ba8c37daec2d43f5637e705420b435", "test_msg_signtx_bcash.py-test_send_bch_multisig_change": "b607b039e864dc9c5f616ee6f5b780184552ff5c6b8e984ccc8eed133b3d36dd", "test_msg_signtx_bcash.py-test_send_bch_multisig_wrongchange": "8d5c2c06f8d3dd75a03bdf6ecff865e81f8748e4ef5394d75ade3e50512ea087", "test_msg_signtx_bcash.py-test_send_bch_nochange": "3895b874e18582ea77dea2d10ea44906fce4e67e3b7ce3118f5c959fc428d037", "test_msg_signtx_bcash.py-test_send_bch_oldaddr": "4a832b4cec5ae0108b8f2155a08156dbbb9ce82403af98532d6ccd89e65d70e3", -"test_msg_signtx_bgold.py-test_attack_change_input": "de2fe54950938864480fd40866db18a73565fdc9de2f7867ab7e0a8ae7f65ce4", -"test_msg_signtx_bgold.py-test_send_bitcoin_gold_change": "de2fe54950938864480fd40866db18a73565fdc9de2f7867ab7e0a8ae7f65ce4", -"test_msg_signtx_bgold.py-test_send_bitcoin_gold_nochange": "65a3fa31182748333a44e8cedcee653d7532428126d6df1ef3514424adcb10f1", -"test_msg_signtx_bgold.py-test_send_btg_multisig_change": "4ed4962fa425498e4d7ae158d1233b01319dfa071edcb2d71f2f4d4e57c4b4fd", -"test_msg_signtx_bgold.py-test_send_mixed_inputs": "ed137c7c45d1bd9f2e73b4ca6ea0eff63b601e8ad73d79a90aefd2046e2d51b2", -"test_msg_signtx_bgold.py-test_send_multisig_1": "d049b3b25042c732ce26a253e7de49581adc83003713860924b8d951cb46de0c", -"test_msg_signtx_bgold.py-test_send_p2sh": "ddd48151ce1d74ade0b9858cbcdba316581991ec92c2ef54b5893e3aae75f995", +"test_msg_signtx_bgold.py-test_attack_change_input": "8e127323823058532b7960ef9507aa24c38c9f22055015d86fdf8132124fb727", +"test_msg_signtx_bgold.py-test_send_bitcoin_gold_change": "8e127323823058532b7960ef9507aa24c38c9f22055015d86fdf8132124fb727", +"test_msg_signtx_bgold.py-test_send_bitcoin_gold_nochange": "6a5adba8117be6e07405372866bf2ac4054d86f2cffb63d64fa0db1f8f3de500", +"test_msg_signtx_bgold.py-test_send_btg_multisig_change": "6a210a01310014a61c7df66558d48a5503b8e8b5644c404b193cefc94bb7dadb", +"test_msg_signtx_bgold.py-test_send_mixed_inputs": "6a5adba8117be6e07405372866bf2ac4054d86f2cffb63d64fa0db1f8f3de500", +"test_msg_signtx_bgold.py-test_send_multisig_1": "0a611e9cc266a5aec9017373cec013756b1715da3bf9d08281194b20ebad72d2", +"test_msg_signtx_bgold.py-test_send_p2sh": "7f481a8cd3474b05cf38aab47592bc754751af7e0f009677fdda95ddaa7b07ca", "test_msg_signtx_bgold.py-test_send_p2sh_witness_change": "02e44d4c1072eb774486210f885b1bee53acfb3b7fd787207b9f955853fef055", "test_msg_signtx_dash.py-test_send_dash": "291f1a3ace22877641494a1a470a1a4a8dab6e363fc4402dadaeb52c1288c72b", "test_msg_signtx_dash.py-test_send_dash_dip2_input": "cf7fc7e6fe3a9e4063e743da6fc44c27dac013917bc00cfc63d13a183c091d91", @@ -273,7 +272,7 @@ "test_msg_signtx_komodo.py-test_one_one_rewards_claim": "e53f221fda81469027e39e21877a81a8fafbffbece0a45aeda12aae8873b0464", "test_msg_signtx_peercoin.py::test_timestamp_included": "825b9bdf5238c5c6415a254a6bae4b2bd9df8fc5cb31f66f0c20145cb4e60bbb", "test_msg_signtx_segwit.py-test_attack_change_input_address": "5ae71202c062ef7942626a80a4ceeb8d8c4ea5065a97f0de6a97505e9cb82c2c", -"test_msg_signtx_segwit.py-test_attack_mixed_inputs": "5bc10a7cc5fab955f0e9003cf1eea603b5a55917e344ced106870bb3d5bb0306", +"test_msg_signtx_segwit.py-test_attack_mixed_inputs": "1ae5200c6ce74cefae77ab1cfd6e032d0660aa4d106b8c54e092856f656f1e39", "test_msg_signtx_segwit.py-test_send_multisig_1": "958a0741070e057dcb889b2000e5487d391bc513e4a5d86193a355261c5f361b", "test_msg_signtx_segwit.py-test_send_p2sh": "ca593e31e919b9e920289b13e4c70b9607f34b93d06ace69835e3d08ecf046c8", "test_msg_signtx_segwit.py-test_send_p2sh_change": "562c7ee5a2e264c9f93387dd165403dab32bb305a4c3a6143a902c4a4c9e5950", From 24ceb0ab6b35dda150afd1495c8838e8e2987e80 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Ond=C5=99ej=20Vejpustek?= Date: Sat, 20 Apr 2019 15:56:50 +0200 Subject: [PATCH 20/24] crypto/bignum: change limb size to 29, add tests --- .../modtrezorcrypto/modtrezorcrypto-monero.h | 16 +- crypto/bignum.c | 2414 +++++++++++------ crypto/bignum.h | 206 +- crypto/ecdsa.c | 54 +- crypto/nist256p1.c | 29 +- crypto/nist256p1.table | 2048 +++++++------- crypto/secp256k1.c | 25 +- crypto/secp256k1.table | 2048 +++++++------- crypto/tests/test_bignum.py | 1028 +++++++ crypto/tests/test_check.c | 122 +- crypto/tests/test_curves.py | 216 +- crypto/tools/mktable.c | 3 +- 12 files changed, 4954 insertions(+), 3255 deletions(-) create mode 100755 crypto/tests/test_bignum.py diff --git a/core/embed/extmod/modtrezorcrypto/modtrezorcrypto-monero.h b/core/embed/extmod/modtrezorcrypto/modtrezorcrypto-monero.h index a2c246eeb8..939f6a4ab8 100644 --- a/core/embed/extmod/modtrezorcrypto/modtrezorcrypto-monero.h +++ b/core/embed/extmod/modtrezorcrypto/modtrezorcrypto-monero.h @@ -519,13 +519,21 @@ STATIC mp_obj_t mod_trezorcrypto_monero_inv256_modm(size_t n_args, assert_scalar(args[1 + off]); // bn_prime = curve order, little endian encoded - bignum256 bn_prime = {.val = {0x1cf5d3ed, 0x20498c69, 0x2f79cd65, 0x37be77a8, - 0x14, 0x0, 0x0, 0x0, 0x1000}}; + bignum256 bn_prime = {.val = {0x1cf5d3ed, 0x9318d2, 0x1de73596, 0x1df3bd45, + 0x14d, 0x0, 0x0, 0x0, 0x100000}}; bignum256 bn_x; + bignum256modm bm_x; + uint8_t raw_x[32]; + + memcpy(bm_x, MP_OBJ_C_SCALAR(args[1 + off]), sizeof(bignum256modm)); + contract256_modm(raw_x, bm_x); + bn_read_le(raw_x, &bn_x); - memcpy(&bn_x.val, MP_OBJ_C_SCALAR(args[1 + off]), sizeof(bignum256modm)); bn_inverse(&bn_x, &bn_prime); - memcpy(MP_OBJ_SCALAR(res), bn_x.val, sizeof(bignum256modm)); + + bn_write_le(&bn_x, raw_x); + expand_raw256_modm(bm_x, raw_x); + memcpy(MP_OBJ_SCALAR(res), bm_x, sizeof(bignum256modm)); return res; } diff --git a/crypto/bignum.c b/crypto/bignum.c index 11f3dba520..8336aa7e9f 100644 --- a/crypto/bignum.c +++ b/crypto/bignum.c @@ -24,172 +24,172 @@ */ #include "bignum.h" + #include +#include #include #include + #include "memzero.h" +#include "script.h" -/* big number library */ +/* + This library implements 256-bit numbers arithmetic. -/* The structure bignum256 is an array of nine 32-bit values, which - * are digits in base 2^30 representation. I.e. the number - * bignum256 a; - * represents the value - * sum_{i=0}^8 a.val[i] * 2^{30 i}. - * - * The number is *normalized* iff every digit is < 2^30. - * - * As the name suggests, a bignum256 is intended to represent a 256 - * bit number, but it can represent 270 bits. Numbers are usually - * reduced using a prime, either the group order or the field prime. - * The reduction is often partly done by bn_fast_mod, and similarly - * implicitly in bn_multiply. A *partly reduced number* is a - * normalized number between 0 (inclusive) and 2*prime (exclusive). - * - * A partly reduced number can be fully reduced by calling bn_mod. - * Only a fully reduced number is guaranteed to fit in 256 bit. - * - * All functions assume that the prime in question is slightly smaller - * than 2^256. In particular it must be between 2^256-2^224 and - * 2^256 and it must be a prime number. + An unsigned 256-bit number is represented by a bignum256 structure, that is an + array of nine 32-bit values called limbs. Limbs are digits of the number in + the base 2**29 representation in the little endian order. This means that + bignum256 x; + represents the value + sum([x[i] * 2**(29*i) for i in range(9)). + + A limb of a bignum256 is *normalized* iff it's less than 2**29. + A bignum256 is *normalized* iff every its limb is normalized. + A number is *fully reduced modulo p* iff it is less than p. + A number is *partly reduced modulo p* iff is is less than 2*p. + The number p is usually a prime number such that 2^256 - 2^224 <= p <= 2^256. + + All functions except bn_fast_mod expect that all their bignum256 inputs are + normalized. (The function bn_fast_mod allows the input number to have the + most significant limb unnormalized). All bignum256 outputs of all functions + are guaranteed to be normalized. + + A number can be partly reduced with bn_fast_mod, a partly reduced number can + be fully reduced with bn_mod. + + A function has *constant control flow with regard to its argument* iff the + order in which instructions of the function are executed doesn't depend on the + value of the argument. + A function has *constant memory access flow with regard to its argument* iff + the memory addresses that are acessed and the order in which they are accessed + don't depend on the value of the argument. + A function *has contant control (memory access) flow* iff it has constant + control (memory access) flow with regard to all its arguments. + + The following function has contant control flow with regard to its arugment + n, however is doesn't have constant memory access flow with regard to it: + void (int n, int *a) } + a[0] = 0; + a[n] = 0; // memory address reveals the value of n + } + + Unless stated otherwise all functions are supposed to have both constant + control flow and constant memory access flow. */ -inline uint32_t read_be(const uint8_t *data) { - return (((uint32_t)data[0]) << 24) | (((uint32_t)data[1]) << 16) | - (((uint32_t)data[2]) << 8) | (((uint32_t)data[3])); -} +#define BN_MAX_DECIMAL_DIGITS \ + 79 // floor(log(2**(LIMBS * BITS_PER_LIMB), 10)) + 1 -inline void write_be(uint8_t *data, uint32_t x) { - data[0] = x >> 24; - data[1] = x >> 16; - data[2] = x >> 8; - data[3] = x; -} - -inline uint32_t read_le(const uint8_t *data) { - return (((uint32_t)data[3]) << 24) | (((uint32_t)data[2]) << 16) | - (((uint32_t)data[1]) << 8) | (((uint32_t)data[0])); -} - -inline void write_le(uint8_t *data, uint32_t x) { - data[3] = x >> 24; - data[2] = x >> 16; - data[1] = x >> 8; - data[0] = x; -} - -// convert a raw bigendian 256 bit value into a normalized bignum. -// out_number is partly reduced (since it fits in 256 bit). +// out_number = (bignum256) in_number +// Assumes in_number is a raw bigendian 256-bit number +// Guarantees out_number is normalized void bn_read_be(const uint8_t *in_number, bignum256 *out_number) { - int i; uint32_t temp = 0; - for (i = 0; i < 8; i++) { - // invariant: temp = (in_number % 2^(32i)) >> 30i - // get next limb = (in_number % 2^(32(i+1))) >> 32i - uint32_t limb = read_be(in_number + (7 - i) * 4); - // temp = (in_number % 2^(32(i+1))) << 30i - temp |= limb << (2 * i); - // store 30 bits into val[i] - out_number->val[i] = temp & 0x3FFFFFFF; - // prepare temp for next round - temp = limb >> (30 - 2 * i); + + for (int i = 0; i < BN_LIMBS - 1; i++) { + uint32_t limb = read_be(in_number + (BN_LIMBS - 2 - i) * 4); + + temp |= limb << (BN_EXTRA_BITS * i); + out_number->val[i] = temp & BN_LIMB_MASK; + + temp = limb >> (32 - BN_EXTRA_BITS * (i + 1)); } - out_number->val[8] = temp; + + out_number->val[BN_LIMBS - 1] = temp; } -// convert a normalized bignum to a raw bigendian 256 bit number. -// in_number must be fully reduced. +// out_number = (256BE) in_number +// Assumes in_number < 2**256 +// Guarantess out_number is a raw bigendian 256-bit number void bn_write_be(const bignum256 *in_number, uint8_t *out_number) { - int i; - uint32_t temp = in_number->val[8]; - for (i = 0; i < 8; i++) { - // invariant: temp = (in_number >> 30*(8-i)) - uint32_t limb = in_number->val[7 - i]; - temp = (temp << (16 + 2 * i)) | (limb >> (14 - 2 * i)); - write_be(out_number + i * 4, temp); + uint32_t temp = in_number->val[BN_LIMBS - 1]; + for (int i = BN_LIMBS - 2; i >= 0; i--) { + uint32_t limb = in_number->val[i]; + + temp = (temp << (BN_BITS_PER_LIMB - BN_EXTRA_BITS * i)) | + (limb >> (BN_EXTRA_BITS * i)); + write_be(out_number + (BN_LIMBS - 2 - i) * 4, temp); + temp = limb; } } -// convert a raw little endian 256 bit value into a normalized bignum. -// out_number is partly reduced (since it fits in 256 bit). +// out_number = (bignum256) in_number +// Assumes in_number is a raw little endian 256-bit number +// Guarantees out_number is normalized void bn_read_le(const uint8_t *in_number, bignum256 *out_number) { - int i; uint32_t temp = 0; - for (i = 0; i < 8; i++) { - // invariant: temp = (in_number % 2^(32i)) >> 30i - // get next limb = (in_number % 2^(32(i+1))) >> 32i + for (int i = 0; i < BN_LIMBS - 1; i++) { uint32_t limb = read_le(in_number + i * 4); - // temp = (in_number % 2^(32(i+1))) << 30i - temp |= limb << (2 * i); - // store 30 bits into val[i] - out_number->val[i] = temp & 0x3FFFFFFF; - // prepare temp for next round - temp = limb >> (30 - 2 * i); + + temp |= limb << (BN_EXTRA_BITS * i); + out_number->val[i] = temp & BN_LIMB_MASK; + temp = limb >> (32 - BN_EXTRA_BITS * (i + 1)); } - out_number->val[8] = temp; + + out_number->val[BN_LIMBS - 1] = temp; } -// convert a normalized bignum to a raw little endian 256 bit number. -// in_number must be fully reduced. +// out_number = (256LE) in_number +// Assumes in_number < 2**256 +// Guarantess out_number is a raw little endian 256-bit number void bn_write_le(const bignum256 *in_number, uint8_t *out_number) { - int i; - uint32_t temp = in_number->val[8]; - for (i = 0; i < 8; i++) { - // invariant: temp = (in_number >> 30*(8-i)) - uint32_t limb = in_number->val[7 - i]; - temp = (temp << (16 + 2 * i)) | (limb >> (14 - 2 * i)); - write_le(out_number + (7 - i) * 4, temp); + uint32_t temp = in_number->val[BN_LIMBS - 1]; + + for (int i = BN_LIMBS - 2; i >= 0; i--) { + uint32_t limb = in_number->val[i]; + temp = (temp << (BN_BITS_PER_LIMB - BN_EXTRA_BITS * i)) | + (limb >> (BN_EXTRA_BITS * i)); + write_le(out_number + i * 4, temp); temp = limb; } } +// out_number = (bignum256) in_number +// Guarantees out_number is normalized void bn_read_uint32(uint32_t in_number, bignum256 *out_number) { - out_number->val[0] = in_number & 0x3FFFFFFF; - out_number->val[1] = in_number >> 30; - out_number->val[2] = 0; - out_number->val[3] = 0; - out_number->val[4] = 0; - out_number->val[5] = 0; - out_number->val[6] = 0; - out_number->val[7] = 0; - out_number->val[8] = 0; + out_number->val[0] = in_number & BN_LIMB_MASK; + out_number->val[1] = in_number >> BN_BITS_PER_LIMB; + for (uint32_t i = 2; i < BN_LIMBS; i++) out_number->val[i] = 0; } +// out_number = (bignum256) in_number +// Guarantees out_number is normalized void bn_read_uint64(uint64_t in_number, bignum256 *out_number) { - out_number->val[0] = in_number & 0x3FFFFFFF; - out_number->val[1] = (in_number >>= 30) & 0x3FFFFFFF; - out_number->val[2] = in_number >>= 30; - out_number->val[3] = 0; - out_number->val[4] = 0; - out_number->val[5] = 0; - out_number->val[6] = 0; - out_number->val[7] = 0; - out_number->val[8] = 0; + out_number->val[0] = in_number & BN_LIMB_MASK; + out_number->val[1] = (in_number >>= BN_BITS_PER_LIMB) & BN_LIMB_MASK; + out_number->val[2] = in_number >> BN_BITS_PER_LIMB; + for (uint32_t i = 3; i < BN_LIMBS; i++) out_number->val[i] = 0; } -// a must be normalized -int bn_bitcount(const bignum256 *a) { - int i; - for (i = 8; i >= 0; i--) { - int tmp = a->val[i]; - if (tmp != 0) { - return i * 30 + (32 - __builtin_clz(tmp)); +// Returns the bitsize of x +// Assumes x is normalized +// The function doesn't have neither constant control flow nor constant memory +// access flow +int bn_bitcount(const bignum256 *x) { + for (int i = BN_LIMBS - 1; i >= 0; i--) { + uint32_t limb = x->val[i]; + if (limb != 0) { + // __builtin_clz returns the number of leading zero bits starting at the + // most significant bit position + return i * BN_BITS_PER_LIMB + (32 - __builtin_clz(limb)); } } return 0; } -#define DIGITS 78 // log10(2 ^ 256) - -unsigned int bn_digitcount(const bignum256 *a) { - bignum256 val; - memcpy(&val, a, sizeof(bignum256)); +// Returns the number of decimal digits of x; if x is 0, returns 1 +// Assumes x is normalized +// The function doesn't have neither constant control flow nor constant memory +// access flow +unsigned int bn_digitcount(const bignum256 *x) { + bignum256 val = {0}; + bn_copy(x, &val); unsigned int digits = 1; + for (unsigned int i = 0; i < BN_MAX_DECIMAL_DIGITS; i += 3) { + uint32_t limb = 0; - for (unsigned int i = 0; i < DIGITS; i += 3) { - uint32_t limb; bn_divmod1000(&val, &limb); if (limb >= 100) { @@ -201,868 +201,1612 @@ unsigned int bn_digitcount(const bignum256 *a) { } } + memzero(&val, sizeof(val)); + return digits; } -// sets a bignum to zero. -void bn_zero(bignum256 *a) { - int i; - for (i = 0; i < 9; i++) { - a->val[i] = 0; +// x = 0 +// Guarantees x is normalized +void bn_zero(bignum256 *x) { + for (int i = 0; i < BN_LIMBS; i++) { + x->val[i] = 0; } } -// sets a bignum to one. -void bn_one(bignum256 *a) { - a->val[0] = 1; - a->val[1] = 0; - a->val[2] = 0; - a->val[3] = 0; - a->val[4] = 0; - a->val[5] = 0; - a->val[6] = 0; - a->val[7] = 0; - a->val[8] = 0; +// x = 1 +// Guarantees x is normalized +void bn_one(bignum256 *x) { + x->val[0] = 1; + for (int i = 1; i < BN_LIMBS; i++) { + x->val[i] = 0; + } } -// checks that a bignum is zero. -// a must be normalized -// function is constant time (on some architectures, in particular ARM). -int bn_is_zero(const bignum256 *a) { - int i; +// Returns x == 0 +// Assumes x is normalized +int bn_is_zero(const bignum256 *x) { uint32_t result = 0; - for (i = 0; i < 9; i++) { - result |= a->val[i]; + for (int i = 0; i < BN_LIMBS; i++) { + result |= x->val[i]; } return !result; } -// Check whether a < b -// a and b must be normalized -// function is constant time (on some architectures, in particular ARM). -int bn_is_less(const bignum256 *a, const bignum256 *b) { - int i; +// Returns x == 1 +// Assumes x is normalized +int bn_is_one(const bignum256 *x) { + uint32_t result = x->val[0] ^ 1; + for (int i = 1; i < BN_LIMBS; i++) { + result |= x->val[i]; + } + return !result; +} + +// Returns x < y +// Assumes x, y are normalized +int bn_is_less(const bignum256 *x, const bignum256 *y) { uint32_t res1 = 0; uint32_t res2 = 0; - for (i = 8; i >= 0; i--) { - res1 = (res1 << 1) | (a->val[i] < b->val[i]); - res2 = (res2 << 1) | (a->val[i] > b->val[i]); + for (int i = BN_LIMBS - 1; i >= 0; i--) { + res1 = (res1 << 1) | (x->val[i] < y->val[i]); + res2 = (res2 << 1) | (x->val[i] > y->val[i]); } return res1 > res2; } -// Check whether a == b -// a and b must be normalized -// function is constant time (on some architectures, in particular ARM). -int bn_is_equal(const bignum256 *a, const bignum256 *b) { - int i; +// Returns x == y +// Assumes x, y are normalized +int bn_is_equal(const bignum256 *x, const bignum256 *y) { uint32_t result = 0; - for (i = 0; i < 9; i++) { - result |= (a->val[i] ^ b->val[i]); + for (int i = 0; i < BN_LIMBS; i++) { + result |= x->val[i] ^ y->val[i]; } return !result; } -// Assigns res = cond ? truecase : falsecase -// assumes that cond is either 0 or 1. -// function is constant time. -void bn_cmov(bignum256 *res, int cond, const bignum256 *truecase, +// res = cond if truecase else falsecase +// Assumes cond is either 0 or 1 +// Works properly even if &res == &truecase or &res == &falsecase or +// &truecase == &falsecase or &res == &truecase == &falsecase +void bn_cmov(bignum256 *res, volatile uint32_t cond, const bignum256 *truecase, const bignum256 *falsecase) { - int i; - uint32_t tmask = (uint32_t)-cond; - uint32_t fmask = ~tmask; + assert((cond == 1) | (cond == 0)); - assert(cond == 1 || cond == 0); - for (i = 0; i < 9; i++) { + uint32_t tmask = -cond; // tmask = 0xFFFFFFFF if cond else 0x00000000 + uint32_t fmask = ~tmask; // fmask = 0x00000000 if cond else 0xFFFFFFFF + + for (int i = 0; i < BN_LIMBS; i++) { res->val[i] = (truecase->val[i] & tmask) | (falsecase->val[i] & fmask); } } -// shift number to the left, i.e multiply it by 2. -// a must be normalized. The result is normalized but not reduced. -void bn_lshift(bignum256 *a) { - int i; - for (i = 8; i > 0; i--) { - a->val[i] = - ((a->val[i] << 1) & 0x3FFFFFFF) | ((a->val[i - 1] & 0x20000000) >> 29); +// x = -x % prime if cond else x, +// Explicitly x = (3 * prime - x if x > prime else 2 * prime - x) if cond else +// else (x if x > prime else x + prime) +// Assumes x is normalized and partly reduced +// Assumes cond is either 1 or 0 +// Guarantees x is normalized and partly reduced +// Assumes prime is normalized and +// 0 < prime < 2**260 == 2**(BITS_PER_LIMB * LIMBS - 1) +void bn_cnegate(volatile uint32_t cond, bignum256 *x, const bignum256 *prime) { + assert((cond == 1) | (cond == 0)); + + uint32_t tmask = -cond; // tmask = 0xFFFFFFFF if cond else 0x00000000 + uint32_t fmask = ~tmask; // fmask = 0x00000000 if cond else 0xFFFFFFFF + + bn_mod(x, prime); + // x < prime + + uint32_t acc1 = 1; + uint32_t acc2 = 0; + + for (int i = 0; i < BN_LIMBS; i++) { + acc1 += (BN_BASE - 1) + 2 * prime->val[i] - x->val[i]; + // acc1 neither overflows 32 bits nor underflows 0 + // Proof: + // acc1 + (BASE - 1) + 2 * prime[i] - x[i] + // >= (BASE - 1) - x >= (2**BITS_PER_LIMB - 1) - (2**BITS_PER_LIMB - 1) + // == 0 + // acc1 + (BASE - 1) + 2 * prime[i] - x[i] + // <= acc1 + (BASE - 1) + 2 * prime[i] + // <= (2**(32 - BITS_PER_LIMB) - 1) + 2 * (2**BITS_PER_LIMB - 1) + + // (2**BITS_PER_LIMB - 1) + // == 7 + 3 * 2**29 < 2**32 + + acc2 += prime->val[i] + x->val[i]; + // acc2 doesn't overflow 32 bits + // Proof: + // acc2 + prime[i] + x[i] + // <= 2**(32 - BITS_PER_LIMB) - 1 + 2 * (2**BITS_PER_LIMB - 1) + // == 2**(32 - BITS_PER_LIMB) + 2**(BITS_PER_LIMB + 1) - 2 + // == 2**30 + 5 < 2**32 + + // x = acc1 & LIMB_MASK if cond else acc2 & LIMB_MASK + x->val[i] = ((acc1 & tmask) | (acc2 & fmask)) & BN_LIMB_MASK; + + acc1 >>= BN_BITS_PER_LIMB; + // acc1 <= 7 == 2**(32 - BITS_PER_LIMB) - 1 + // acc1 == 2**(BITS_PER_LIMB * (i + 1)) + 2 * prime[:i + 1] - x[:i + 1] + // >> BITS_PER_LIMB * (i + 1) + + acc2 >>= BN_BITS_PER_LIMB; + // acc2 <= 7 == 2**(32 - BITS_PER_LIMB) - 1 + // acc2 == prime[:i + 1] + x[:i + 1] >> BITS_PER_LIMB * (i + 1) } - a->val[0] = (a->val[0] << 1) & 0x3FFFFFFF; + + // assert(acc1 == 1); // assert prime <= 2**260 + // assert(acc2 == 0); + + // clang-format off + // acc1 == 1 + // Proof: + // acc1 == 2**(BITS_PER_LIMB * LIMBS) + 2 * prime[:LIMBS] - x[:LIMBS] >> BITS_PER_LIMB * LIMBS + // == 2**(BITS_PER_LIMB * LIMBS) + 2 * prime - x >> BITS_PER_LIMB * LIMBS + // <= 2**(BITS_PER_LIMB * LIMBS) + 2 * prime >> BITS_PER_LIMB * LIMBS + // <= 2**(BITS_PER_LIMB * LIMBS) + 2 * (2**(BITS_PER_LIMB * LIMBS - 1) - 1) >> BITS_PER_LIMB * LIMBS + // <= 2**(BITS_PER_LIMB * LIMBS) + 2**(BITS_PER_LIMB * LIMBS) - 2 >> BITS_PER_LIMB * LIMBS + // == 1 + + // acc1 == 2**(BITS_PER_LIMB * LIMBS) + 2 * prime[:LIMBS] - x[:LIMBS] >> BITS_PER_LIMB * LIMBS + // == 2**(BITS_PER_LIMB * LIMBS) + 2 * prime - x >> BITS_PER_LIMB * LIMBS + // >= 2**(BITS_PER_LIMB * LIMBS) + 0 >> BITS_PER_LIMB * LIMBS + // == 1 + + // acc2 == 0 + // Proof: + // acc2 == prime[:LIMBS] + x[:LIMBS] >> BITS_PER_LIMB * LIMBS + // == prime + x >> BITS_PER_LIMB * LIMBS + // <= 2 * prime - 1 >> BITS_PER_LIMB * LIMBS + // <= 2 * (2**(BITS_PER_LIMB * LIMBS - 1) - 1) - 1 >> 261 + // == 2**(BITS_PER_LIMB * LIMBS) - 3 >> BITS_PER_LIMB * LIMBS + // == 0 + // clang-format on } -// shift number to the right, i.e divide by 2 while rounding down. -// a must be normalized. The result is normalized. -void bn_rshift(bignum256 *a) { - int i; - for (i = 0; i < 8; i++) { - a->val[i] = (a->val[i] >> 1) | ((a->val[i + 1] & 1) << 29); +// x <<= 1 +// Assumes x is normalized, x < 2**260 == 2**(LIMBS*BITS_PER_LIMB - 1) +// Guarantees x is normalized +void bn_lshift(bignum256 *x) { + for (int i = BN_LIMBS - 1; i > 0; i--) { + x->val[i] = ((x->val[i] << 1) & BN_LIMB_MASK) | + (x->val[i - 1] >> (BN_BITS_PER_LIMB - 1)); } - a->val[8] >>= 1; + x->val[0] = (x->val[0] << 1) & BN_LIMB_MASK; } -// sets bit in bignum -void bn_setbit(bignum256 *a, uint8_t bit) { - a->val[bit / 30] |= (1u << (bit % 30)); +// x >>= 1, i.e. x = floor(x/2) +// Assumes x is normalized +// Guarantees x is normalized +// If x is partly reduced (fully reduced) modulo prime, +// guarantess x will be partly reduced (fully reduced) modulo prime +void bn_rshift(bignum256 *x) { + for (int i = 0; i < BN_LIMBS - 1; i++) { + x->val[i] = + (x->val[i] >> 1) | ((x->val[i + 1] & 1) << (BN_BITS_PER_LIMB - 1)); + } + x->val[BN_LIMBS - 1] >>= 1; } -// clears bit in bignum -void bn_clearbit(bignum256 *a, uint8_t bit) { - a->val[bit / 30] &= ~(1u << (bit % 30)); +// Sets i-th least significant bit (counting from zero) +// Assumes x is normalized and 0 <= i < 261 == LIMBS*BITS_PER_LIMB +// Guarantees x is normalized +// The function has constant control flow but not constant memory access flow +// with regard to i +void bn_setbit(bignum256 *x, uint16_t i) { + assert(i < BN_LIMBS * BN_BITS_PER_LIMB); + x->val[i / BN_BITS_PER_LIMB] |= (1u << (i % BN_BITS_PER_LIMB)); } -// tests bit in bignum -uint32_t bn_testbit(bignum256 *a, uint8_t bit) { - return a->val[bit / 30] & (1u << (bit % 30)); +// clears i-th least significant bit (counting from zero) +// Assumes x is normalized and 0 <= i < 261 == LIMBS*BITS_PER_LIMB +// Guarantees x is normalized +// The function has constant control flow but not constant memory access flow +// with regard to i +void bn_clearbit(bignum256 *x, uint16_t i) { + assert(i < BN_LIMBS * BN_BITS_PER_LIMB); + x->val[i / BN_BITS_PER_LIMB] &= ~(1u << (i % BN_BITS_PER_LIMB)); } -// a = b ^ c -void bn_xor(bignum256 *a, const bignum256 *b, const bignum256 *c) { - int i; - for (i = 0; i < 9; i++) { - a->val[i] = b->val[i] ^ c->val[i]; +// returns i-th least significant bit (counting from zero) +// Assumes x is normalized and 0 <= i < 261 == LIMBS*BITS_PER_LIMB +// The function has constant control flow but not constant memory access flow +// with regard to i +uint32_t bn_testbit(const bignum256 *x, uint16_t i) { + assert(i < BN_LIMBS * BN_BITS_PER_LIMB); + return (x->val[i / BN_BITS_PER_LIMB] >> (i % BN_BITS_PER_LIMB)) & 1; +} + +// res = x ^ y +// Assumes x, y are normalized +// Guarantees res is normalized +// Works properly even if &res == &x or &res == &y or &res == &x == &y +void bn_xor(bignum256 *res, const bignum256 *x, const bignum256 *y) { + for (int i = 0; i < BN_LIMBS; i++) { + res->val[i] = x->val[i] ^ y->val[i]; } } -// multiply x by 1/2 modulo prime. -// it computes x = (x & 1) ? (x + prime) >> 1 : x >> 1. -// assumes x is normalized. -// if x was partly reduced, it is also partly reduced on exit. -// function is constant time. +// x = x / 2 % prime +// Explicitly x = x / 2 if is_even(x) else (x + prime) / 2 +// Assumes x is normalized, x + prime < 261 == LIMBS * BITS_PER_LIMB +// Guarantees x is normalized +// If x is partly reduced (fully reduced) modulo prime, +// guarantess x will be partly reduced (fully reduced) modulo prime +// Assumes prime is an odd number and normalized void bn_mult_half(bignum256 *x, const bignum256 *prime) { - int j; - uint32_t xodd = -(x->val[0] & 1); - // compute x = x/2 mod prime - // if x is odd compute (x+prime)/2 - uint32_t tmp1 = (x->val[0] + (prime->val[0] & xodd)) >> 1; - for (j = 0; j < 8; j++) { - uint32_t tmp2 = (x->val[j + 1] + (prime->val[j + 1] & xodd)); - tmp1 += (tmp2 & 1) << 29; - x->val[j] = tmp1 & 0x3fffffff; - tmp1 >>= 30; - tmp1 += tmp2 >> 1; + // x = x / 2 if is_even(x) else (x + prime) / 2 + + uint32_t x_is_odd_mask = + -(x->val[0] & 1); // x_is_odd_mask = 0xFFFFFFFF if is_odd(x) else 0 + + uint32_t acc = (x->val[0] + (prime->val[0] & x_is_odd_mask)) >> 1; + // acc < 2**BITS_PER_LIMB + // Proof: + // acc == x[0] + prime[0] & x_is_odd_mask >> 1 + // <= (2**(BITS_PER_LIMB) - 1) + (2**(BITS_PER_LIMB) - 1) >> 1 + // == 2**(BITS_PER_LIMB + 1) - 2 >> 1 + // < 2**(BITS_PER_LIMB) + + for (int i = 0; i < BN_LIMBS - 1; i++) { + uint32_t temp = (x->val[i + 1] + (prime->val[i + 1] & x_is_odd_mask)); + // temp < 2**(BITS_PER_LIMB + 1) + // Proof: + // temp == x[i + 1] + val[i + 1] & x_is_odd_mask + // <= (2**(BITS_PER_LIMB) - 1) + (2**(BITS_PER_LIMB) - 1) + // < 2**(BITS_PER_LIMB + 1) + + acc += (temp & 1) << (BN_BITS_PER_LIMB - 1); + // acc doesn't overflow 32 bits + // Proof: + // acc + (temp & 1 << BITS_PER_LIMB - 1) + // <= 2**(BITS_PER_LIMB + 1) + 2**(BITS_PER_LIMB - 1) + // <= 2**30 + 2**28 < 2**32 + + x->val[i] = acc & BN_LIMB_MASK; + acc >>= BN_BITS_PER_LIMB; + acc += temp >> 1; + // acc < 2**(BITS_PER_LIMB + 1) + // Proof: + // acc + (temp >> 1) + // <= (2**(32 - BITS_PER_LIMB) - 1) + (2**(BITS_PER_LIMB + 1) - 1 >> 1) + // == 7 + 2**(BITS_PER_LIMB) - 1 < 2**(BITS_PER_LIMB + 1) + + // acc == x[:i+2]+(prime[:i+2] & x_is_odd_mask) >> BITS_PER_LIMB * (i+1) } - x->val[8] = tmp1; + x->val[BN_LIMBS - 1] = acc; + + // assert(acc >> BITS_PER_LIMB == 0); + // acc >> BITS_PER_LIMB == 0 + // Proof: + // acc + // == x[:LIMBS] + (prime[:LIMBS] & x_is_odd_mask) >> BITS_PER_LIMB*LIMBS + // == x + (prime & x_is_odd_mask) >> BITS_PER_LIMB * LIMBS + // <= x + prime >> BITS_PER_LIMB * LIMBS + // <= 2**(BITS_PER_LIMB * LIMBS) - 1 >> BITS_PER_LIMB * LIMBS + // == 0 } -// multiply x by k modulo prime. -// assumes x is normalized, 0 <= k <= 4. -// guarantees x is partly reduced. +// x = x * k % prime +// Assumes x is normalized, 0 <= k <= 8 = 2**(32 - BITS_PER_LIMB) +// Assumes prime is normalized and 2^256 - 2^224 <= prime <= 2^256 +// Guarantees x is normalized and partly reduced modulo prime void bn_mult_k(bignum256 *x, uint8_t k, const bignum256 *prime) { - int j; - for (j = 0; j < 9; j++) { - x->val[j] = k * x->val[j]; + assert(k <= 8); + + for (int i = 0; i < BN_LIMBS; i++) { + x->val[i] = k * x->val[i]; + // x[i] doesn't overflow 32 bits + // k * x[i] <= 2**(32 - BITS_PER_LIMB) * (2**BITS_PER_LIMB - 1) + // < 2**(32 - BITS_PER_LIMB) * 2**BITS_PER_LIMB == 2**32 } + bn_fast_mod(x, prime); } -// compute x = x mod prime by computing x >= prime ? x - prime : x. -// assumes x partly reduced, guarantees x fully reduced. +// Reduces partly reduced x modulo prime +// Explicitly x = x if x < prime else x - prime +// Assumes x is partly reduced modulo prime +// Guarantees x is fully reduced modulo prime +// Assumes prime is nonzero and normalized void bn_mod(bignum256 *x, const bignum256 *prime) { - const int flag = bn_is_less(x, prime); // x < prime - bignum256 temp; - bn_subtract(x, prime, &temp); // temp = x - prime - bn_cmov(x, flag, x, &temp); + uint32_t x_less_prime = bn_is_less(x, prime); + + bignum256 temp = {0}; + bn_subtract(x, prime, &temp); + bn_cmov(x, x_less_prime, x, &temp); + + memzero(&temp, sizeof(temp)); } -// auxiliary function for multiplication. -// compute k * x as a 540 bit number in base 2^30 (normalized). -// assumes that k and x are normalized. +// Auxiliary function for bn_multiply +// res = k * x +// Assumes k and x are normalized +// Guarantees res is normalized 18 digit little endian number in base 2**29 void bn_multiply_long(const bignum256 *k, const bignum256 *x, - uint32_t res[18]) { - int i, j; - uint64_t temp = 0; + uint32_t res[2 * BN_LIMBS]) { + // Uses long multiplication in base 2**29, see + // https://en.wikipedia.org/wiki/Multiplication_algorithm#Long_multiplication - // compute lower half of long multiplication - for (i = 0; i < 9; i++) { - for (j = 0; j <= i; j++) { - // no overflow, since 9*2^60 < 2^64 - temp += k->val[j] * (uint64_t)x->val[i - j]; + uint64_t acc = 0; + + // compute lower half + for (int i = 0; i < BN_LIMBS; i++) { + for (int j = 0; j <= i; j++) { + acc += k->val[j] * (uint64_t)x->val[i - j]; + // acc doesn't overflow 64 bits + // Proof: + // acc <= acc + sum([k[j] * x[i-j] for j in range(i)]) + // <= (2**(64 - BITS_PER_LIMB) - 1) + + // LIMBS * (2**BITS_PER_LIMB - 1) * (2**BITS_PER_LIMB - 1) + // == (2**35 - 1) + 9 * (2**29 - 1) * (2**29 - 1) + // <= 2**35 + 9 * 2**58 < 2**64 } - res[i] = temp & 0x3FFFFFFFu; - temp >>= 30; + + res[i] = acc & BN_LIMB_MASK; + acc >>= BN_BITS_PER_LIMB; + // acc <= 2**35 - 1 == 2**(64 - BITS_PER_LIMB) - 1 } + // compute upper half - for (; i < 17; i++) { - for (j = i - 8; j < 9; j++) { - // no overflow, since 9*2^60 < 2^64 - temp += k->val[j] * (uint64_t)x->val[i - j]; + for (int i = BN_LIMBS; i < 2 * BN_LIMBS - 1; i++) { + for (int j = i - BN_LIMBS + 1; j < BN_LIMBS; j++) { + acc += k->val[j] * (uint64_t)x->val[i - j]; + // acc doesn't overflow 64 bits + // Proof: + // acc <= acc + sum([k[j] * x[i-j] for j in range(i)]) + // <= (2**(64 - BITS_PER_LIMB) - 1) + // LIMBS * (2**BITS_PER_LIMB - 1) * (2**BITS_PER_LIMB - 1) + // == (2**35 - 1) + 9 * (2**29 - 1) * (2**29 - 1) + // <= 2**35 + 9 * 2**58 < 2**64 } - res[i] = temp & 0x3FFFFFFFu; - temp >>= 30; + + res[i] = acc & (BN_BASE - 1); + acc >>= BN_BITS_PER_LIMB; + // acc < 2**35 == 2**(64 - BITS_PER_LIMB) } - res[17] = temp; + + res[2 * BN_LIMBS - 1] = acc; } -// auxiliary function for multiplication. -// reduces res modulo prime. -// assumes i >= 8 and i <= 16 -// assumes res normalized, res < 2^(30(i-7)) * 2 * prime -// guarantees res normalized, res < 2^(30(i-8)) * 2 * prime -void bn_multiply_reduce_step(uint32_t res[18], const bignum256 *prime, - uint32_t i) { - // let k = i-8. - // on entry: - // 0 <= res < 2^(30k + 31) * prime - // estimate coef = (res / prime / 2^30k) - // by coef = res / 2^(30k + 256) rounded down - // 0 <= coef < 2^31 - // subtract (coef * 2^(30k) * prime) from res - // note that we unrolled the first iteration - assert(i >= 8 && i <= 16); - uint32_t j; - uint32_t coef = (res[i] >> 16) + (res[i + 1] << 14); - uint64_t temp = - 0x2000000000000000ull + res[i - 8] - prime->val[0] * (uint64_t)coef; - assert(coef < 0x80000000u); - res[i - 8] = temp & 0x3FFFFFFF; - for (j = 1; j < 9; j++) { - temp >>= 30; - // Note: coeff * prime->val[j] <= (2^31-1) * (2^30-1) - // Hence, this addition will not underflow. - temp += - 0x1FFFFFFF80000000ull + res[i - 8 + j] - prime->val[j] * (uint64_t)coef; - res[i - 8 + j] = temp & 0x3FFFFFFF; - // 0 <= temp < 2^61 + 2^30 +// Auxiliary function for bn_multiply +// Assumes 0 <= d <= 8 == LIMBS - 1 +// Assumes res is normalized and res < 2**(256 + 29*d + 31) +// Guarantess res in normalized and res < 2 * prime * 2**(29*d) +// Assumes prime is normalized, 2**256 - 2**224 <= prime <= 2**256 +void bn_multiply_reduce_step(uint32_t res[2 * BN_LIMBS], const bignum256 *prime, + uint32_t d) { + // clang-format off + // Computes res = res - (res // 2**(256 + BITS_PER_LIMB * d)) * prime * 2**(BITS_PER_LIMB * d) + + // res - (res // 2**(256 + BITS_PER_LIMB * d)) * prime * 2**(BITS_PER_LIMB * d) < 2 * prime * 2**(BITS_PER_LIMB * d) + // Proof: + // res - res // (2**(256 + BITS_PER_LIMB * d)) * 2**(BITS_PER_LIMB * d) * prime + // == res - res // (2**(256 + BITS_PER_LIMB * d)) * 2**(BITS_PER_LIMB * d) * (2**256 - (2**256 - prime)) + // == res - res // (2**(256 + BITS_PER_LIMB * d)) * 2**(BITS_PER_LIMB * d) * 2**256 + res // (2**(256 + BITS_PER_LIMB * d)) * 2**(BITS_PER_LIMB * d) * (2**256 - prime) + // == (res % 2**(256 + BITS_PER_LIMB * d)) + res // (2**256 + BITS_PER_LIMB * d) * 2**(BITS_PER_LIMB * d) * (2**256 - prime) + // <= (2**(256 + 29*d + 31) % 2**(256 + 29*d)) + (2**(256 + 29*d + 31) - 1) / (2**256 + 29*d) * 2**(29*d) * (2**256 - prime) + // <= 2**(256 + 29*d) + 2**(256 + 29*d + 31) / (2**256 + 29*d) * 2**(29*d) * (2**256 - prime) + // == 2**(256 + 29*d) + 2**31 * 2**(29*d) * (2**256 - prime) + // == 2**(29*d) * (2**256 + 2**31 * (2*256 - prime)) + // <= 2**(29*d) * (2**256 + 2**31 * 2*224) + // <= 2**(29*d) * (2**256 + 2**255) + // <= 2**(29*d) * 2 * (2**256 - 2**224) + // <= 2 * prime * 2**(29*d) + // clang-format on + + uint32_t coef = + (res[d + BN_LIMBS - 1] >> (256 - (BN_LIMBS - 1) * BN_BITS_PER_LIMB)) + + (res[d + BN_LIMBS] << ((BN_LIMBS * BN_BITS_PER_LIMB) - 256)); + + // coef == res // 2**(256 + BITS_PER_LIMB * d) + + // coef < 2**31 + // Proof: + // coef == res // 2**(256 + BITS_PER_LIMB * d) + // < 2**(256 + 29 * d + 31) // 2**(256 + 29 * d) + // == 2**31 + + const int shift = 31; + uint64_t acc = 1ull << shift; + + for (int i = 0; i < BN_LIMBS; i++) { + acc += (((uint64_t)(BN_BASE - 1)) << shift) + res[d + i] - + prime->val[i] * (uint64_t)coef; + // acc neither overflow 64 bits nor underflow zero + // Proof: + // acc + ((BASE - 1) << shift) + res[d + i] - prime[i] * coef + // >= ((BASE - 1) << shift) - prime[i] * coef + // == 2**shift * (2**BITS_PER_LIMB - 1) - (2**BITS_PER_LIMB - 1) * + // (2**31 - 1) + // == (2**shift - 2**31 + 1) * (2**BITS_PER_LIMB - 1) + // == (2**31 - 2**31 + 1) * (2**29 - 1) + // == 2**29 - 1 > 0 + // acc + ((BASE - 1) << shift) + res[d + i] - prime[i] * coef + // <= acc + ((BASE - 1) << shift) + res[d+i] + // <= (2**(64 - BITS_PER_LIMB) - 1) + 2**shift * (2**BITS_PER_LIMB - 1) + // + (2*BITS_PER_LIMB - 1) + // == (2**(64 - BITS_PER_LIMB) - 1) + (2**shift + 1) * + // (2**BITS_PER_LIMB - 1) + // == (2**35 - 1) + (2**31 + 1) * (2**29 - 1) + // <= 2**35 + 2**60 + 2**29 < 2**64 + + res[d + i] = acc & BN_LIMB_MASK; + acc >>= BN_BITS_PER_LIMB; + // acc <= 2**(64 - BITS_PER_LIMB) - 1 == 2**35 - 1 + + // acc == (1 << BITS_PER_LIMB * (i + 1) + shift) + res[d : d + i + 1] + // - coef * prime[:i + 1] >> BITS_PER_LIMB * (i + 1) } - temp >>= 30; - temp += 0x1FFFFFFF80000000ull + res[i - 8 + j]; - res[i - 8 + j] = temp & 0x3FFFFFFF; - // we rely on the fact that prime > 2^256 - 2^224 - // res = oldres - coef*2^(30k) * prime; - // and - // coef * 2^(30k + 256) <= oldres < (coef+1) * 2^(30k + 256) - // Hence, 0 <= res < 2^30k (2^256 + coef * (2^256 - prime)) - // < 2^30k (2^256 + 2^31 * 2^224) - // < 2^30k (2 * prime) + + // acc += (((uint64_t)(BASE - 1)) << shift) + res[d + LIMBS]; + // acc >>= BITS_PER_LIMB; + // assert(acc <= 1ul << shift); + + // clang-format off + // acc == 1 << shift + // Proof: + // acc + // == (1 << BITS_PER_LIMB * (LIMBS + 1) + shift) + res[d : d + LIMBS + 1] - coef * prime[:LIMBS] >> BITS_PER_LIMB * (LIMBS + 1) + // == (1 << BITS_PER_LIMB * (LIMBS + 1) + shift) + res[d : d + LIMBS + 1] - coef * prime >> BITS_PER_LIMB * (LIMBS + 1) + + // == (1 << BITS_PER_LIMB * (LIMBS + 1) + shift) + (res[d : d + LIMBS + 1] - coef * prime) >> BITS_PER_LIMB * (LIMBS + 1) + // <= (1 << BITS_PER_LIMB * (LIMBS + 1) + shift) + (res[:d] + BASE**d * res[d : d + LIMBS + 1] - BASE**d * coef * prime)//BASE**d >> BITS_PER_LIMB * (LIMBS + 1) + // <= (1 << BITS_PER_LIMB * (LIMBS + 1) + shift) + (res - BASE**d * coef * prime) // BASE**d >> BITS_PER_LIMB * (LIMBS + 1) + // == (1 << BITS_PER_LIMB * (LIMBS + 1) + shift) + (2 * prime * BASE**d) // BASE**d >> BITS_PER_LIMB * (LIMBS + 1) + // <= (1 << 321) + 2 * 2**256 >> 290 + // == 1 << 31 == 1 << shift + + // == (1 << BITS_PER_LIMB * (LIMBS + 1) + shift) + res[d : d + LIMBS + 1] - coef * prime[:LIMBS + 1] >> BITS_PER_LIMB * (LIMBS + 1) + // >= (1 << BITS_PER_LIMB * (LIMBS + 1) + shift) + 0 >> BITS_PER_LIMB * (LIMBS + 1) + // == 1 << shift + // clang-format on + + res[d + BN_LIMBS] = 0; } -// auxiliary function for multiplication. -// reduces x = res modulo prime. -// assumes res normalized, res < 2^270 * 2 * prime -// guarantees x partly reduced, i.e., x < 2 * prime -void bn_multiply_reduce(bignum256 *x, uint32_t res[18], +// Auxiliary function for bn_multiply +// Partly reduces res and stores both in x and res +// Assumes res in normalized and res < 2**519 +// Guarantees x is normalized and partly reduced modulo prime +// Assumes prime is normalized, 2**256 - 2**224 <= prime <= 2**256 +void bn_multiply_reduce(bignum256 *x, uint32_t res[2 * BN_LIMBS], const bignum256 *prime) { - int i; - // res = k * x is a normalized number (every limb < 2^30) - // 0 <= res < 2^270 * 2 * prime. - for (i = 16; i >= 8; i--) { + for (int i = BN_LIMBS - 1; i >= 0; i--) { + // res < 2**(256 + 29*i + 31) + // Proof: + // if i == LIMBS - 1: + // res < 2**519 + // == 2**(256 + 29 * 8 + 31) + // == 2**(256 + 29 * (LIMBS - 1) + 31) + // else: + // res < 2 * prime * 2**(29 * (i + 1)) + // <= 2**256 * 2**(29*i + 29) < 2**(256 + 29*i + 31) bn_multiply_reduce_step(res, prime, i); - assert(res[i + 1] == 0); } - // store the result - for (i = 0; i < 9; i++) { + + for (int i = 0; i < BN_LIMBS; i++) { x->val[i] = res[i]; } } -// Compute x := k * x (mod prime) -// both inputs must be smaller than 180 * prime. -// result is partly reduced (0 <= x < 2 * prime) -// This only works for primes between 2^256-2^224 and 2^256. +// x = k * x % prime +// Assumes k, x are normalized, k * x < 2**519 +// Guarantees x is normalized and partly reduced modulo prime +// Assumes prime is normalized, 2**256 - 2**224 <= prime <= 2**256 void bn_multiply(const bignum256 *k, bignum256 *x, const bignum256 *prime) { - uint32_t res[18] = {0}; + uint32_t res[2 * BN_LIMBS] = {0}; + bn_multiply_long(k, x, res); bn_multiply_reduce(x, res, prime); + memzero(res, sizeof(res)); } -// partly reduce x modulo prime -// input x does not have to be normalized. -// x can be any number that fits. -// prime must be between (2^256 - 2^224) and 2^256 -// result is partly reduced, smaller than 2*prime +// Partly reduces x modulo prime +// Assumes limbs of x except the last (the most significant) one are normalized +// Assumes prime is normalized and 2^256 - 2^224 <= prime <= 2^256 +// Guarantees x is normalized and partly reduced modulo prime void bn_fast_mod(bignum256 *x, const bignum256 *prime) { - int j; - uint32_t coef; - uint64_t temp; + // Computes x = x - (x // 2**256) * prime - coef = x->val[8] >> 16; - // substract (coef * prime) from x - // note that we unrolled the first iteration - temp = 0x2000000000000000ull + x->val[0] - prime->val[0] * (uint64_t)coef; - x->val[0] = temp & 0x3FFFFFFF; - for (j = 1; j < 9; j++) { - temp >>= 30; - temp += 0x1FFFFFFF80000000ull + x->val[j] - prime->val[j] * (uint64_t)coef; - x->val[j] = temp & 0x3FFFFFFF; + // x < 2**((LIMBS - 1) * BITS_PER_LIMB + 32) == 2**264 + + // x - (x // 2**256) * prime < 2 * prime + // Proof: + // x - (x // 2**256) * prime + // == x - (x // 2**256) * (2**256 - (2**256 - prime)) + // == x - ((x // 2**256) * 2**256) + (x // 2**256) * (2**256 - prime) + // == (x % prime) + (x // 2**256) * (2**256 - prime) + // <= prime - 1 + (2**264 // 2**256) * (2**256 - prime) + // <= 2**256 + 2**8 * 2**224 == 2**256 + 2**232 + // < 2 * (2**256 - 2**224) + // <= 2 * prime + + // x - (x // 2**256 - 1) * prime < 2 * prime + // Proof: + // x - (x // 2**256) * prime + prime + // == x - (x // 2**256) * (2**256 - (2**256 - prime)) + prime + // == x - ((x//2**256) * 2**256) + (x//2**256) * (2**256 - prime) + prime + // == (x % prime) + (x // 2**256) * (2**256 - prime) + prime + // <= 2 * prime - 1 + (2**264 // 2**256) * (2**256 - prime) + // <= 2 * prime + 2**8 * 2**224 == 2**256 + 2**232 + 2**256 - 2**224 + // < 2 * (2**256 - 2**224) + // <= 2 * prime + + uint32_t coef = + x->val[BN_LIMBS - 1] >> (256 - ((BN_LIMBS - 1) * BN_BITS_PER_LIMB)); + + // clang-format off + // coef == x // 2**256 + // 0 <= coef < 2**((LIMBS - 1) * BITS_PER_LIMB + 32 - 256) == 256 + // Proof: + //* Let x[[a : b] be the number consisting of a-th to (b-1)-th bit of the number x. + // x[LIMBS - 1] >> (256 - ((LIMBS - 1) * BITS_PER_LIMB)) + // == x[[(LIMBS - 1) * BITS_PER_LIMB : (LIMBS - 1) * BITS_PER_LIMB + 32]] >> (256 - ((LIMBS - 1) * BITS_PER_LIMB)) + // == x[[256 - ((LIMBS - 1) * BITS_PER_LIMB) + (LIMBS - 1) * BITS_PER_LIMB : (LIMBS - 1) * BITS_PER_LIMB + 32]] + // == x[[256 : (LIMBS - 1) * BITS_PER_LIMB + 32]] + // == x[[256 : 264]] == x // 2**256 + // clang-format on + + const int shift = 8; + uint64_t acc = 1ull << shift; + + for (int i = 0; i < BN_LIMBS; i++) { + acc += (((uint64_t)(BN_BASE - 1)) << shift) + x->val[i] - + prime->val[i] * (uint64_t)coef; + // acc neither overflows 64 bits nor underflows 0 + // Proof: + // acc + (BASE - 1 << shift) + x[i] - prime[i] * coef + // >= (BASE - 1 << shift) - prime[i] * coef + // >= 2**shift * (2**BITS_PER_LIMB - 1) - (2**BITS_PER_LIMB - 1) * 255 + // == (2**shift - 255) * (2**BITS_PER_LIMB - 1) + // == (2**8 - 255) * (2**29 - 1) == 2**29 - 1 >= 0 + // acc + (BASE - 1 << shift) + x[i] - prime[i] * coef + // <= acc + ((BASE - 1) << shift) + x[i] + // <= (2**(64 - BITS_PER_LIMB) - 1) + 2**shift * (2**BITS_PER_LIMB - 1) + // + (2**32 - 1) + // == (2**35 - 1) + 2**8 * (2**29 - 1) + 2**32 + // < 2**35 + 2**37 + 2**32 < 2**64 + + x->val[i] = acc & BN_LIMB_MASK; + acc >>= BN_BITS_PER_LIMB; + // acc <= 2**(64 - BITS_PER_LIMB) - 1 == 2**35 - 1 + + // acc == (1 << BITS_PER_LIMB * (i + 1) + shift) + x[:i + 1] + // - coef * prime[:i + 1] >> BITS_PER_LIMB * (i + 1) } + + // assert(acc == 1 << shift); + + // clang-format off + // acc == 1 << shift + // Proof: + // acc + // == (1 << BITS_PER_LIMB * LIMBS + shift) + x[:LIMBS] - coef * prime[:LIMBS] >> BITS_PER_LIMB * LIMBS + // == (1 << BITS_PER_LIMB * LIMBS + shift) + (x - coef * prime) >> BITS_PER_LIMB * LIMBS + // <= (1 << BITS_PER_LIMB * LIMBS + shift) + (2 * prime) >> BITS_PER_LIMB * LIMBS + // <= (1 << BITS_PER_LIMB * LIMBS + shift) + 2 * 2**256 >> BITS_PER_LIMB * LIMBS + // <= 2**269 + 2**257 >> 2**261 + // <= 1 << 8 == 1 << shift + + // acc + // == (1 << BITS_PER_LIMB * LIMBS + shift) + x[:LIMBS] - coef * prime[:LIMBS] >> BITS_PER_LIMB * LIMBS + // >= (1 << BITS_PER_LIMB * LIMBS + shift) + 0 >> BITS_PER_LIMB * LIMBS + // == (1 << BITS_PER_LIMB * LIMBS + shift) + 0 >> BITS_PER_LIMB * LIMBS + // <= 1 << 8 == 1 << shift + // clang-format on } -// square root of x = x^((p+1)/4) -// http://en.wikipedia.org/wiki/Quadratic_residue#Prime_or_prime_power_modulus -// assumes x is normalized but not necessarily reduced. -// guarantees x is reduced +// res = x**e % prime +// Assumes both x and e are normalized, x < 2**259 +// Guarantees res is normalized and partly reduced modulo prime +// Works properly even if &x == &res +// Assumes prime is normalized, 2**256 - 2**224 <= prime <= 2**256 +// The function doesn't have neither constant control flow nor constant memory +// access flow with regard to e +void bn_power_mod(const bignum256 *x, const bignum256 *e, + const bignum256 *prime, bignum256 *res) { + // Uses iterative right-to-left exponentiation by squaring, see + // https://en.wikipedia.org/wiki/Modular_exponentiation#Right-to-left_binary_method + + bignum256 acc = {0}; + bn_copy(x, &acc); + + bn_one(res); + for (int i = 0; i < BN_LIMBS; i++) { + uint32_t limb = e->val[i]; + + for (int j = 0; j < BN_BITS_PER_LIMB; j++) { + // Break if the following bits of the last limb are zero + if (i == BN_LIMBS - 1 && limb == 0) break; + + if (limb & 1) + // acc * res < 2**519 + // Proof: + // acc * res <= max(2**259 - 1, 2 * prime) * (2 * prime) + // == max(2**259 - 1, 2**257) * 2**257 < 2**259 * 2**257 + // == 2**516 < 2**519 + bn_multiply(&acc, res, prime); + + limb >>= 1; + // acc * acc < 2**519 + // Proof: + // acc * acc <= max(2**259 - 1, 2 * prime)**2 + // <= (2**259)**2 == 2**518 < 2**519 + bn_multiply(&acc, &acc, prime); + } + // acc == x**(e[:i + 1]) % prime + } + + memzero(&acc, sizeof(acc)); +} + +// x = sqrt(x) % prime +// Explicitly x = x**((prime+1)/4) % prime +// The other root is -sqrt(x) +// Assumes x is normalized, x < 2**259 and quadratic residuum mod prime +// Assumes prime is a prime number, prime % 4 == 3, it is normalized and +// 2**256 - 2**224 <= prime <= 2**256 +// Guarantees x is normalized and fully reduced modulo prime +// The function doesn't have neither constant control flow nor constant memory +// access flow with regard to prime void bn_sqrt(bignum256 *x, const bignum256 *prime) { - // this method compute x^1/2 = x^(prime+1)/4 - uint32_t i, j, limb; - bignum256 res, p; - bn_one(&res); - // compute p = (prime+1)/4 - memcpy(&p, prime, sizeof(bignum256)); - bn_addi(&p, 1); - bn_rshift(&p); - bn_rshift(&p); - for (i = 0; i < 9; i++) { - // invariants: - // x = old(x)^(2^(i*30)) - // res = old(x)^(p % 2^(i*30)) - // get the i-th limb of prime - 2 - limb = p.val[i]; - for (j = 0; j < 30; j++) { - // invariants: - // x = old(x)^(2^(i*30+j)) - // res = old(x)^(p % 2^(i*30+j)) - // limb = (p % 2^(i*30+30)) / 2^(i*30+j) - if (i == 8 && limb == 0) break; - if (limb & 1) { - bn_multiply(x, &res, prime); - } - limb >>= 1; - bn_multiply(x, x, prime); - } - } - bn_mod(&res, prime); - memcpy(x, &res, sizeof(bignum256)); - memzero(&res, sizeof(res)); - memzero(&p, sizeof(p)); + // Uses the Lagrange formula for the primes of the special form, see + // http://en.wikipedia.org/wiki/Quadratic_residue#Prime_or_prime_power_modulus + // If prime % 4 == 3, then sqrt(x) % prime == x**((prime+1)//4) % prime + + assert(prime->val[BN_LIMBS - 1] % 4 == 3); + + // e = (prime + 1) // 4 + bignum256 e = {0}; + bn_copy(prime, &e); + bn_addi(&e, 1); + bn_rshift(&e); + bn_rshift(&e); + + bn_power_mod(x, &e, prime, x); + bn_mod(x, prime); + + memzero(&e, sizeof(e)); } -#if !USE_INVERSE_FAST +// a = 1/a % 2**n +// Assumes a is odd, 1 <= n <= 32 +// The function doesn't have neither constant control flow nor constant memory +// access flow with regard to n +uint32_t inverse_mod_power_two(uint32_t a, uint32_t n) { + // Uses "Explicit Quadratic Modular inverse modulo 2" from section 3.3 of "On + // Newton-Raphson iteration for multiplicative inverses modulo prime powers" + // by Jean-Guillaume Dumas, see + // https://arxiv.org/pdf/1209.6626.pdf -// in field G_prime, small but slow -void bn_inverse(bignum256 *x, const bignum256 *prime) { - // this method compute x^-1 = x^(prime-2) - uint32_t i, j, limb; - bignum256 res; - bn_one(&res); - for (i = 0; i < 9; i++) { - // invariants: - // x = old(x)^(2^(i*30)) - // res = old(x)^((prime-2) % 2^(i*30)) - // get the i-th limb of prime - 2 - limb = prime->val[i]; - // this is not enough in general but fine for secp256k1 & nist256p1 because - // prime->val[0] > 1 - if (i == 0) limb -= 2; - for (j = 0; j < 30; j++) { - // invariants: - // x = old(x)^(2^(i*30+j)) - // res = old(x)^((prime-2) % 2^(i*30+j)) - // limb = ((prime-2) % 2^(i*30+30)) / 2^(i*30+j) - // early abort when only zero bits follow - if (i == 8 && limb == 0) break; - if (limb & 1) { - bn_multiply(x, &res, prime); - } - limb >>= 1; - bn_multiply(x, x, prime); - } + // 1/a % 2**n + // = (2-a) * product([1 + (a-1)**(2**i) for i in range(1, floor(log2(n)))]) + + uint32_t acc = 2 - a; + uint32_t f = a - 1; + + // mask = (1 << n) - 1 + uint32_t mask = n == 32 ? 0xFFFFFFFF : (1u << n) - 1; + + for (uint32_t i = 1; i < n; i <<= 1) { + f = (f * f) & mask; + acc = (acc * (1 + f)) & mask; } - bn_mod(&res, prime); - memcpy(x, &res, sizeof(bignum256)); + + return acc; } -#else +// x = (x / 2**BITS_PER_LIMB) % prime +// Assumes both x and prime are normalized +// Assumes prime is an odd number and normalized +// Guarantees x is normalized +// If x is partly reduced (fully reduced) modulo prime, +// guarantess x will be partly reduced (fully reduced) modulo prime +void bn_divide_base(bignum256 *x, const bignum256 *prime) { + // Uses an explicit formula for the modular inverse of power of two + // (x / 2**n) % prime == (x + ((-x / prime) % 2**n) * prime) // 2**n + // Proof: + // (x + ((-x / prime) % 2**n) * prime) % 2**n + // == (x - x / prime * prime) % 2**n + // == 0 + // (x + ((-1 / prime) % 2**n) * prime) % prime + // == x + // if x < prime: + // (x + ((-x / prime) % 2**n) * prime) // 2**n + // <= ((prime - 1) + (2**n - 1) * prime) / 2**n + // == (2**n * prime - 1) / 2**n == prime - 1 / 2**n < prime + // if x < 2 * prime: + // (x + ((-x / prime) % 2**n) * prime) // 2**n + // <= ((2 * prime - 1) + (2**n - 1) * prime) / 2**n + // == (2**n * prime + prime - 1) / 2**n + // == prime + (prime - 1) / 2**n < 2 * prime -// in field G_prime, big and complicated but fast -// the input must not be 0 mod prime. -// the result is smaller than prime -void bn_inverse(bignum256 *x, const bignum256 *prime) { - int i, j, k, cmp; - struct combo { - uint32_t a[9]; - int len1; - } us, vr, *odd, *even; - uint32_t pp[8]; - uint32_t temp32; - uint64_t temp; + // m = (-x / prime) % 2**BITS_PER_LIMB + uint32_t m = (x->val[0] * (BN_BASE - inverse_mod_power_two( + prime->val[0], BN_BITS_PER_LIMB))) & + BN_LIMB_MASK; + // m < 2**BITS_PER_LIMB - // The algorithm is based on Schroeppel et. al. "Almost Modular Inverse" - // algorithm. We keep four values u,v,r,s in the combo registers - // us and vr. us stores u in the first len1 limbs (little endian) - // and s in the last 9-len1 limbs (big endian). vr stores v and r. - // This is because both u*s and v*r are guaranteed to fit in 8 limbs, so - // their components are guaranteed to fit in 9. During the algorithm, - // the length of u and v shrinks while r and s grow. - // u,v,r,s correspond to F,G,B,C in Schroeppel's algorithm. + uint64_t acc = x->val[0] + (uint64_t)m * prime->val[0]; + acc >>= BN_BITS_PER_LIMB; + + for (int i = 1; i < BN_LIMBS; i++) { + acc = acc + x->val[i] + (uint64_t)m * prime->val[i]; + // acc does not overflow 64 bits + // acc == acc + x + m * prime + // <= 2**(64 - BITS_PER_LIMB) + 2**(BITS_PER_LIMB) + // 2**(BITS_PER_LIMB) * 2**(BITS_PER_LIMB) + // <= 2**(2 * BITS_PER_LIMB) + 2**(64 - BITS_PER_LIMB) + + // 2**(BITS_PER_LIMB) + // <= 2**58 + 2**35 + 2**29 < 2**64 + + x->val[i - 1] = acc & BN_LIMB_MASK; + acc >>= BN_BITS_PER_LIMB; + // acc < 2**35 == 2**(64 - BITS_PER_LIMB) + + // acc == x[:i + 1] + m * prime[:i + 1] >> BITS_PER_LIMB * (i + 1) + } + + x->val[BN_LIMBS - 1] = acc; + + assert(acc >> BN_BITS_PER_LIMB == 0); + + // clang-format off + // acc >> BITS_PER_LIMB == 0 + // Proof: + // acc >> BITS_PER_LIMB + // == (x[:LIMB] + m * prime[:LIMB] >> BITS_PER_LIMB * LIMBS) >> BITS_PER_LIMB * (LIMBS + 1) + // == x + m * prime >> BITS_PER_LIMB * (LIMBS + 1) + // <= (2**(BITS_PER_LIMB * LIMBS) - 1) + (2**BITS_PER_LIMB - 1) * (2**(BITS_PER_LIMB * LIMBS) - 1) >> BITS_PER_LIMB * (LIMBS + 1) + // == 2**(BITS_PER_LIMB * LIMBS) - 1 + 2**(BITS_PER_LIMB * (LIMBS + 1)) - 2**(BITS_PER_LIMB * LIMBS) - 2**BITS_PER_LIMB + 1 >> BITS_PER_LIMB * (LIMBS + 1) + // == 2**(BITS_PER_LIMB * (LIMBS + 1)) - 2**BITS_PER_LIMB >> BITS_PER_LIMB * (LIMBS + 1) + // == 0 + // clang-format on +} + +// x = 1/x % prime if x != 0 else 0 +// Assumes x is normalized +// Assumes prime is a prime number +// Guarantees x is normalized and fully reduced modulo prime +// Assumes prime is normalized, 2**256 - 2**224 <= prime <= 2**256 +// The function doesn't have neither constant control flow nor constant memory +// access flow with regard to prime +void bn_inverse_slow(bignum256 *x, const bignum256 *prime) { + // Uses formula 1/x % prime == x**(prime - 2) % prime + // See https://en.wikipedia.org/wiki/Fermat%27s_little_theorem + + bn_fast_mod(x, prime); + + // e = prime - 2 + bignum256 e = {0}; + bn_read_uint32(2, &e); + bn_subtract(prime, &e, &e); + + bn_power_mod(x, &e, prime, x); + bn_mod(x, prime); + + memzero(&e, sizeof(e)); +} + +#if false +// x = 1/x % prime if x != 0 else 0 +// Assumes x is is_normalized +// Assumes GCD(x, prime) = 1 +// Guarantees x is normalized and fully reduced modulo prime +// Assumes prime is odd, normalized, 2**256 - 2**224 <= prime <= 2**256 +// The function doesn't have neither constant control flow nor constant memory +// access flow with regard to prime and x +void bn_inverse_fast(bignum256 *x, const bignum256 *prime) { + // "The Almost Montgomery Inverse" from the section 3 of "Constant Time + // Modular Inversion" by Joppe W. Bos + // See http://www.joppebos.com/files/CTInversion.pdf + + /* + u = prime + v = x & prime + s = 1 + r = 0 + + k = 0 + while v != 1: + k += 1 + if is_even(u): + u = u // 2 + s = 2 * s + elif is_even(v): + v = v // 2 + r = 2 * r + elif v < u: + u = (u - v) // 2 + r = r + s + s = 2 * s + else: + v = (v - u) // 2 + s = r + s + r = 2 * r + + s = (s / 2**k) % prime + return s + */ + + if (bn_is_zero(x)) return; - // reduce x modulo prime. This is necessary as it has to fit in 8 limbs. bn_fast_mod(x, prime); bn_mod(x, prime); - // convert x and prime to 8x32 bit limb form - temp32 = prime->val[0]; - for (i = 0; i < 8; i++) { - temp32 |= prime->val[i + 1] << (30 - 2 * i); - us.a[i] = pp[i] = temp32; - temp32 = prime->val[i + 1] >> (2 + 2 * i); - } - temp32 = x->val[0]; - for (i = 0; i < 8; i++) { - temp32 |= x->val[i + 1] << (30 - 2 * i); - vr.a[i] = temp32; - temp32 = x->val[i + 1] >> (2 + 2 * i); - } - us.len1 = 8; - vr.len1 = 8; - // set s = 1 and r = 0 - us.a[8] = 1; - vr.a[8] = 0; - // set k = 0. - k = 0; - // only one of the numbers u,v can be even at any time. We - // let even point to that number and odd to the other. - // Initially the prime u is guaranteed to be odd. - odd = &us; - even = &vr; + bignum256 u = {0}, v = {0}, r = {0}, s = {0}; + bn_copy(prime, &u); + bn_copy(x, &v); + bn_one(&s); + bn_zero(&r); - // u = prime, v = x - // r = 0 , s = 1 - // k = 0 - for (;;) { - // invariants: - // let u = limbs us.a[0..u.len1-1] in little endian, - // let s = limbs us.a[u.len..8] in big endian, - // let v = limbs vr.a[0..u.len1-1] in little endian, - // let r = limbs vr.a[u.len..8] in big endian, - // r,s >= 0 ; u,v >= 1 - // x*-r = u*2^k mod prime - // x*s = v*2^k mod prime - // u*s + v*r = prime - // floor(log2(u)) + floor(log2(v)) + k <= 510 - // max(u,v) <= 2^k (*) see comment at end of loop - // gcd(u,v) = 1 - // {odd,even} = {&us, &vr} - // odd->a[0] and odd->a[8] are odd - // even->a[0] or even->a[8] is even - // - // first u/v are large and r/s small - // later u/v are small and r/s large - assert(odd->a[0] & 1); - assert(odd->a[8] & 1); - - // adjust length of even. - while (even->a[even->len1 - 1] == 0) { - even->len1--; - // if input was 0, return. - // This simple check prevents crashing with stack underflow - // or worse undesired behaviour for illegal input. - if (even->len1 < 0) return; - } - - // reduce even->a while it is even - while (even->a[0] == 0) { - // shift right first part of even by a limb - // and shift left second part of even by a limb. - for (i = 0; i < 8; i++) { - even->a[i] = even->a[i + 1]; - } - even->a[i] = 0; - even->len1--; - k += 32; - } - // count up to 32 zero bits of even->a. - j = 0; - while ((even->a[0] & (1u << j)) == 0) { - j++; - } - if (j > 0) { - // shift first part of even right by j bits. - for (i = 0; i + 1 < even->len1; i++) { - even->a[i] = (even->a[i] >> j) | (even->a[i + 1] << (32 - j)); - } - even->a[i] = (even->a[i] >> j); - if (even->a[i] == 0) { - even->len1--; - } else { - i++; - } - - // shift second part of even left by j bits. - for (; i < 8; i++) { - even->a[i] = (even->a[i] << j) | (even->a[i + 1] >> (32 - j)); - } - even->a[i] = (even->a[i] << j); - // add j bits to k. - k += j; - } - // invariant is reestablished. - // now both a[0] are odd. - assert(odd->a[0] & 1); - assert(odd->a[8] & 1); - assert(even->a[0] & 1); - assert((even->a[8] & 1) == 0); - - // cmp > 0 if us.a[0..len1-1] > vr.a[0..len1-1], - // cmp = 0 if equal, < 0 if less. - cmp = us.len1 - vr.len1; - if (cmp == 0) { - i = us.len1 - 1; - while (i >= 0 && us.a[i] == vr.a[i]) i--; - // both are equal to 1 and we are done. - if (i == -1) break; - cmp = us.a[i] > vr.a[i] ? 1 : -1; - } - if (cmp > 0) { - even = &us; - odd = &vr; + int k = 0; + while (!bn_is_one(&v)) { + if ((u.val[0] & 1) == 0) { + bn_rshift(&u); + bn_lshift(&s); + } else if ((v.val[0] & 1) == 0) { + bn_rshift(&v); + bn_lshift(&r); + } else if (bn_is_less(&v, &u)) { + bn_subtract(&u, &v, &u); + bn_rshift(&u); + bn_add(&r, &s); + bn_lshift(&s); } else { - even = &vr; - odd = &us; + bn_subtract(&v, &u, &v); + bn_rshift(&v); + bn_add(&s, &r); + bn_lshift(&r); } - - // now even > odd. - - // even->a[0..len1-1] = (even->a[0..len1-1] - odd->a[0..len1-1]); - temp = 1; - for (i = 0; i < odd->len1; i++) { - temp += 0xFFFFFFFFull + even->a[i] - odd->a[i]; - even->a[i] = temp & 0xFFFFFFFF; - temp >>= 32; - } - for (; i < even->len1; i++) { - temp += 0xFFFFFFFFull + even->a[i]; - even->a[i] = temp & 0xFFFFFFFF; - temp >>= 32; - } - // odd->a[len1..8] = (odd->b[len1..8] + even->b[len1..8]); - temp = 0; - for (i = 8; i >= even->len1; i--) { - temp += (uint64_t)odd->a[i] + even->a[i]; - odd->a[i] = temp & 0xFFFFFFFF; - temp >>= 32; - } - for (; i >= odd->len1; i--) { - temp += (uint64_t)odd->a[i]; - odd->a[i] = temp & 0xFFFFFFFF; - temp >>= 32; - } - // note that - // if u > v: - // u'2^k = (u - v) 2^k = x(-r) - xs = x(-(r+s)) = x(-r') mod prime - // u's' + v'r' = (u-v)s + v(r+s) = us + vr - // if u < v: - // v'2^k = (v - u) 2^k = xs - x(-r) = x(s+r) = xs' mod prime - // u's' + v'r' = u(s+r) + (v-u)r = us + vr - - // even->a[0] is difference between two odd numbers, hence even. - // odd->a[8] is sum of even and odd number, hence odd. - assert(odd->a[0] & 1); - assert(odd->a[8] & 1); - assert((even->a[0] & 1) == 0); - - // The invariants are (almost) reestablished. - // The invariant max(u,v) <= 2^k can be invalidated at this point, - // because odd->a[len1..8] was changed. We only have - // - // odd->a[len1..8] <= 2^{k+1} - // - // Since even->a[0] is even, k will be incremented at the beginning - // of the next loop while odd->a[len1..8] remains unchanged. - // So after that, odd->a[len1..8] <= 2^k will hold again. - } - // In the last iteration we had u = v and gcd(u,v) = 1. - // Hence, u=1, v=1, s+r = prime, k <= 510, 2^k > max(s,r) >= prime/2 - // This implies 0 <= s < prime and 255 <= k <= 510. - // - // The invariants also give us x*s = 2^k mod prime, - // hence s = 2^k * x^-1 mod prime. - // We need to compute s/2^k mod prime. - - // First we compute inverse = -prime^-1 mod 2^32, which we need later. - // We use the Explicit Quadratic Modular inverse algorithm. - // http://arxiv.org/pdf/1209.6626.pdf - // a^-1 = (2-a) * PROD_i (1 + (a - 1)^(2^i)) mod 2^32 - // the product will converge quickly, because (a-1)^(2^i) will be - // zero mod 2^32 after at most five iterations. - // We want to compute -prime^-1 so we start with (pp[0]-2). - assert(pp[0] & 1); - uint32_t amone = pp[0] - 1; - uint32_t inverse = pp[0] - 2; - while (amone) { - amone *= amone; - inverse *= (amone + 1); + k += 1; + assert(!bn_is_zero(&v)); // assert GCD(x, prime) == 1 } - while (k >= 32) { - // compute s / 2^32 modulo prime. - // Idea: compute factor, such that - // s + factor*prime mod 2^32 == 0 - // i.e. factor = s * -1/prime mod 2^32. - // Then compute s + factor*prime and shift right by 32 bits. - uint32_t factor = (inverse * us.a[8]) & 0xffffffff; - temp = us.a[8] + (uint64_t)pp[0] * factor; - assert((temp & 0xffffffff) == 0); - temp >>= 32; - for (i = 0; i < 7; i++) { - temp += us.a[8 - (i + 1)] + (uint64_t)pp[i + 1] * factor; - us.a[8 - i] = temp & 0xffffffff; - temp >>= 32; - } - us.a[8 - i] = temp & 0xffffffff; - k -= 32; - } - if (k > 0) { - // compute s / 2^k modulo prime. - // Same idea: compute factor, such that - // s + factor*prime mod 2^k == 0 - // i.e. factor = s * -1/prime mod 2^k. - // Then compute s + factor*prime and shift right by k bits. - uint32_t mask = (1u << k) - 1; - uint32_t factor = (inverse * us.a[8]) & mask; - temp = (us.a[8] + (uint64_t)pp[0] * factor) >> k; - assert(((us.a[8] + pp[0] * factor) & mask) == 0); - for (i = 0; i < 7; i++) { - temp += (us.a[8 - (i + 1)] + (uint64_t)pp[i + 1] * factor) << (32 - k); - us.a[8 - i] = temp & 0xffffffff; - temp >>= 32; - } - us.a[8 - i] = temp & 0xffffffff; + // s = s / 2**(k // BITS_PER_LIMB * BITS_PER_LIMB) + for (int i = 0; i < k / BITS_PER_LIMB; i++) { + bn_divide_base(&s, prime); } - // convert s to bignum style - temp32 = 0; - for (i = 0; i < 8; i++) { - x->val[i] = ((us.a[8 - i] << (2 * i)) & 0x3FFFFFFFu) | temp32; - temp32 = us.a[8 - i] >> (30 - 2 * i); + // s = s / 2**(k % BITS_PER_LIMB) + for (int i = 0; i < k % BN_BITS_PER_LIMB; i++) { + bn_mult_half(&s, prime); } - x->val[i] = temp32; - // let's wipe all temp buffers - memzero(pp, sizeof(pp)); - memzero(&us, sizeof(us)); - memzero(&vr, sizeof(vr)); + bn_copy(&s, x); + + memzero(&u, sizeof(u)); + memzero(&v, sizeof(v)); + memzero(&r, sizeof(r)); + memzero(&s, sizeof(s)); } #endif -void bn_normalize(bignum256 *a) { bn_addi(a, 0); } +// x = 1/x % prime if x != 0 else 0 +// Assumes x is is_normalized +// Assumes GCD(x, prime) = 1 +// Guarantees x is normalized and fully reduced modulo prime +// Assumes prime is odd, normalized, 2**256 - 2**224 <= prime <= 2**256 +// The function has constant control flow but not constant memory access flow +// with regard to prime and x +void bn_inverse_fast(bignum256 *x, const bignum256 *prime) { + // Custom constant time version of "The Almost Montgomery Inverse" from the + // section 3 of "Constant Time Modular Inversion" by Joppe W. Bos + // See http://www.joppebos.com/files/CTInversion.pdf -// add two numbers a = a + b -// assumes that a, b are normalized -// guarantees that a is normalized -void bn_add(bignum256 *a, const bignum256 *b) { - int i; - uint32_t tmp = 0; - for (i = 0; i < 9; i++) { - tmp += a->val[i] + b->val[i]; - a->val[i] = tmp & 0x3FFFFFFF; - tmp >>= 30; + /* + u = prime + v = x % prime + s = 1 + r = 0 + + k = 0 + while v != 1: + k += 1 + if is_even(u): # b1 + u = u // 2 + s = 2 * s + elif is_even(v): # b2 + v = v // 2 + r = 2 * r + elif v < u: # b3 + u = (u - v) // 2 + r = r + s + s = 2 * s + else: # b4 + v = (v - u) // 2 + s = r + s + r = 2 * r + + s = (s / 2**k) % prime + return s + */ + + bn_fast_mod(x, prime); + bn_mod(x, prime); + + bignum256 u = {0}, v = {0}, r = {0}, s = {0}; + bn_copy(prime, &u); + bn_copy(x, &v); + bn_one(&s); + bn_zero(&r); + + bignum256 zero = {0}; + bn_zero(&zero); + + int k = 0; + + int finished = 0, u_even = 0, v_even = 0, v_less_u = 0, b1 = 0, b2 = 0, + b3 = 0, b4 = 0; + finished = 0; + + for (int i = 0; i < 2 * BN_LIMBS * BN_BITS_PER_LIMB; i++) { + finished = finished | -bn_is_one(&v); + u_even = -bn_is_even(&u); + v_even = -bn_is_even(&v); + v_less_u = -bn_is_less(&v, &u); + + b1 = ~finished & u_even; + b2 = ~finished & ~b1 & v_even; + b3 = ~finished & ~b1 & ~b2 & v_less_u; + b4 = ~finished & ~b1 & ~b2 & ~b3; + +// The ternary operator for pointers with constant control flow +// BN_INVERSE_FAST_TERNARY(c, t, f) = t if c else f +// Very nasty hack, sorry for that +#define BN_INVERSE_FAST_TERNARY(c, t, f) \ + ((void *)(((c) & (uintptr_t)(t)) | (~(c) & (uintptr_t)(f)))) + + bn_subtract(BN_INVERSE_FAST_TERNARY(b3, &u, &v), + BN_INVERSE_FAST_TERNARY( + b3 | b4, BN_INVERSE_FAST_TERNARY(b3, &v, &u), &zero), + BN_INVERSE_FAST_TERNARY(b3, &u, &v)); + + bn_add(BN_INVERSE_FAST_TERNARY(b3, &r, &s), + BN_INVERSE_FAST_TERNARY(b3 | b4, BN_INVERSE_FAST_TERNARY(b3, &s, &r), + &zero)); + bn_rshift(BN_INVERSE_FAST_TERNARY(b1 | b3, &u, &v)); + bn_lshift(BN_INVERSE_FAST_TERNARY(b1 | b3, &s, &r)); + + k = k - ~finished; + } + + // s = s / 2**(k // BITS_PER_LIMB * BITS_PER_LIMB) + for (int i = 0; i < 2 * BN_LIMBS; i++) { + // s = s / 2**BITS_PER_LIMB % prime if i < k // BITS_PER_LIMB else s + bn_copy(&s, &r); + bn_divide_base(&r, prime); + bn_cmov(&s, i < k / BN_BITS_PER_LIMB, &r, &s); + } + + // s = s / 2**(k % BITS_PER_LIMB) + for (int i = 0; i < BN_BITS_PER_LIMB; i++) { + // s = s / 2 % prime if i < k % BITS_PER_LIMB else s + bn_copy(&s, &r); + bn_mult_half(&r, prime); + bn_cmov(&s, i < k % BN_BITS_PER_LIMB, &r, &s); + } + + bn_cmov(x, bn_is_zero(x), x, &s); + + memzero(&u, sizeof(u)); + memzero(&v, sizeof(v)); + memzero(&r, sizeof(s)); + memzero(&s, sizeof(s)); +} + +#if false +// x = 1/x % prime if x != 0 else 0 +// Assumes x is is_normalized +// Assumes GCD(x, prime) = 1 +// Guarantees x is normalized and fully reduced modulo prime +// Assumes prime is odd, normalized, 2**256 - 2**224 <= prime <= 2**256 +void bn_inverse_fast(bignum256 *x, const bignum256 *prime) { + // Custom constant time version of "The Almost Montgomery Inverse" from the + // section 3 of "Constant Time Modular Inversion" by Joppe W. Bos + // See http://www.joppebos.com/files/CTInversion.pdf + + /* + u = prime + v = x % prime + s = 1 + r = 0 + + k = 0 + while v != 1: + k += 1 + if is_even(u): # b1 + u = u // 2 + s = 2 * s + elif is_even(v): # b2 + v = v // 2 + r = 2 * r + elif v < u: # b3 + u = (u - v) // 2 + r = r + s + s = 2 * s + else: # b4 + v = (v - u) // 2 + s = r + s + r = 2 * r + + s = (s / 2**k) % prime + return s + */ + + bn_fast_mod(x, prime); + bn_mod(x, prime); + + bignum256 u = {0}, v = {0}, r = {0}, s = {0}; + bn_copy(prime, &u); + bn_copy(x, &v); + bn_one(&s); + bn_zero(&r); + + bignum256 zero = {0}; + bn_zero(&zero); + + int k = 0; + + uint32_t finished = 0, u_even = 0, v_even = 0, v_less_u = 0, b1 = 0, b2 = 0, + b3 = 0, b4 = 0; + finished = 0; + + bignum256 u_half = {0}, v_half = {0}, u_minus_v_half = {0}, v_minus_u_half = {0}, r_plus_s = {0}, r_twice = {0}, s_twice = {0}; + for (int i = 0; i < 2 * BN_LIMBS * BN_BITS_PER_LIMB; i++) { + finished = finished | bn_is_one(&v); + u_even = bn_is_even(&u); + v_even = bn_is_even(&v); + v_less_u = bn_is_less(&v, &u); + + b1 = (finished ^ 1) & u_even; + b2 = (finished ^ 1) & (b1 ^ 1) & v_even; + b3 = (finished ^ 1) & (b1 ^ 1) & (b2 ^ 1) & v_less_u; + b4 = (finished ^ 1) & (b1 ^ 1) & (b2 ^ 1) & (b3 ^ 1); + + // u_half = u // 2 + bn_copy(&u, &u_half); + bn_rshift(&u_half); + + // v_half = v // 2 + bn_copy(&v, &v_half); + bn_rshift(&v_half); + + // u_minus_v_half = (u - v) // 2 + bn_subtract(&u, &v, &u_minus_v_half); + bn_rshift(&u_minus_v_half); + + // v_minus_u_half = (v - u) // 2 + bn_subtract(&v, &u, &v_minus_u_half); + bn_rshift(&v_minus_u_half); + + // r_plus_s = r + s + bn_copy(&r, &r_plus_s); + bn_add(&r_plus_s, &s); + + // r_twice = 2 * r + bn_copy(&r, &r_twice); + bn_lshift(&r_twice); + + // s_twice = 2 * s + bn_copy(&s, &s_twice); + bn_lshift(&s_twice); + + bn_cmov(&u, b1, &u_half, &u); + bn_cmov(&u, b3, &u_minus_v_half, &u); + + bn_cmov(&v, b2, &v_half, &v); + bn_cmov(&v, b4, &v_minus_u_half, &v); + + bn_cmov(&r, b2 | b4, &r_twice, &r); + bn_cmov(&r, b3, &r_plus_s, &r); + + bn_cmov(&s, b1 | b3, &s_twice, &s); + bn_cmov(&s, b4, &r_plus_s, &s); + + k = k + (finished ^ 1); + } + + // s = s / 2**(k // BITS_PER_LIMB * BITS_PER_LIMB) + for (int i = 0; i < 2 * BN_LIMBS; i++) { + // s = s / 2**BITS_PER_LIMB % prime if i < k // BITS_PER_LIMB else s + bn_copy(&s, &r); + bn_divide_base(&r, prime); + bn_cmov(&s, i < k / BITS_PER_LIMB, &r, &s); + } + + // s = s / 2**(k % BITS_PER_LIMB) + for (int i = 0; i < BN_BITS_PER_LIMB; i++) { + // s = s / 2 % prime if i < k % BITS_PER_LIMB else s + bn_copy(&s, &r); + bn_mult_half(&r, prime); + bn_cmov(&s, i < k % BN_BITS_PER_LIMB, &r, &s); + } + + bn_cmov(x, bn_is_zero(x), x, &s); + + memzero(&u, sizeof(u)); + memzero(&v, sizeof(v)); + memzero(&r, sizeof(r)); + memzero(&s, sizeof(s)); + memzero(&u_half, sizeof(u_half)); + memzero(&v_half, sizeof(v_half)); + memzero(&u_minus_v_half, sizeof(u_minus_v_half)); + memzero(&v_minus_u_half, sizeof(v_minus_u_half)); + memzero(&r_twice, sizeof(r_twice)); + memzero(&s_twice, sizeof(s_twice)); + memzero(&r_plus_s, sizeof(r_plus_s)); +} +#endif + +// Normalizes x +// Assumes x < 2**261 == 2**(LIMBS * BITS_PER_LIMB) +// Guarantees x is normalized +void bn_normalize(bignum256 *x) { + uint32_t acc = 0; + + for (int i = 0; i < BN_LIMBS; i++) { + acc += x->val[i]; + // acc doesn't overflow 32 bits + // Proof: + // acc + x[i] + // <= (2**(32 - BITS_PER_LIMB) - 1) + (2**BITS_PER_LIMB - 1) + // == 7 + 2**29 - 1 < 2**32 + + x->val[i] = acc & BN_LIMB_MASK; + acc >>= (BN_BITS_PER_LIMB); + // acc <= 7 == 2**(32 - BITS_PER_LIMB) - 1 } } -void bn_addmod(bignum256 *a, const bignum256 *b, const bignum256 *prime) { - int i; - for (i = 0; i < 9; i++) { - a->val[i] += b->val[i]; +// x = x + y +// Assumes x, y are normalized, x + y < 2**(LIMBS*BITS_PER_LIMB) == 2**261 +// Guarantees x is normalized +// Works properly even if &x == &y +void bn_add(bignum256 *x, const bignum256 *y) { + uint32_t acc = 0; + for (int i = 0; i < BN_LIMBS; i++) { + acc += x->val[i] + y->val[i]; + // acc doesn't overflow 32 bits + // Proof: + // acc + x[i] + y[i] + // <= (2**(32 - BITS_PER_LIMB) - 1) + 2 * (2**BITS_PER_LIMB - 1) + // == (2**(32 - BITS_PER_LIMB) - 1) + 2**(BITS_PER_LIMB + 1) - 2 + // == 7 + 2**30 - 2 < 2**32 + + x->val[i] = acc & BN_LIMB_MASK; + acc >>= BN_BITS_PER_LIMB; + // acc <= 7 == 2**(32 - BITS_PER_LIMB) - 1 + + // acc == x[:i + 1] + y[:i + 1] >> BITS_PER_LIMB * (i + 1) } - bn_fast_mod(a, prime); + + // assert(acc == 0); // assert x + y < 2**261 + // acc == 0 + // Proof: + // acc == x[:LIMBS] + y[:LIMBS] >> LIMBS * BITS_PER_LIMB + // == x + y >> LIMBS * BITS_PER_LIMB + // <= 2**(LIMBS * BITS_PER_LIMB) - 1 >> LIMBS * BITS_PER_LIMB == 0 } -void bn_addi(bignum256 *a, uint32_t b) { - int i; - uint32_t tmp = b; - for (i = 0; i < 9; i++) { - tmp += a->val[i]; - a->val[i] = tmp & 0x3FFFFFFF; - tmp >>= 30; +// x = x + y % prime +// Assumes x, y are normalized +// Guarantees x is normalized and partly reduced modulo prime +// Assumes prime is normalized and 2^256 - 2^224 <= prime <= 2^256 +void bn_addmod(bignum256 *x, const bignum256 *y, const bignum256 *prime) { + for (int i = 0; i < BN_LIMBS; i++) { + x->val[i] += y->val[i]; + // x[i] doesn't overflow 32 bits + // Proof: + // x[i] + y[i] + // <= 2 * (2**BITS_PER_LIMB - 1) + // == 2**30 - 2 < 2**32 } + + bn_fast_mod(x, prime); } -void bn_subi(bignum256 *a, uint32_t b, const bignum256 *prime) { - assert(b <= prime->val[0]); - // the possible underflow will be taken care of when adding the prime - a->val[0] -= b; - bn_add(a, prime); +// x = x + y +// Assumes x is normalized +// Assumes y <= 2**32 - 2**29 == 2**32 - 2**BITS_PER_LIMB and +// x + y < 2**261 == 2**(LIMBS * BITS_PER_LIMB) +// Guarantees x is normalized +void bn_addi(bignum256 *x, uint32_t y) { + // assert(y <= 3758096384); // assert y <= 2**32 - 2**29 + uint32_t acc = y; + + for (int i = 0; i < BN_LIMBS; i++) { + acc += x->val[i]; + // acc doesn't overflow 32 bits + // Proof: + // if i == 0: + // acc + x[i] == y + x[0] + // <= (2**32 - 2**BITS_PER_LIMB) + (2**BITS_PER_LIMB - 1) + // == 2**32 - 1 < 2**32 + // else: + // acc + x[i] + // <= (2**(32 - BITS_PER_LIMB) - 1) + (2**BITS_PER_LIMB - 1) + // == 7 + 2**29 - 1 < 2**32 + + x->val[i] = acc & BN_LIMB_MASK; + acc >>= (BN_BITS_PER_LIMB); + // acc <= 7 == 2**(32 - BITS_PER_LIMB) - 1 + + // acc == x[:i + 1] + y >> BITS_PER_LIMB * (i + 1) + } + + // assert(acc == 0); // assert x + y < 2**261 + // acc == 0 + // Proof: + // acc == x[:LIMBS] + y << LIMBS * BITS_PER_LIMB + // == x + y << LIMBS * BITS_PER_LIMB + // <= 2**(LIMBS + BITS_PER_LIMB) - 1 << LIMBS * BITS_PER_LIMB + // == 0 } -// res = a - b mod prime. More exactly res = a + (2*prime - b). -// b must be a partly reduced number -// result is normalized but not reduced. -void bn_subtractmod(const bignum256 *a, const bignum256 *b, bignum256 *res, +// x = x - y % prime +// Explicitly x = x + prime - y +// Assumes x, y are normalized +// Assumes y < prime[0], x + prime - y < 2**261 == 2**(LIMBS * BITS_PER_LIMB) +// Guarantees x is normalized +// If x is fully reduced modulo prime, +// guarantess x will be partly reduced modulo prime +// Assumes prime is nonzero and normalized +void bn_subi(bignum256 *x, uint32_t y, const bignum256 *prime) { + assert(y < prime->val[0]); + + // x = x + prime - y + + uint32_t acc = -y; + for (int i = 0; i < BN_LIMBS; i++) { + acc += x->val[i] + prime->val[i]; + // acc neither overflows 32 bits nor underflows 0 + // Proof: + // acc + x[i] + prime[i] + // <= (2**(32 - BITS_PER_LIMB) - 1) + 2 * (2**BITS_PER_LIMB - 1) + // <= 7 + 2**30 - 2 < 2**32 + // acc + x[i] + prime[i] + // >= -y + prime[0] >= 0 + + x->val[i] = acc & BN_LIMB_MASK; + acc >>= BN_BITS_PER_LIMB; + // acc <= 7 == 2**(32 - BITS_PER_LIMB) - 1 + + // acc == x[:i + 1] + prime[:i + 1] - y >> BITS_PER_LIMB * (i + 1) + } + + // assert(acc == 0); // assert x + prime - y < 2**261 + // acc == 0 + // Proof: + // acc == x[:LIMBS] + prime[:LIMBS] - y >> BITS_PER_LIMB * LIMBS + // == x + prime - y >> BITS_PER_LIMB * LIMBS + // <= 2**(LIMBS * BITS_PER_LIMB) - 1 >> BITS_PER_LIMB * LIMBS == 0 +} + +// res = x - y % prime +// Explicitly res = x + (2 * prime - y) +// Assumes x, y are normalized, y is partly reduced +// Assumes x + 2 * prime - y < 2**261 == 2**(BITS_PER_LIMB * LIMBS) +// Guarantees res is normalized +// Assumes prime is nonzero and normalized +void bn_subtractmod(const bignum256 *x, const bignum256 *y, bignum256 *res, const bignum256 *prime) { - int i; - uint32_t temp = 1; - for (i = 0; i < 9; i++) { - temp += 0x3FFFFFFF + a->val[i] + 2u * prime->val[i] - b->val[i]; - res->val[i] = temp & 0x3FFFFFFF; - temp >>= 30; + // res = x + (2 * prime - y) + + uint32_t acc = 1; + + for (int i = 0; i < BN_LIMBS; i++) { + acc += (BN_BASE - 1) + x->val[i] + 2 * prime->val[i] - y->val[i]; + // acc neither overflows 32 bits nor underflows 0 + // Proof: + // acc + (BASE - 1) + x[i] + 2 * prime[i] - y[i] + // >= (BASE - 1) - y[i] + // == (2**BITS_PER_LIMB - 1) - (2**BITS_PER_LIMB - 1) == 0 + // acc + (BASE - 1) + x[i] + 2 * prime[i] - y[i] + // <= acc + (BASE - 1) + x[i] + 2 * prime[i] + // <= (2**(32 - BITS_PER_LIMB) - 1) + (2**BITS_PER_LIMB - 1) + + // (2**BITS_PER_LIMB - 1) + 2 * (2**BITS_PER_LIMB - 1) + // <= (2**(32 - BITS_PER_LIMB) - 1) + 4 * (2**BITS_PER_LIMB - 1) + // == 7 + 4 * 2**29 - 4 == 2**31 + 3 < 2**32 + + res->val[i] = acc & (BN_BASE - 1); + acc >>= BN_BITS_PER_LIMB; + // acc <= 7 == 2**(32 - BITS_PER_LIMB) - 1 + + // acc == 2**(BITS_PER_LIMB * (i + 1)) + x[:i+1] - y[:i+1] + 2*prime[:i+1] + // >> BITS_PER_LIMB * (i+1) + } + + // assert(acc == 1); // assert x + 2 * prime - y < 2**261 + + // clang-format off + // acc == 1 + // Proof: + // acc == 2**(BITS_PER_LIMB * LIMBS) + x[:LIMBS] - y[:LIMBS] + 2 * prime[:LIMBS] >> BITS_PER_LIMB * LIMBS + // == 2**(BITS_PER_LIMB * LIMBS) + x - y + 2 * prime >> BITS_PER_LIMB * LIMBS + // == 2**(BITS_PER_LIMB * LIMBS) + x + (2 * prime - y) >> BITS_PER_LIMB * LIMBS + // <= 2**(BITS_PER_LIMB * LIMBS) + 2**(BITS_PER_LIMB * LIMBS) - 1 >> BITS_PER_LIMB * LIMBS + // <= 2 * 2**(BITS_PER_LIMB * LIMBS) - 1 >> BITS_PER_LIMB * LIMBS + // == 1 + + // acc == 2**(BITS_PER_LIMB * LIMBS) + x[:LIMBS] - y[:LIMBS] + 2 * prime[:LIMBS] >> BITS_PER_LIMB * LIMBS + // == 2**(BITS_PER_LIMB * LIMBS) + x - y + 2 * prime >> BITS_PER_LIMB * LIMBS + // == 2**(BITS_PER_LIMB * LIMBS) + x + (2 * prime - y) >> BITS_PER_LIMB * LIMBS + // >= 2**(BITS_PER_LIMB * LIMBS) + 0 + 1 >> BITS_PER_LIMB * LIMBS + // == 1 + // clang-format on +} + +// res = x - y +// Assumes x, y are normalized and x >= y +// Guarantees res is normalized +// Works properly even if &x == &y or &x == &res or &y == &res or +// &x == &y == &res +void bn_subtract(const bignum256 *x, const bignum256 *y, bignum256 *res) { + uint32_t acc = 1; + for (int i = 0; i < BN_LIMBS; i++) { + acc += (BN_BASE - 1) + x->val[i] - y->val[i]; + // acc neither overflows 32 bits nor underflows 0 + // Proof: + // acc + (BASE - 1) + x[i] - y[i] + // >= (BASE - 1) - y == (2**BITS_PER_LIMB - 1) - (2**BITS_PER_LIMB - 1) + // == 0 + // acc + (BASE - 1) + x[i] - y[i] + // <= acc + (BASE - 1) + x[i] + // <= (2**(32 - BITS_PER_LIMB) - 1) + (2**BITS_PER_LIMB - 1) + + // (2**BITS_PER_LIMB - 1) + // == 7 + 2 * 2**29 < 2 **32 + + res->val[i] = acc & BN_LIMB_MASK; + acc >>= BN_BITS_PER_LIMB; + // acc <= 7 == 2**(32 - BITS_PER_LIMB) - 1 + + // acc == 2**(BITS_PER_LIMB * (i + 1)) + x[:i + 1] - y[:i + 1] + // >> BITS_PER_LIMB * (i + 1) + } + + // assert(acc == 1); // assert x >= y + + // clang-format off + // acc == 1 + // Proof: + // acc == 2**(BITS_PER_LIMB * LIMBS) + x[:LIMBS] - y[:LIMBS] >> BITS_PER_LIMB * LIMBS + // == 2**(BITS_PER_LIMB * LIMBS) + x - y >> BITS_PER_LIMB * LIMBS + // == 2**(BITS_PER_LIMB * LIMBS) + x >> BITS_PER_LIMB * LIMBS + // <= 2**(BITS_PER_LIMB * LIMBS) + 2**(BITS_PER_LIMB * LIMBS) - 1 >> BITS_PER_LIMB * LIMBS + // <= 2 * 2**(BITS_PER_LIMB * LIMBS) - 1 >> BITS_PER_LIMB * LIMBS + // == 1 + + // acc == 2**(BITS_PER_LIMB * LIMBS) + x[:LIMBS] - y[:LIMBS] >> BITS_PER_LIMB * LIMBS + // == 2**(BITS_PER_LIMB * LIMBS) + x - y >> BITS_PER_LIMB * LIMBS + // >= 2**(BITS_PER_LIMB * LIMBS) >> BITS_PER_LIMB * LIMBS + // == 1 +} + +// q = x // d, r = x % d +// Assumes x is normalized, 1 <= d <= 61304 +// Guarantees q is normalized +void bn_long_division(bignum256 *x, uint32_t d, bignum256 *q, uint32_t *r) { + assert(1 <= d && d < 61304); + + uint32_t acc = 0; + + *r = x->val[BN_LIMBS - 1] % d; + q->val[BN_LIMBS - 1] = x->val[BN_LIMBS - 1] / d; + + for (int i = BN_LIMBS - 2; i >= 0; i--) { + acc = *r * (BN_BASE % d) + x->val[i]; + // acc doesn't overflow 32 bits + // Proof: + // r * (BASE % d) + x[i] + // <= (d - 1) * (d - 1) + (2**BITS_PER_LIMB - 1) + // == d**2 - 2*d + 2**BITS_PER_LIMB + // == 61304**2 - 2 * 61304 + 2**29 + // == 3758057808 + 2**29 < 2**32 + + q->val[i] = *r * (BN_BASE / d) + (acc / d); + // q[i] doesn't overflow 32 bits + // Proof: + // r * (BASE // d) + (acc // d) + // <= (d - 1) * (2**BITS_PER_LIMB / d) + + // ((d**2 - 2*d + 2**BITS_PER_LIMB) / d) + // <= (d - 1) * (2**BITS_PER_LIMB / d) + (d - 2 + 2**BITS_PER_LIMB / d) + // == (d - 1 + 1) * (2**BITS_PER_LIMB / d) + d - 2 + // == 2**BITS_PER_LIMB + d - 2 <= 2**29 + 61304 < 2**32 + + // q[i] == (r * BASE + x[i]) // d + // Proof: + // q[i] == r * (BASE // d) + (acc // d) + // == r * (BASE // d) + (r * (BASE % d) + x[i]) // d + // == (r * d * (BASE // d) + r * (BASE % d) + x[i]) // d + // == (r * (d * (BASE // d) + (BASE % d)) + x[i]) // d + // == (r * BASE + x[i]) // d + + // q[i] < 2**BITS_PER_LIMB + // Proof: + // q[i] == (r * BASE + x[i]) // d + // <= ((d - 1) * 2**BITS_PER_LIMB + (2**BITS_PER_LIMB - 1)) / d + // == (d * 2**BITS_PER_LIMB - 1) / d == 2**BITS_PER_LIMB - 1 / d + // < 2**BITS_PER_LIMB + + *r = acc % d; + // r == (r * BASE + x[i]) % d + // Proof: + // r == acc % d == (r * (BASE % d) + x[i]) % d + // == (r * BASE + x[i]) % d + + // x[:i] == q[:i] * d + r } } -// res = a - b ; a > b -void bn_subtract(const bignum256 *a, const bignum256 *b, bignum256 *res) { - int i; - uint32_t tmp = 1; - for (i = 0; i < 9; i++) { - tmp += 0x3FFFFFFF + a->val[i] - b->val[i]; - res->val[i] = tmp & 0x3FFFFFFF; - tmp >>= 30; - } +// x = x // 58, r = x % 58 +// Assumes x is normalized +// Guarantees x is normalized +void bn_divmod58(bignum256 *x, uint32_t *r) { bn_long_division(x, 58, x, r); } + +// x = x // 1000, r = x % 1000 +// Assumes x is normalized +// Guarantees x is normalized +void bn_divmod1000(bignum256 *x, uint32_t *r) { + bn_long_division(x, 1000, x, r); } -// a / 58 = a (+r) -void bn_divmod58(bignum256 *a, uint32_t *r) { - int i; - uint32_t rem, tmp; - rem = a->val[8] % 58; - a->val[8] /= 58; - for (i = 7; i >= 0; i--) { - // invariants: - // rem = old(a) >> 30(i+1) % 58 - // a[i+1..8] = old(a[i+1..8])/58 - // a[0..i] = old(a[0..i]) - // 2^30 == 18512790*58 + 4 - tmp = rem * 4 + a->val[i]; - // set a[i] = (rem * 2^30 + a[i])/58 - // = rem * 18512790 + (rem * 4 + a[i])/58 - a->val[i] = rem * 18512790 + (tmp / 58); - // set rem = (rem * 2^30 + a[i]) mod 58 - // = (rem * 4 + a[i]) mod 58 - rem = tmp % 58; - } - *r = rem; -} +// x = x // 10, r = x % 10 +// Assumes x is normalized +// Guarantees x is normalized +void bn_divmod10(bignum256 *x, uint32_t *r) { bn_long_division(x, 10, x, r); } -// a / 1000 = a (+r) -void bn_divmod1000(bignum256 *a, uint32_t *r) { - int i; - uint32_t rem, tmp; - rem = a->val[8] % 1000; - a->val[8] /= 1000; - for (i = 7; i >= 0; i--) { - // invariants: - // rem = old(a) >> 30(i+1) % 1000 - // a[i+1..8] = old(a[i+1..8])/1000 - // a[0..i] = old(a[0..i]) - // 2^30 == 1073741*1000 + 824 - tmp = rem * 824 + a->val[i]; - // set a[i] = (rem * 2^30 + a[i])/1000 - // = rem * 1073741 + (rem * 824 + a[i])/1000 - a->val[i] = rem * 1073741 + (tmp / 1000); - // set rem = (rem * 2^30 + a[i]) mod 1000 - // = (rem * 824 + a[i]) mod 1000 - rem = tmp % 1000; - } - *r = rem; -} +// Formats amount +// Assumes amount is normalized +// Assumes prefix and suffix are null-terminated strings +// Assumes output is an array of length output_length +// The function doesn't have neither constant control flow nor constant memory +// access flow with regard to any its argument +size_t bn_format(const bignum256 *amount, const char *prefix, const char *suffix, unsigned int decimals, int exponent, bool trailing, char *output, size_t output_length) { -size_t bn_format(const bignum256 *amnt, const char *prefix, const char *suffix, - unsigned int decimals, int exponent, bool trailing, char *out, - size_t outlen) { - // sanity check, 2**256 ~ 10**77; we should never need decimals/exponent - // bigger than that - if (decimals > 80 || exponent < -20 || exponent > 80) { - memzero(out, outlen); - return 0; +/* + Python prototype of the function: + + def format(amount, prefix, suffix, decimals, exponent, trailing): + if exponent >= 0: + amount *= 10 ** exponent + else: + amount //= 10 ** (-exponent) + + d = pow(10, decimals) + + if decimals: + output = "%d.%0*d" % (amount // d, decimals, amount % d) + if not trailing: + output = output.rstrip("0").rstrip(".") + else: + output = "%d" % (amount // d) + + return prefix + output + suffix +*/ + +// Auxiliary macro for bn_format +// If enough space adds one character to output starting from the end +#define BN_FORMAT_ADD_OUTPUT_CHAR(c) \ + { \ + --position; \ + if (output <= position && position < output + output_length) { \ + *position = (c); \ + } else { \ + memset(output, '\0', output_length); \ + return 0; \ + } \ } - size_t prefixlen = prefix ? strlen(prefix) : 0; - size_t suffixlen = suffix ? strlen(suffix) : 0; + bignum256 temp = {0}; + bn_copy(amount, &temp); + uint32_t digit = 0; - /* add prefix to beginning of out buffer */ - if (prefixlen) { - memcpy(out, prefix, prefixlen); - } - /* add suffix to end of out buffer */ - if (suffixlen) { - memcpy(&out[outlen - suffixlen - 1], suffix, suffixlen); - } - /* nul terminate (even if suffix = NULL) */ - out[outlen - 1] = '\0'; + char *position = output + output_length; - /* fill number between prefix and suffix (between start and end) */ - char *start = &out[prefixlen], *end = &out[outlen - suffixlen - 1]; - char *str = end; + // Add string ending character + BN_FORMAT_ADD_OUTPUT_CHAR('\0'); -#define BN_FORMAT_PUSH_CHECKED(c) \ - do { \ - if (str == start) return 0; \ - *--str = (c); \ - } while (0) + // Add suffix + size_t suffix_length = suffix ? strlen(suffix) : 0; + for (int i = suffix_length - 1; i >= 0; --i) + BN_FORMAT_ADD_OUTPUT_CHAR(suffix[i]) -#define BN_FORMAT_PUSH(n) \ - do { \ - if (exponent < 0) { \ - exponent++; \ - } else { \ - if ((n) > 0 || trailing || str != end || decimals <= 1) { \ - BN_FORMAT_PUSH_CHECKED('0' + (n)); \ - } \ - if (decimals > 0 && decimals-- == 1) { \ - BN_FORMAT_PUSH_CHECKED('.'); \ - } \ - } \ - } while (0) - - bignum256 val; - memcpy(&val, amnt, sizeof(bignum256)); - - if (bn_is_zero(&val)) { - exponent = 0; - } - - for (; exponent > 0; exponent--) { - BN_FORMAT_PUSH(0); - } - - unsigned int digits = bn_digitcount(&val); - for (unsigned int i = 0; i < digits / 3; i++) { - uint32_t limb; - bn_divmod1000(&val, &limb); - - BN_FORMAT_PUSH(limb % 10); - limb /= 10; - BN_FORMAT_PUSH(limb % 10); - limb /= 10; - BN_FORMAT_PUSH(limb % 10); - } - - if (digits % 3 != 0) { - uint32_t limb; - bn_divmod1000(&val, &limb); - - switch (digits % 3) { - case 2: - BN_FORMAT_PUSH(limb % 10); - limb /= 10; - //-fallthrough - - case 1: - BN_FORMAT_PUSH(limb % 10); - break; + // amount //= 10**exponent + if (exponent < 0) { + for (; exponent < 0; ++exponent) { + bn_divmod10(&temp, &digit); } } + // exponent >= 0 && decimals >= 0 - while (decimals > 0 || str[0] == '\0' || str[0] == '.') { - BN_FORMAT_PUSH(0); + bool fractional_part = false; // is fractional-part of amount present + + { // Add fractional-part digits of amount + // Add trailing zeroes + for (; exponent > 0 && decimals > 0; --exponent, --decimals) { + if (trailing) { + BN_FORMAT_ADD_OUTPUT_CHAR('0') + fractional_part = true; + } + } + // exponent == 0 || decimals == 0 + + // Add significant digits and leading zeroes + for (; decimals > 0; --decimals) { + bn_divmod10(&temp, &digit); + + if (fractional_part || digit || trailing) { + fractional_part = true; + BN_FORMAT_ADD_OUTPUT_CHAR('0' + digit) + } + } + // decimals == 0 } - /* finally move number to &out[prefixlen] to close the gap between - * prefix and str. len is length of number + suffix + traling 0 - */ - size_t len = &out[outlen] - str; - memmove(&out[prefixlen], str, len); + if (fractional_part) { + BN_FORMAT_ADD_OUTPUT_CHAR('.') + } - /* return length of number including prefix and suffix without trailing 0 */ - return prefixlen + len - 1; + { // Add integer-part digits of amount + // Add trailing zeroes + if (!bn_is_zero(&temp)) { + for (; exponent > 0; --exponent) { + BN_FORMAT_ADD_OUTPUT_CHAR('0') + } + } + // decimals == 0 && exponent == 0 + + // Add significant digits + do { + bn_divmod10(&temp, &digit); + BN_FORMAT_ADD_OUTPUT_CHAR('0' + digit) + } while (!bn_is_zero(&temp)); + } + + // Add prefix + size_t prefix_length = prefix ? strlen(prefix) : 0; + for (int i = prefix_length - 1; i >= 0; --i) + BN_FORMAT_ADD_OUTPUT_CHAR(prefix[i]) + + // Move formatted amount to the start of output + int length = output - position + output_length; + memmove(output, position, length); + return length - 1; } #if USE_BN_PRINT -void bn_print(const bignum256 *a) { - printf("%04x", a->val[8] & 0x0000FFFF); - printf("%08x", (a->val[7] << 2) | ((a->val[6] & 0x30000000) >> 28)); - printf("%07x", a->val[6] & 0x0FFFFFFF); - printf("%08x", (a->val[5] << 2) | ((a->val[4] & 0x30000000) >> 28)); - printf("%07x", a->val[4] & 0x0FFFFFFF); - printf("%08x", (a->val[3] << 2) | ((a->val[2] & 0x30000000) >> 28)); - printf("%07x", a->val[2] & 0x0FFFFFFF); - printf("%08x", (a->val[1] << 2) | ((a->val[0] & 0x30000000) >> 28)); - printf("%07x", a->val[0] & 0x0FFFFFFF); +// Prints x in hexadecimal +// Assumes x is normalized and x < 2**256 +void bn_print(const bignum256 *x) { + printf("%06x", x->val[8]); + printf("%08x", ((x->val[7] << 3) | (x->val[6] >> 26))); + printf("%07x", ((x->val[6] << 2) | (x->val[5] >> 27)) & 0x0FFFFFFF); + printf("%07x", ((x->val[5] << 1) | (x->val[4] >> 28)) & 0x0FFFFFFF); + printf("%07x", x->val[4] & 0x0FFFFFFF); + printf("%08x", ((x->val[3] << 3) | (x->val[2] >> 26))); + printf("%07x", ((x->val[2] << 2) | (x->val[1] >> 27)) & 0x0FFFFFFF); + printf("%07x", ((x->val[1] << 1) | (x->val[0] >> 28)) & 0x0FFFFFFF); + printf("%07x", x->val[0] & 0x0FFFFFFF); } -void bn_print_raw(const bignum256 *a) { - int i; - for (i = 0; i <= 8; i++) { - printf("0x%08x, ", a->val[i]); +// Prints comma separated list of limbs of x +void bn_print_raw(const bignum256 *x) { + for (int i = 0; i < BN_LIMBS - 1; i++) { + printf("0x%08x, ", x->val[i]); } + printf("0x%08x", x->val[BN_LIMBS - 1]); +} +#endif + +#if USE_INVERSE_FAST +void bn_inverse(bignum256 *x, const bignum256 *prime) { + bn_inverse_fast(x, prime); +} +#else +void bn_inverse(bignum256 *x, const bignum256 *prime) { + bn_inverse_slow(x, prime); } #endif diff --git a/crypto/bignum.h b/crypto/bignum.h index e0225be200..00ab0a43d8 100644 --- a/crypto/bignum.h +++ b/crypto/bignum.h @@ -28,141 +28,145 @@ #include #include #include + #include "options.h" -// bignum256 are 256 bits stored as 8*30 bit + 1*16 bit -// val[0] are lowest 30 bits, val[8] highest 16 bits +#define BN_LIMBS 9 +#define BN_BITS_PER_LIMB 29 +#define BN_BASE (1u << BN_BITS_PER_LIMB) +#define BN_LIMB_MASK ((1u << BN_BITS_PER_LIMB) - 1) +#define BN_EXTRA_BITS (32 - BN_BITS_PER_LIMB) +#define BN_BITS_LAST_LIMB (256 - (BN_LIMBS - 1) * BN_BITS_PER_LIMB) + +// Represents the number sum([val[i] * 2**(29*i) for i in range(9)) typedef struct { - uint32_t val[9]; + uint32_t val[BN_LIMBS]; } bignum256; -// read 4 big endian bytes into uint32 -uint32_t read_be(const uint8_t *data); +static inline uint32_t read_be(const uint8_t *data) { + return (((uint32_t)data[0]) << 24) | (((uint32_t)data[1]) << 16) | + (((uint32_t)data[2]) << 8) | (((uint32_t)data[3])); +} -// write 4 big endian bytes -void write_be(uint8_t *data, uint32_t x); +static inline void write_be(uint8_t *data, uint32_t x) { + data[0] = x >> 24; + data[1] = x >> 16; + data[2] = x >> 8; + data[3] = x; +} -// read 4 little endian bytes into uint32 -uint32_t read_le(const uint8_t *data); +static inline uint32_t read_le(const uint8_t *data) { + return (((uint32_t)data[3]) << 24) | (((uint32_t)data[2]) << 16) | + (((uint32_t)data[1]) << 8) | (((uint32_t)data[0])); +} -// write 4 little endian bytes -void write_le(uint8_t *data, uint32_t x); +static inline void write_le(uint8_t *data, uint32_t x) { + data[3] = x >> 24; + data[2] = x >> 16; + data[1] = x >> 8; + data[0] = x; +} void bn_read_be(const uint8_t *in_number, bignum256 *out_number); - void bn_write_be(const bignum256 *in_number, uint8_t *out_number); - void bn_read_le(const uint8_t *in_number, bignum256 *out_number); - void bn_write_le(const bignum256 *in_number, uint8_t *out_number); - void bn_read_uint32(uint32_t in_number, bignum256 *out_number); - void bn_read_uint64(uint64_t in_number, bignum256 *out_number); - -static inline uint32_t bn_write_uint32(const bignum256 *in_number) { - return in_number->val[0] | (in_number->val[1] << 30); -} - -static inline uint64_t bn_write_uint64(const bignum256 *in_number) { - uint64_t tmp; - tmp = in_number->val[2]; - tmp <<= 30; - tmp |= in_number->val[1]; - tmp <<= 30; - tmp |= in_number->val[0]; - return tmp; -} - -// copies number a to b -static inline void bn_copy(const bignum256 *a, bignum256 *b) { *b = *a; } - -int bn_bitcount(const bignum256 *a); - -unsigned int bn_digitcount(const bignum256 *a); - -void bn_zero(bignum256 *a); - -int bn_is_zero(const bignum256 *a); - -void bn_one(bignum256 *a); - -static inline int bn_is_even(const bignum256 *a) { - return (a->val[0] & 1) == 0; -} - -static inline int bn_is_odd(const bignum256 *a) { return (a->val[0] & 1) == 1; } - -int bn_is_less(const bignum256 *a, const bignum256 *b); - -int bn_is_equal(const bignum256 *a, const bignum256 *b); - -void bn_cmov(bignum256 *res, int cond, const bignum256 *truecase, +int bn_bitcount(const bignum256 *x); +unsigned int bn_digitcount(const bignum256 *x); +void bn_zero(bignum256 *x); +void bn_one(bignum256 *x); +int bn_is_zero(const bignum256 *x); +int bn_is_one(const bignum256 *x); +int bn_is_less(const bignum256 *x, const bignum256 *y); +int bn_is_equal(const bignum256 *x, const bignum256 *y); +void bn_cmov(bignum256 *res, volatile uint32_t cond, const bignum256 *truecase, const bignum256 *falsecase); - -void bn_lshift(bignum256 *a); - -void bn_rshift(bignum256 *a); - -void bn_setbit(bignum256 *a, uint8_t bit); - -void bn_clearbit(bignum256 *a, uint8_t bit); - -uint32_t bn_testbit(bignum256 *a, uint8_t bit); - -void bn_xor(bignum256 *a, const bignum256 *b, const bignum256 *c); - +void bn_cnegate(volatile uint32_t cond, bignum256 *x, const bignum256 *prime); +void bn_lshift(bignum256 *x); +void bn_rshift(bignum256 *x); +void bn_setbit(bignum256 *x, uint16_t i); +void bn_clearbit(bignum256 *x, uint16_t i); +uint32_t bn_testbit(const bignum256 *x, uint16_t i); +void bn_xor(bignum256 *res, const bignum256 *x, const bignum256 *y); void bn_mult_half(bignum256 *x, const bignum256 *prime); - void bn_mult_k(bignum256 *x, uint8_t k, const bignum256 *prime); - void bn_mod(bignum256 *x, const bignum256 *prime); - void bn_multiply(const bignum256 *k, bignum256 *x, const bignum256 *prime); - +void bn_fast_mod_old(bignum256 *x, const bignum256 *prime); void bn_fast_mod(bignum256 *x, const bignum256 *prime); - +void bn_power_mod(const bignum256 *x, const bignum256 *e, + const bignum256 *prime, bignum256 *res); void bn_sqrt(bignum256 *x, const bignum256 *prime); - -void bn_inverse(bignum256 *x, const bignum256 *prime); - -void bn_normalize(bignum256 *a); - -void bn_add(bignum256 *a, const bignum256 *b); - -void bn_addmod(bignum256 *a, const bignum256 *b, const bignum256 *prime); - -void bn_addi(bignum256 *a, uint32_t b); - -void bn_subi(bignum256 *a, uint32_t b, const bignum256 *prime); - -void bn_subtractmod(const bignum256 *a, const bignum256 *b, bignum256 *res, +uint32_t inverse_mod_power_two(uint32_t a, uint32_t n); +void bn_divide_base(bignum256 *x, const bignum256 *prime); +void bn_inverse_slow(bignum256 *x, const bignum256 *prime); +void bn_inverse_fast_1(bignum256 *x, const bignum256 *prime); +void bn_inverse_fast_2(bignum256 *x, const bignum256 *prime); +void bn_inverse_fast_3(bignum256 *x, const bignum256 *prime); +void bn_inverse_old(bignum256 *x, const bignum256 *prime); +void bn_normalize(bignum256 *x); +void bn_add(bignum256 *x, const bignum256 *y); +void bn_addmod(bignum256 *x, const bignum256 *y, const bignum256 *prime); +void bn_addi(bignum256 *x, uint32_t y); +void bn_subi(bignum256 *x, uint32_t y, const bignum256 *prime); +void bn_subtractmod(const bignum256 *x, const bignum256 *y, bignum256 *res, const bignum256 *prime); +void bn_subtract(const bignum256 *x, const bignum256 *y, bignum256 *res); +void bn_long_division(bignum256 *x, uint32_t d, bignum256 *q, uint32_t *r); +void bn_divmod58(bignum256 *x, uint32_t *r); +void bn_divmod1000(bignum256 *x, uint32_t *r); +void bn_inverse(bignum256 *x, const bignum256 *prime); +size_t bn_format(const bignum256 *amount, const char *prefix, + const char *suffix, unsigned int decimals, int exponent, + bool trailing, char *output, size_t output_length); -void bn_subtract(const bignum256 *a, const bignum256 *b, bignum256 *res); +// Returns (uint32_t) in_number +// Assumes in_number < 2**32 +// Assumes in_number is normalized +static inline uint32_t bn_write_uint32(const bignum256 *in_number) { + return in_number->val[0] | (in_number->val[1] << BN_BITS_PER_LIMB); +} -void bn_divmod58(bignum256 *a, uint32_t *r); +// Returns (uint64_t) in_number +// Assumes in_number < 2**64 +// Assumes in_number is normalized +static inline uint64_t bn_write_uint64(const bignum256 *in_number) { + uint64_t acc; + acc = in_number->val[2]; + acc <<= BN_BITS_PER_LIMB; + acc |= in_number->val[1]; + acc <<= BN_BITS_PER_LIMB; + acc |= in_number->val[0]; + return acc; +} -void bn_divmod1000(bignum256 *a, uint32_t *r); +// y = x +static inline void bn_copy(const bignum256 *x, bignum256 *y) { *y = *x; } -size_t bn_format(const bignum256 *amnt, const char *prefix, const char *suffix, - unsigned int decimals, int exponent, bool trailing, char *out, - size_t outlen); +// Returns x % 2 == 0 +static inline int bn_is_even(const bignum256 *x) { + return (x->val[0] & 1) == 0; +} + +// Returns x % 2 == 0 +static inline int bn_is_odd(const bignum256 *x) { return (x->val[0] & 1) == 1; } static inline size_t bn_format_uint64(uint64_t amount, const char *prefix, const char *suffix, unsigned int decimals, - int exponent, bool trailing, char *out, - size_t outlen) { - bignum256 amnt; - bn_read_uint64(amount, &amnt); + int exponent, bool trailing, char *output, + size_t output_length) { + bignum256 bn_amount; + bn_read_uint64(amount, &bn_amount); - return bn_format(&amnt, prefix, suffix, decimals, exponent, trailing, out, - outlen); + return bn_format(&bn_amount, prefix, suffix, decimals, exponent, trailing, + output, output_length); } #if USE_BN_PRINT -void bn_print(const bignum256 *a); -void bn_print_raw(const bignum256 *a); +void bn_print(const bignum256 *x); +void bn_print_raw(const bignum256 *x); #endif #endif diff --git a/crypto/ecdsa.c b/crypto/ecdsa.c index cceb58d399..ad0e009336 100644 --- a/crypto/ecdsa.c +++ b/crypto/ecdsa.c @@ -61,6 +61,7 @@ void point_add(const ecdsa_curve *curve, const curve_point *cp1, return; } + // lambda = (y2 - y1) / (x2 - x1) bn_subtractmod(&(cp2->x), &(cp1->x), &inv, &curve->prime); bn_inverse(&inv, &curve->prime); bn_subtractmod(&(cp2->y), &(cp1->y), &lambda, &curve->prime); @@ -101,6 +102,8 @@ void point_double(const ecdsa_curve *curve, curve_point *cp) { // lambda = (3 x^2 + a) / (2 y) lambda = cp->y; bn_mult_k(&lambda, 2, &curve->prime); + bn_fast_mod(&lambda, &curve->prime); + bn_mod(&lambda, &curve->prime); bn_inverse(&lambda, &curve->prime); xr = cp->x; @@ -162,22 +165,6 @@ int point_is_negative_of(const curve_point *p, const curve_point *q) { return !bn_is_equal(&(p->y), &(q->y)); } -// Negate a (modulo prime) if cond is 0xffffffff, keep it if cond is 0. -// The timing of this function does not depend on cond. -void conditional_negate(uint32_t cond, bignum256 *a, const bignum256 *prime) { - int j = 0; - uint32_t tmp = 1; - assert(a->val[8] < 0x20000); - for (j = 0; j < 8; j++) { - tmp += 0x3fffffff + 2 * prime->val[j] - a->val[j]; - a->val[j] = ((tmp & 0x3fffffff) & cond) | (a->val[j] & ~cond); - tmp >>= 30; - } - tmp += 0x3fffffff + 2 * prime->val[j] - a->val[j]; - a->val[j] = ((tmp & 0x3fffffff) & cond) | (a->val[j] & ~cond); - assert(a->val[8] < 0x20000); -} - typedef struct jacobian_curve_point { bignum256 x, y, z; } jacobian_curve_point; @@ -187,9 +174,9 @@ static void generate_k_random(bignum256 *k, const bignum256 *prime) { do { int i = 0; for (i = 0; i < 8; i++) { - k->val[i] = random32() & 0x3FFFFFFF; + k->val[i] = random32() & ((1u << BN_BITS_PER_LIMB) - 1); } - k->val[8] = random32() & 0xFFFF; + k->val[8] = random32() & ((1u << BN_BITS_LAST_LIMB) - 1); // check that k is in range and not zero. } while (bn_is_zero(k) || !bn_is_less(k, prime)); } @@ -443,12 +430,12 @@ void point_multiply(const ecdsa_curve *curve, const bignum256 *k, uint32_t is_non_zero = 0; for (j = 0; j < 8; j++) { is_non_zero |= k->val[j]; - tmp += 0x3fffffff + k->val[j] - (curve->order.val[j] & is_even); - a.val[j] = tmp & 0x3fffffff; - tmp >>= 30; + tmp += (BN_BASE - 1) + k->val[j] - (curve->order.val[j] & is_even); + a.val[j] = tmp & (BN_BASE - 1); + tmp >>= BN_BITS_PER_LIMB; } is_non_zero |= k->val[j]; - a.val[j] = tmp + 0xffff + k->val[j] - (curve->order.val[j] & is_even); + a.val[j] = tmp + 0xffffff + k->val[j] - (curve->order.val[j] & is_even); assert((a.val[0] & 1) != 0); // special case 0*p: just return zero. We don't care about constant time. @@ -490,7 +477,7 @@ void point_multiply(const ecdsa_curve *curve, const bignum256 *k, // since a is odd. aptr = &a.val[8]; abits = *aptr; - ashift = 12; + ashift = 256 - (BN_BITS_PER_LIMB * 8) - 4; bits = abits >> ashift; sign = (bits >> 4) - 1; bits ^= sign; @@ -513,7 +500,7 @@ void point_multiply(const ecdsa_curve *curve, const bignum256 *k, // leaks no private information to a side-channel. bits = abits << (-ashift); abits = *(--aptr); - ashift += 30; + ashift += BN_BITS_PER_LIMB; bits |= abits >> ashift; } else { bits = abits >> ashift; @@ -525,13 +512,13 @@ void point_multiply(const ecdsa_curve *curve, const bignum256 *k, // negate last result to make signs of this round and the // last round equal. - conditional_negate(sign ^ nsign, &jres.z, prime); + bn_cnegate((sign ^ nsign) & 1, &jres.z, prime); // add odd factor point_jacobian_add(&pmult[bits >> 1], &jres, curve); sign = nsign; } - conditional_negate(sign, &jres.z, prime); + bn_cnegate(sign & 1, &jres.z, prime); jacobian_to_curve(&jres, res, prime); memzero(&a, sizeof(a)); memzero(&jres, sizeof(jres)); @@ -560,12 +547,12 @@ void scalar_multiply(const ecdsa_curve *curve, const bignum256 *k, uint32_t is_non_zero = 0; for (j = 0; j < 8; j++) { is_non_zero |= k->val[j]; - tmp += 0x3fffffff + k->val[j] - (curve->order.val[j] & is_even); - a.val[j] = tmp & 0x3fffffff; - tmp >>= 30; + tmp += (BN_BASE - 1) + k->val[j] - (curve->order.val[j] & is_even); + a.val[j] = tmp & (BN_BASE - 1); + tmp >>= BN_BITS_PER_LIMB; } is_non_zero |= k->val[j]; - a.val[j] = tmp + 0xffff + k->val[j] - (curve->order.val[j] & is_even); + a.val[j] = tmp + 0xffffff + k->val[j] - (curve->order.val[j] & is_even); assert((a.val[0] & 1) != 0); // special case 0*G: just return zero. We don't care about constant time. @@ -603,7 +590,8 @@ void scalar_multiply(const ecdsa_curve *curve, const bignum256 *k, // shift a by 4 places. for (j = 0; j < 8; j++) { - a.val[j] = (a.val[j] >> 4) | ((a.val[j + 1] & 0xf) << 26); + a.val[j] = + (a.val[j] >> 4) | ((a.val[j + 1] & 0xf) << (BN_BITS_PER_LIMB - 4)); } a.val[j] >>= 4; // a = old(a)>>(4*i) @@ -614,12 +602,12 @@ void scalar_multiply(const ecdsa_curve *curve, const bignum256 *k, lowbits &= 15; // negate last result to make signs of this round and the // last round equal. - conditional_negate((lowbits & 1) - 1, &jres.y, prime); + bn_cnegate(~lowbits & 1, &jres.y, prime); // add odd factor point_jacobian_add(&curve->cp[i][lowbits >> 1], &jres, curve); } - conditional_negate(((a.val[0] >> 4) & 1) - 1, &jres.y, prime); + bn_cnegate(~(a.val[0] >> 4) & 1, &jres.y, prime); jacobian_to_curve(&jres, res, prime); memzero(&a, sizeof(a)); memzero(&jres, sizeof(jres)); diff --git a/crypto/nist256p1.c b/crypto/nist256p1.c index e7e9f3a691..1082d334ca 100644 --- a/crypto/nist256p1.c +++ b/crypto/nist256p1.c @@ -24,30 +24,31 @@ #include "nist256p1.h" const ecdsa_curve nist256p1 = { - /* .prime */ {/*.val =*/{0x3fffffff, 0x3fffffff, 0x3fffffff, 0x3f, 0x0, 0x0, - 0x1000, 0x3fffc000, 0xffff}}, + /* .prime */ {/*.val =*/{0x1fffffff, 0x1fffffff, 0x1fffffff, 0x000001ff, + 0x00000000, 0x00000000, 0x00040000, 0x1fe00000, + 0xffffff}}, /* G */ - {/*.x =*/{/*.val =*/{0x1898c296, 0x1284e517, 0x1eb33a0f, 0xdf604b, - 0x2440f277, 0x339b958e, 0x4247f8b, 0x347cb84b, - 0x6b17}}, - /*.y =*/{/*.val =*/{0x37bf51f5, 0x2ed901a0, 0x3315ecec, 0x338cd5da, - 0xf9e162b, 0x1fad29f0, 0x27f9b8ee, 0x10b8bf86, - 0x4fe3}}}, + {/*.x =*/{/*.val =*/{0x1898c296, 0x0509ca2e, 0x1acce83d, 0x06fb025b, + 0x040f2770, 0x1372b1d2, 0x091fe2f3, 0x1e5c2588, + 0x6b17d1}}, + /*.y =*/{/*.val =*/{0x17bf51f5, 0x1db20341, 0x0c57b3b2, 0x1c66aed6, + 0x19e162bc, 0x15a53e07, 0x1e6e3b9f, 0x1c5fc34f, + 0x4fe342}}}, /* order */ - {/*.val =*/{0x3c632551, 0xee72b0b, 0x3179e84f, 0x39beab69, 0x3fffffbc, - 0x3fffffff, 0xfff, 0x3fffc000, 0xffff}}, + {/*.val =*/{0x1c632551, 0x1dce5617, 0x05e7a13c, 0x0df55b4e, 0x1ffffbce, + 0x1fffffff, 0x0003ffff, 0x1fe00000, 0xffffff}}, /* order_half */ - {/*.val =*/{0x3e3192a8, 0x27739585, 0x38bcf427, 0x1cdf55b4, 0x3fffffde, - 0x3fffffff, 0x7ff, 0x3fffe000, 0x7fff}}, + {/*.val =*/{0x1e3192a8, 0x0ee72b0b, 0x02f3d09e, 0x06faada7, 0x1ffffde7, + 0x1fffffff, 0x0001ffff, 0x1ff00000, 0x7fffff}}, /* a */ -3, /* b */ - {/*.val =*/{0x27d2604b, 0x2f38f0f8, 0x53b0f63, 0x741ac33, 0x1886bc65, - 0x2ef555da, 0x293e7b3e, 0xd762a8e, 0x5ac6}} + {/*.val =*/{0x07d2604b, 0x1e71e1f1, 0x14ec3d8e, 0x1a0d6198, 0x086bc651, + 0x1eaabb4c, 0x0f9ecfae, 0x1b154752, 0x005ac635}} #if USE_PRECOMPUTED_CP , diff --git a/crypto/nist256p1.table b/crypto/nist256p1.table index c4fc224753..6be01b4d62 100644 --- a/crypto/nist256p1.table +++ b/crypto/nist256p1.table @@ -1,1664 +1,1664 @@ { /* 1*16^0*G: */ - {{{0x1898c296, 0x1284e517, 0x1eb33a0f, 0x00df604b, 0x2440f277, 0x339b958e, 0x04247f8b, 0x347cb84b, 0x6b17}}, - {{0x37bf51f5, 0x2ed901a0, 0x3315ecec, 0x338cd5da, 0x0f9e162b, 0x1fad29f0, 0x27f9b8ee, 0x10b8bf86, 0x4fe3}}}, + {{{0x1898c296, 0x0509ca2e, 0x1acce83d, 0x06fb025b, 0x040f2770, 0x1372b1d2, 0x091fe2f3, 0x1e5c2588, 0x6b17d1}}, + {{0x17bf51f5, 0x1db20341, 0x0c57b3b2, 0x1c66aed6, 0x19e162bc, 0x15a53e07, 0x1e6e3b9f, 0x1c5fc34f, 0x4fe342}}}, /* 3*16^0*G: */ - {{{0x06e7fd6c, 0x2d05986f, 0x3ada985f, 0x31adc87b, 0x0bf165e6, 0x1fbe5475, 0x30a44c8f, 0x3934698c, 0x5ecb}}, - {{0x227d5032, 0x29e6c49e, 0x04fb83d9, 0x0aac0d8e, 0x24a2ecd8, 0x2c1b3869, 0x0ff7e374, 0x19031266, 0x8734}}}, + {{{0x06e7fd6c, 0x1a0b30de, 0x0b6a617e, 0x0d6e43df, 0x1f165e6c, 0x17ca8ea5, 0x091323df, 0x1a34c661, 0x5ecbe4}}, + {{0x027d5032, 0x13cd893d, 0x13ee0f66, 0x15606c70, 0x0a2ecd82, 0x03670d32, 0x1df8dd2c, 0x0189331f, 0x873464}}}, /* 5*16^0*G: */ - {{{0x03d033ed, 0x05552837, 0x35be5242, 0x2320bf47, 0x268fdfef, 0x13215821, 0x140d2d78, 0x02de9454, 0x5159}}, - {{0x3da16da4, 0x0742ed13, 0x0d80888d, 0x004bc035, 0x0a79260d, 0x06fcdafe, 0x2727d8ae, 0x1f6a2412, 0xe0c1}}}, + {{{0x03d033ed, 0x0aaa506e, 0x16f94908, 0x1905fa3e, 0x08fdfef8, 0x042b0433, 0x034b5e13, 0x0f4a2a28, 0x51590b}}, + {{0x1da16da4, 0x0e85da27, 0x16022234, 0x025e01a9, 0x079260d0, 0x1f9b5fc5, 0x09f62b86, 0x1512094e, 0xe0c17d}}}, /* 7*16^0*G: */ - {{{0x3187b2a3, 0x0018a1c0, 0x00fef5b3, 0x3e7e2e2a, 0x01fb607e, 0x2cc199f0, 0x37b4625b, 0x0edbe82f, 0x8e53}}, - {{0x01f400b4, 0x15786a1b, 0x3041b21c, 0x31cd8cf2, 0x35900053, 0x1a7e0e9b, 0x318366d0, 0x076f780c, 0x73eb}}}, + {{{0x1187b2a3, 0x00314381, 0x03fbd6cc, 0x13f17150, 0x1fb607ef, 0x18333e00, 0x0d1896ec, 0x0df417ef, 0x8e533b}}, + {{0x01f400b4, 0x0af0d436, 0x0106c871, 0x0e6c6796, 0x1900053c, 0x0fc1d37a, 0x00d9b41a, 0x17bc0663, 0x73eb1d}}}, /* 9*16^0*G: */ - {{{0x10949ee0, 0x1e7a292e, 0x06df8b3d, 0x02b2e30b, 0x31f8729e, 0x24e35475, 0x30b71878, 0x35edbfb7, 0xea68}}, - {{0x0dd048fa, 0x21688929, 0x0de823fe, 0x1c53faa9, 0x0ea0c84d, 0x052a592a, 0x1fce7870, 0x11325cb2, 0x2a27}}}, + {{{0x10949ee0, 0x1cf4525c, 0x1b7e2cf5, 0x15971858, 0x1f8729e0, 0x1c6a8eb8, 0x0dc61e24, 0x16dfdbe1, 0xea68d7}}, + {{0x0dd048fa, 0x02d11252, 0x17a08ffa, 0x029fd549, 0x0a0c84d7, 0x054b2547, 0x139e1c05, 0x192e593f, 0x2a2744}}}, /* 11*16^0*G: */ - {{{0x34bc21d1, 0x0cce474d, 0x15048bf4, 0x1d0bb409, 0x021cda16, 0x20de76c3, 0x34c59063, 0x04ede20e, 0x3ed1}}, - {{0x282a3740, 0x0be3bbf3, 0x29889dae, 0x03413697, 0x34c68a09, 0x210ebe93, 0x0c8a224c, 0x0826b331, 0x9099}}}, + {{{0x14bc21d1, 0x199c8e9b, 0x14122fd0, 0x085da04a, 0x01cda167, 0x1bced861, 0x116418e0, 0x16f10769, 0x3ed113}}, + {{0x082a3740, 0x17c777e7, 0x062276b8, 0x1a09b4bd, 0x0c68a090, 0x01d7d27a, 0x02889321, 0x13599899, 0x909920}}}, /* 13*16^0*G: */ - {{{0x06072c01, 0x23857675, 0x1ead58a9, 0x0b8a12d9, 0x1ee2fc79, 0x0177cb61, 0x0495a618, 0x20deb82b, 0x177c}}, - {{0x2fc7bfd8, 0x310eef8b, 0x1fb4df39, 0x3b8530e8, 0x0f4e7226, 0x0246b6d0, 0x2a558a24, 0x163353af, 0x63bb}}}, + {{{0x06072c01, 0x070aecea, 0x1ab562a6, 0x1c5096cb, 0x0e2fc792, 0x0ef96c2f, 0x05698601, 0x0f5c1589, 0x177c83}}, + {{0x0fc7bfd8, 0x021ddf17, 0x1ed37ce7, 0x1c298743, 0x14e7226e, 0x08d6da07, 0x15628902, 0x19a9d7d4, 0x63bb58}}}, /* 15*16^0*G: */ - {{{0x259b9d5f, 0x0d9a318f, 0x23a0ef16, 0x00ebe4b7, 0x088265ae, 0x2cde2666, 0x2bae7adf, 0x1371a5c6, 0xf045}}, - {{0x0d034f36, 0x1f967378, 0x1b5fa3f4, 0x0ec8739d, 0x1643e62a, 0x1653947e, 0x22d1f4e6, 0x0fb8d64b, 0xb5b9}}} + {{{0x059b9d5f, 0x1b34631f, 0x0e83bc58, 0x075f25bc, 0x08265ae0, 0x1bc4ccc4, 0x0b9eb7ec, 0x18d2e357, 0xf0454d}}, + {{0x0d034f36, 0x1f2ce6f0, 0x0d7e8fd1, 0x16439ceb, 0x043e62a3, 0x0a728fcb, 0x147d3996, 0x1c6b25c5, 0xb5b93e}}} }, { /* 1*16^1*G: */ - {{{0x21277c6e, 0x17ad1e1f, 0x36ca038a, 0x0a0e4bbf, 0x36315fcd, 0x08718a60, 0x341858b8, 0x1344e29a, 0x76a9}}, - {{0x0b8c5110, 0x3a7775c9, 0x3c78baa0, 0x26680103, 0x1e872085, 0x0286d784, 0x3260e6cb, 0x3f984d07, 0xa985}}}, + {{{0x01277c6e, 0x0f5a3c3f, 0x1b280e29, 0x10725dfe, 0x0315fcd2, 0x0e314c1b, 0x06162e08, 0x02714d68, 0x76a94d}}, + {{0x0b8c5110, 0x14eeeb92, 0x11e2ea83, 0x1340081f, 0x08720859, 0x10daf08f, 0x1839b2c2, 0x0c2683e4, 0xa985fe}}}, /* 3*16^1*G: */ - {{{0x1e4536ca, 0x2fee771a, 0x2201a61a, 0x0ba4a582, 0x30cda11c, 0x39d16f81, 0x139ec8cc, 0x3ec39249, 0x9482}}, - {{0x358cc1c8, 0x3eb618ef, 0x307bfbb1, 0x0f578a55, 0x134e63f6, 0x358e329d, 0x157f91a5, 0x2729d17c, 0x351d}}}, + {{{0x1e4536ca, 0x1fdcee34, 0x0806986a, 0x1d252c14, 0x0cda11c2, 0x1a2df038, 0x07b23339, 0x01c924a7, 0x9482fb}}, + {{0x158cc1c8, 0x1d6c31df, 0x01efeec7, 0x1abc52ae, 0x14e63f63, 0x11c653a9, 0x1fe46975, 0x14e8be2a, 0x351d9c}}}, /* 5*16^1*G: */ - {{{0x15ecff13, 0x26c76b8a, 0x3d0633c4, 0x1d928736, 0x081eeb63, 0x0d69454c, 0x131195b8, 0x2df05eba, 0xb2e1}}, - {{0x32187d44, 0x0ee92626, 0x3dea2e6a, 0x3686a605, 0x1758c387, 0x0e868aab, 0x3ebccf23, 0x1104c4e8, 0xe6c0}}}, + {{{0x15ecff13, 0x0d8ed714, 0x1418cf12, 0x0c9439b7, 0x01eeb637, 0x0d28a984, 0x04656e0d, 0x182f5d26, 0xb2e1b7}}, + {{0x12187d44, 0x1dd24c4d, 0x17a8b9a8, 0x1435302f, 0x158c387d, 0x10d1556b, 0x0f33c8ce, 0x0262747d, 0xe6c044}}}, /* 7*16^1*G: */ - {{{0x2ef87286, 0x22eeccd3, 0x02309e43, 0x00fa1f7f, 0x06ee3407, 0x105df72f, 0x36bc2cb3, 0x118b9fc6, 0xb433}}, - {{0x041496d9, 0x2b011fda, 0x22cea4b7, 0x3388201a, 0x292e6f9d, 0x3d39cb05, 0x2b5fe383, 0x15149bb4, 0xa0da}}}, + {{{0x0ef87286, 0x05dd99a7, 0x08c2790e, 0x07d0fbf8, 0x0ee34070, 0x0bbee5e3, 0x0f0b2cd0, 0x05cfe36d, 0xb43346}}, + {{0x041496d9, 0x16023fb4, 0x0b3a92de, 0x1c4100d4, 0x12e6f9dc, 0x073960b4, 0x17f8e0fd, 0x0a4dda56, 0xa0da54}}}, /* 9*16^1*G: */ - {{{0x19794381, 0x2e61ad6c, 0x2b0c7601, 0x245621d7, 0x167b1918, 0x1ba416d5, 0x1a24cc18, 0x0833934f, 0xa474}}, - {{0x22769c52, 0x25b38e9f, 0x1f6ac786, 0x2970236e, 0x167afff3, 0x37e4d866, 0x1bfe0e73, 0x3ff7def8, 0x2ebb}}}, + {{{0x19794381, 0x1cc35ad8, 0x0c31d806, 0x02b10ebd, 0x07b19189, 0x1482daab, 0x0933061b, 0x19c9a7b4, 0xa47420}}, + {{0x02769c52, 0x0b671d3f, 0x1dab1e1a, 0x0b811b73, 0x07afff3a, 0x1c9b0ccb, 0x1f839cf7, 0x1bef7c37, 0x2ebbff}}}, /* 11*16^1*G: */ - {{{0x09a5185a, 0x31d11992, 0x35e6f2be, 0x21c2b227, 0x0da3195b, 0x335004ac, 0x091485fe, 0x1e866e74, 0x05ba}}, - {{0x01de3a4e, 0x150f2238, 0x105ae001, 0x018882f2, 0x23d48e76, 0x1e08f893, 0x01896e46, 0x34ad7a0b, 0x30e0}}}, + {{{0x09a5185a, 0x03a23324, 0x179bcafb, 0x0e15913e, 0x1a3195b8, 0x0a009586, 0x05217fb3, 0x03373a12, 0x5ba7a}}, + {{0x01de3a4e, 0x0a1e4470, 0x016b8005, 0x0c441792, 0x1d48e760, 0x011f1271, 0x025b919e, 0x16bd0583, 0x30e0d2}}}, /* 13*16^1*G: */ - {{{0x399b85fe, 0x2a8e62d7, 0x23a5dfd5, 0x03bfa6ab, 0x03e0b79c, 0x26364602, 0x3e2fd697, 0x1d327437, 0xb29f}}, - {{0x2da604dc, 0x2e990a5d, 0x3f59e80d, 0x3bd8f4c2, 0x17c6d92d, 0x01c4ba5b, 0x29785d5d, 0x16f0e9b0, 0xa3ce}}}, + {{{0x199b85fe, 0x151cc5af, 0x0e977f56, 0x1dfd355c, 0x1e0b79c0, 0x06c8c041, 0x0bf5a5e6, 0x193a1bfc, 0xb29f74}}, + {{0x0da604dc, 0x1d3214bb, 0x1d67a036, 0x1ec7a617, 0x1c6d92de, 0x18974b6b, 0x1e175741, 0x1874d852, 0xa3ce5b}}}, /* 15*16^1*G: */ - {{{0x07e030ef, 0x1d9d15ba, 0x0d50e962, 0x1acac15f, 0x082b0857, 0x32fc0fc9, 0x1bcf5076, 0x26eaa2e4, 0x9929}}, - {{0x18d9aa9a, 0x3639adf7, 0x34008444, 0x304b1267, 0x0eaa7957, 0x0e04069b, 0x38e18bf3, 0x38f4cccf, 0x5cc2}}} + {{{0x07e030ef, 0x1b3a2b74, 0x1543a589, 0x16560af9, 0x02b08576, 0x1f81f924, 0x13d41db2, 0x15517237, 0x99299b}}, + {{0x18d9aa9a, 0x0c735bee, 0x10021113, 0x0258933e, 0x0aa7957c, 0x0080d367, 0x1862fcce, 0x1a6667f1, 0x5cc2e3}}} }, { /* 1*16^2*G: */ - {{{0x12d0441b, 0x36cb8d7c, 0x16a564c2, 0x0342dc43, 0x03ed6119, 0x3f454a18, 0x1165987f, 0x3528ec02, 0x34a2}}, - {{0x1e93b146, 0x10939e11, 0x2ddd81db, 0x35d9ae77, 0x377fc0e7, 0x29c411b9, 0x1e3c22bc, 0x3b5a94e8, 0xbeaa}}}, + {{{0x12d0441b, 0x0d971af8, 0x1a95930b, 0x1a16e21a, 0x1ed61190, 0x08a94301, 0x19661fff, 0x14760122, 0x34a2d4}}, + {{0x1e93b146, 0x01273c22, 0x1776076d, 0x0ecd73bd, 0x17fc0e7d, 0x1882373b, 0x0f08af29, 0x0d4a743c, 0xbeaaed}}}, /* 3*16^2*G: */ - {{{0x3da08424, 0x3392b8ce, 0x0f644a9d, 0x2fedeadd, 0x1d23ed3a, 0x2317fea5, 0x359aa1b5, 0x0281eb70, 0xa98b}}, - {{0x2831800c, 0x184a1e83, 0x0df582d3, 0x0afa02e8, 0x1d132075, 0x067a3238, 0x19b66e53, 0x3191c892, 0x4754}}}, + {{{0x1da08424, 0x0725719d, 0x1d912a77, 0x1f6f56e9, 0x123ed3ab, 0x02ffd4ae, 0x06a86d63, 0x00f5b86b, 0xa98b0a}}, + {{0x0831800c, 0x10943d07, 0x17d60b4d, 0x17d01741, 0x11320752, 0x0f46470e, 0x0d9b94c6, 0x08e44933, 0x4754c6}}}, /* 5*16^2*G: */ - {{{0x083c2d6a, 0x14b5f97a, 0x1bd29b3b, 0x0be46360, 0x1a696dd2, 0x2dade321, 0x1aac5d21, 0x3c027223, 0xa034}}, - {{0x02c30e72, 0x10cdbbcb, 0x2267e7cf, 0x0180d7c5, 0x2ceb06be, 0x36e15173, 0x19c1fb0c, 0x000db2a2, 0xfe1b}}}, + {{{0x083c2d6a, 0x096bf2f4, 0x0f4a6ced, 0x1f231b03, 0x0696dd22, 0x15bc642d, 0x0b17486d, 0x013911b5, 0xa034f0}}, + {{0x02c30e72, 0x019b7796, 0x099f9f3d, 0x0c06be2c, 0x0eb06be0, 0x1c2a2e76, 0x107ec336, 0x06d95133, 0xfe1b00}}}, /* 7*16^2*G: */ - {{{0x28be8c78, 0x05a94774, 0x3793e4d7, 0x025b3e0a, 0x22e9a14a, 0x1b8ad025, 0x14401a07, 0x09bfcc67, 0xb522}}, - {{0x11686903, 0x00cd9f29, 0x1b58ff32, 0x27dff239, 0x12851a81, 0x2cd9a5fa, 0x1f540ca1, 0x38327d4e, 0x701e}}}, + {{{0x08be8c78, 0x0b528ee9, 0x1e4f935c, 0x12d9f056, 0x0e9a14a0, 0x115a04b1, 0x100681db, 0x1fe633a8, 0xb52226}}, + {{0x11686903, 0x019b3e52, 0x0d63fcc8, 0x1eff91cb, 0x0851a819, 0x1b34bf49, 0x1503286c, 0x193ea73e, 0x701ee0}}}, /* 9*16^2*G: */ - {{{0x2058b5a4, 0x0103f902, 0x131979b7, 0x11193e1e, 0x0c4713de, 0x233b33f3, 0x205b3d96, 0x221861a3, 0xa3e3}}, - {{0x27113aef, 0x3cc1b643, 0x371a2948, 0x3ba116ed, 0x17e68f3c, 0x239aceba, 0x0d12c384, 0x15e21f7c, 0xcfd4}}}, + {{{0x0058b5a4, 0x0207f205, 0x0c65e6dc, 0x08c9f0f2, 0x04713de4, 0x07667e66, 0x16cf65a3, 0x0c30d1c0, 0xa3e388}}, + {{0x07113aef, 0x19836c87, 0x1c68a523, 0x1d08b76e, 0x1e68f3ce, 0x1359d74b, 0x04b0e123, 0x110fbe1a, 0xcfd457}}}, /* 11*16^2*G: */ - {{{0x04a08314, 0x017d7b24, 0x1c7dff7a, 0x3f8db6cb, 0x21197a82, 0x332ae688, 0x3a539333, 0x151284c7, 0x2099}}, - {{0x27573ccc, 0x1fe32717, 0x2fcfe96e, 0x01b969cd, 0x1048dfd4, 0x2ea3972e, 0x33b1890f, 0x0f7f4aa8, 0xa5cf}}}, + {{{0x04a08314, 0x02faf648, 0x11f7fde8, 0x1c6db65b, 0x1197a82f, 0x055cd110, 0x14e4ccf3, 0x094263f4, 0x209954}}, + {{0x07573ccc, 0x1fc64e2f, 0x1f3fa5b9, 0x0dcb4e6d, 0x048dfd40, 0x1472e5c8, 0x0c6243ee, 0x1fa55467, 0xa5cf3d}}}, /* 13*16^2*G: */ - {{{0x29078c18, 0x00bfe52b, 0x2ede9295, 0x3830f2bb, 0x1fd39b99, 0x3db9caab, 0x0ec70308, 0x1944eb30, 0x751d}}, - {{0x0ece0d67, 0x2635ba57, 0x3e05ac79, 0x02523072, 0x2a2a4ef0, 0x152ebda8, 0x24158853, 0x0fff7292, 0xba9c}}}, + {{{0x09078c18, 0x017fca57, 0x1b7a4a54, 0x018795dd, 0x1d39b99e, 0x1739556f, 0x11c0c23d, 0x0275981d, 0x751d65}}, + {{0x0ece0d67, 0x0c6b74ae, 0x1816b1e6, 0x12918397, 0x02a4ef00, 0x05d7b515, 0x056214d5, 0x1fb94948, 0xba9c3f}}}, /* 15*16^2*G: */ - {{{0x1e86d900, 0x0b3f3572, 0x3a3db449, 0x17b82745, 0x3a3b3640, 0x120c2280, 0x3801117b, 0x3d489711, 0x5be0}}, - {{0x358a5755, 0x13375a6f, 0x1b34f5ac, 0x085c9490, 0x35423df9, 0x1f8e939e, 0x2c422d34, 0x3679b7fc, 0x83d1}}} + {{{0x1e86d900, 0x167e6ae4, 0x08f6d124, 0x1dc13a2f, 0x03b36405, 0x0184501d, 0x00445ed2, 0x044b88f0, 0x5be0f5}}, + {{0x158a5755, 0x066eb4df, 0x0cd3d6b1, 0x02e4a483, 0x1423df92, 0x11d273da, 0x108b4d1f, 0x1cdbfe58, 0x83d1d9}}} }, { /* 1*16^3*G: */ - {{{0x2245573f, 0x01dfa36a, 0x0fd0a64f, 0x219dbcbd, 0x2d6bd250, 0x1e259cb9, 0x29e4d997, 0x2bb4b3c1, 0xe716}}, - {{0x069218d1, 0x017f09ad, 0x207c9b35, 0x0f437cbe, 0x39a851d1, 0x0ac19a1e, 0x072ab591, 0x18f9a53f, 0x3536}}}, + {{{0x0245573f, 0x03bf46d5, 0x1f42993c, 0x0cede5e9, 0x16bd2508, 0x04b39736, 0x193665de, 0x1a59e0d3, 0xe716ae}}, + {{0x069218d1, 0x02fe135a, 0x01f26cd4, 0x1a1be5f4, 0x1a851d13, 0x183343dc, 0x0aad644a, 0x1cd29f8e, 0x353663}}}, /* 3*16^3*G: */ - {{{0x257008ac, 0x3e61e4c1, 0x329edfb7, 0x3387b3b8, 0x1da22d19, 0x15562930, 0x07ce864e, 0x22635bd4, 0xd2bf}}, - {{0x327beb55, 0x04454d29, 0x1ff07988, 0x273842ad, 0x290c5667, 0x06576cfe, 0x377aa3f8, 0x2c72d69a, 0x69c0}}}, + {{{0x057008ac, 0x1cc3c983, 0x0a7b7edf, 0x1c3d9dc6, 0x1a22d19c, 0x0ac5260e, 0x13a19395, 0x11adea0f, 0xd2bf89}}, + {{0x127beb55, 0x088a9a53, 0x1fc1e620, 0x19c2156b, 0x10c56679, 0x0aed9fd4, 0x1ea8fe06, 0x196b4d6e, 0x69c0b1}}}, /* 5*16^3*G: */ - {{{0x382f1580, 0x3435f2a5, 0x0203eb7f, 0x39377b89, 0x3064f8b0, 0x295ce47c, 0x3ce6087f, 0x0c13b960, 0x4d88}}, - {{0x1616edd7, 0x303ec5b5, 0x0eb1e110, 0x3f28ef5a, 0x3d6518aa, 0x1a002263, 0x0636ce8d, 0x139c26ac, 0x28a9}}}, + {{{0x182f1580, 0x086be54b, 0x080fadff, 0x09bbdc48, 0x064f8b0e, 0x0b9c8f98, 0x19821fe9, 0x09dcb079, 0x4d8830}}, + {{0x1616edd7, 0x007d8b6a, 0x1ac78443, 0x19477ad1, 0x16518aaf, 0x00044c7e, 0x0db3a35a, 0x0e13560c, 0x28a94e}}}, /* 7*16^3*G: */ - {{{0x20c38e11, 0x3e130f6b, 0x26e26ba5, 0x159086fa, 0x25af9e71, 0x1ce6480b, 0x00eeb326, 0x09c9f23f, 0x17c7}}, - {{0x2e90decd, 0x360d9aee, 0x20cdae3c, 0x14e65169, 0x01802e7e, 0x00bf33a4, 0x24b3c406, 0x293d3f99, 0x95c5}}}, + {{{0x00c38e11, 0x1c261ed7, 0x1b89ae97, 0x0c8437d4, 0x1af9e715, 0x1cc90172, 0x1bacc99c, 0x04f91f81, 0x17c727}}, + {{0x0e90decd, 0x0c1b35dd, 0x0336b8f3, 0x07328b4c, 0x1802e7e5, 0x17e67480, 0x0cf10180, 0x1e9fccc9, 0x95c5a4}}}, /* 9*16^3*G: */ - {{{0x232f36ea, 0x2557f62b, 0x13541c3d, 0x13d1a9ca, 0x0cb8b3cd, 0x0ec73f21, 0x050a8846, 0x3f6ab11d, 0x7e03}}, - {{0x0a68b8af, 0x2b308ff2, 0x05009d68, 0x27a5e693, 0x04af9941, 0x39ac5c06, 0x228da668, 0x357c4804, 0xdcf6}}}, + {{{0x032f36ea, 0x0aafec57, 0x0d5070f6, 0x1e8d4e52, 0x0b8b3cd4, 0x18e7e426, 0x02a2118e, 0x15588e8a, 0x7e03fd}}, + {{0x0a68b8af, 0x16611fe4, 0x140275a2, 0x1d2f3498, 0x0af99419, 0x158b80c2, 0x03699a39, 0x1e240245, 0xdcf6d5}}}, /* 11*16^3*G: */ - {{{0x1953baa9, 0x10f94a9b, 0x1e18de8d, 0x056ba192, 0x20b21426, 0x0deb0772, 0x3cf07616, 0x369a12c6, 0x8ce6}}, - {{0x352689e5, 0x239d70a3, 0x2a9341d7, 0x3ce61aed, 0x21b56807, 0x2cef2401, 0x3120be69, 0x13ee3ea4, 0x3d9f}}}, + {{{0x1953baa9, 0x01f29536, 0x18637a35, 0x0b5d0c93, 0x0b214261, 0x1d60ee50, 0x1c1d858d, 0x0d096379, 0x8ce6da}}, + {{0x152689e5, 0x073ae147, 0x0a4d075e, 0x0730d76d, 0x1b56807f, 0x1de48030, 0x082f9a6c, 0x171f5262, 0x3d9f4f}}}, /* 13*16^3*G: */ - {{{0x2f22a96a, 0x2ae3614e, 0x06ab8f94, 0x2c6ea767, 0x3ae2b008, 0x14d525d6, 0x0054a20a, 0x39cc1037, 0xb570}}, - {{0x085d1b00, 0x2ccfd987, 0x055cc9cc, 0x326ede96, 0x00cfbda7, 0x30dda6d7, 0x1e77f028, 0x2898e3dc, 0xdcd8}}}, + {{{0x0f22a96a, 0x15c6c29d, 0x1aae3e52, 0x03753b38, 0x0e2b008b, 0x1aa4badd, 0x15288294, 0x06081b80, 0xb570e7}}, + {{0x085d1b00, 0x199fb30e, 0x15732732, 0x1376f4b0, 0x0cfbda7c, 0x1bb4dae0, 0x1dfc0a30, 0x0c71ee3c, 0xdcd8a2}}}, /* 15*16^3*G: */ - {{{0x189a7509, 0x3903ae51, 0x1fa80549, 0x09c2e590, 0x07f20de1, 0x0468f9d7, 0x3943b04a, 0x10c8f2ea, 0x44d9}}, - {{0x20437234, 0x0828ae6d, 0x14dd126e, 0x24f87f7c, 0x3b93586f, 0x08ef349d, 0x01f0a034, 0x2ce00210, 0xb2c5}}} + {{{0x189a7509, 0x12075ca2, 0x1ea01527, 0x0e172c83, 0x1f20de12, 0x0d1f3ae3, 0x10ec1284, 0x04797572, 0x44d943}}, + {{0x00437234, 0x10515cdb, 0x137449b8, 0x07c3fbe2, 0x193586f9, 0x1de693bd, 0x1c280d08, 0x10010803, 0xb2c5b3}}} }, { /* 1*16^4*G: */ - {{{0x2eade3c4, 0x0fa11971, 0x1052a050, 0x12add272, 0x2586b471, 0x3190cd03, 0x1e90d8e5, 0x0d9bd3a4, 0xa018}}, - {{0x2b26e8d0, 0x11710809, 0x0614f37f, 0x3dca1391, 0x1d8369d5, 0x3395e0d2, 0x10b167c6, 0x3b05c504, 0xe2bb}}}, + {{{0x0eade3c4, 0x1f4232e3, 0x014a8140, 0x156e9392, 0x186b4714, 0x1219a072, 0x04363971, 0x0de9d23d, 0xa01836}}, + {{0x0b26e8d0, 0x02e21013, 0x1853cdfd, 0x0e509c88, 0x18369d5f, 0x12bc1a4e, 0x0c59f1b3, 0x02e28221, 0xe2bbec}}}, /* 3*16^4*G: */ - {{{0x19e0af06, 0x38737ab1, 0x2ed958d6, 0x3ce62958, 0x05055c92, 0x34ed69b5, 0x1896450b, 0x07c02e23, 0x9cdf}}, - {{0x2216ade7, 0x35e8cb6d, 0x17ca5468, 0x2148b706, 0x0d94b082, 0x162ef372, 0x2ad664d9, 0x097fb4fc, 0x916d}}}, + {{{0x19e0af06, 0x10e6f562, 0x1b65635b, 0x07314ac5, 0x1055c92f, 0x1dad36a2, 0x059142f4, 0x001711b1, 0x9cdf1f}}, + {{0x0216ade7, 0x0bd196db, 0x1f2951a3, 0x0a45b832, 0x194b0828, 0x05de6e46, 0x15993656, 0x1fda7e55, 0x916d25}}}, /* 5*16^4*G: */ - {{{0x1305097e, 0x04dcae4e, 0x03ba5198, 0x3585c3a1, 0x00448338, 0x2c6cb415, 0x263edab6, 0x36757469, 0x45bf}}, - {{0x108ddc04, 0x12e8163a, 0x3d2c1595, 0x0ee74cef, 0x0ce90868, 0x220c151c, 0x2fd2bbad, 0x3704a156, 0x09d1}}}, + {{{0x1305097e, 0x09b95c9c, 0x0ee94660, 0x0c2e1d08, 0x0448338d, 0x0d9682a0, 0x0fb6adac, 0x1aba34cc, 0x45bfd9}}, + {{0x108ddc04, 0x05d02c74, 0x14b05655, 0x173a677f, 0x0e908683, 0x0182a386, 0x14aeeb62, 0x0250ab5f, 0x9d1dc}}}, /* 7*16^4*G: */ - {{{0x363bd6df, 0x34c7c682, 0x166aec3c, 0x3f08f0b7, 0x095e6fd1, 0x3a7e700a, 0x2693b671, 0x2b45591d, 0xb599}}, - {{0x0efa09ac, 0x3a873a8e, 0x1134b458, 0x10313da4, 0x23c4166a, 0x1cd82e2c, 0x2b332463, 0x3477b13e, 0x6979}}}, + {{{0x163bd6df, 0x098f8d05, 0x19abb0f3, 0x184785ba, 0x15e6fd1f, 0x0fce0144, 0x04ed9c7a, 0x02ac8ecd, 0xb599ad}}, + {{0x0efa09ac, 0x150e751c, 0x04d2d163, 0x0189ed22, 0x1c4166a4, 0x1b05c591, 0x0cc918dc, 0x1bd89f56, 0x6979d1}}}, /* 9*16^4*G: */ - {{{0x27142d62, 0x3e184fcc, 0x03bc26da, 0x269a8d7e, 0x2854c11d, 0x18ac489f, 0x2ac0e926, 0x287c59cc, 0xf4dc}}, - {{0x3a618fc9, 0x327b3301, 0x1cd3d7fa, 0x25e6b3bf, 0x2bc659bb, 0x3ce06e46, 0x0cd46d49, 0x19f96d2d, 0x5511}}}, + {{{0x07142d62, 0x1c309f99, 0x0ef09b6b, 0x14d46bf0, 0x054c11d9, 0x158913f4, 0x103a4998, 0x1e2ce655, 0xf4dca1}}, + {{0x1a618fc9, 0x04f66603, 0x134f5feb, 0x0f359dfb, 0x1c659bb9, 0x1c0dc8d5, 0x151b527c, 0x1cb69699, 0x551167}}}, /* 11*16^4*G: */ - {{{0x215fae61, 0x3b2c7fd1, 0x3395f821, 0x0571f713, 0x16bb5a7f, 0x1389039c, 0x09b66d9c, 0x1e2839b8, 0xf072}}, - {{0x096376f9, 0x1f432dd2, 0x037eabcf, 0x09c1c56e, 0x18f7d42c, 0x1e820862, 0x31ea5f7d, 0x06cac529, 0x1a68}}}, + {{{0x015fae61, 0x1658ffa3, 0x0e57e087, 0x0b8fb89e, 0x0bb5a7f1, 0x1120738b, 0x0d9b6713, 0x141cdc13, 0xf07278}}, + {{0x096376f9, 0x1e865ba4, 0x0dfaaf3d, 0x0e0e2b70, 0x0f7d42c2, 0x10410c4c, 0x1a97df5e, 0x056294e3, 0x1a681b}}}, /* 13*16^4*G: */ - {{{0x2466591f, 0x31381054, 0x3c68d6a0, 0x05cbaa3f, 0x2858ccbe, 0x0ead4cee, 0x20db0f14, 0x0915ebc2, 0x1fc5}}, - {{0x396f8cdb, 0x13bfbd5c, 0x2ec78224, 0x3e32b08c, 0x034e1629, 0x31dbf96d, 0x2bc11e9e, 0x060e0227, 0x489c}}}, + {{{0x0466591f, 0x027020a9, 0x11a35a83, 0x0e5d51ff, 0x058ccbe1, 0x15a99dd4, 0x16c3c50e, 0x0af5e141, 0x1fc524}}, + {{0x196f8cdb, 0x077f7ab9, 0x1b1e0891, 0x11958465, 0x14e1629f, 0x1b7f2da1, 0x1047a7b1, 0x070113d7, 0x489c18}}}, /* 15*16^4*G: */ - {{{0x322a8ebc, 0x09742e30, 0x0f967151, 0x24736dc6, 0x0a56d5a2, 0x3c2d6cc3, 0x0c5f4fd7, 0x006cc692, 0xfa25}}, - {{0x2a8a775b, 0x03649ed6, 0x0bc83318, 0x1638239b, 0x2fa8cbea, 0x14799869, 0x18962338, 0x0cac53e1, 0x71c9}}} + {{{0x122a8ebc, 0x12e85c61, 0x1e59c544, 0x039b6e31, 0x056d5a29, 0x05ad9865, 0x17d3f5fc, 0x16634918, 0xfa2501}}, + {{0x0a8a775b, 0x06c93dad, 0x0f20cc60, 0x11c11cd9, 0x1a8cbea5, 0x0f330d37, 0x0588ce14, 0x1629f0b1, 0x71c932}}} }, { /* 1*16^5*G: */ - {{{0x3d96dff1, 0x3df73b2d, 0x2d5fcfe8, 0x390c706a, 0x0d98d530, 0x1a82d5c3, 0x3e54ffef, 0x0e214507, 0x0ec7}}, - {{0x3c7b552c, 0x3b2106b1, 0x3ed78aa9, 0x149933a1, 0x0652511d, 0x3313bd60, 0x2875d91a, 0x13d3a1eb, 0xd622}}}, + {{{0x1d96dff1, 0x1bee765b, 0x157f3fa3, 0x08638355, 0x198d530e, 0x105ab866, 0x153ffbda, 0x10a283fc, 0xec738}}, + {{0x1c7b552c, 0x16420d63, 0x1b5e2aa7, 0x04c99d0f, 0x052511d5, 0x0277ac03, 0x1d7646b3, 0x09d0f5d0, 0xd6224f}}}, /* 3*16^5*G: */ - {{{0x088d58e9, 0x070c92ac, 0x0e318385, 0x12970719, 0x02a7b6e9, 0x0a91a9f1, 0x24a86e99, 0x30ff71c1, 0x96da}}, - {{0x2ebebc5e, 0x00d24c4a, 0x087e6e38, 0x16fa26e5, 0x02c43968, 0x3312524e, 0x2c1ad856, 0x2bfceb51, 0xcb1f}}}, + {{{0x088d58e9, 0x0e192558, 0x18c60e14, 0x14b838c9, 0x0a7b6e94, 0x12353e21, 0x0a1ba64a, 0x1fb8e0c9, 0x96dac3}}, + {{0x0ebebc5e, 0x01a49895, 0x01f9b8e0, 0x17d13729, 0x0c439685, 0x024a49c1, 0x06b615b3, 0x1e75a8d8, 0xcb1faf}}}, /* 5*16^5*G: */ - {{{0x2db29f92, 0x254ab44c, 0x147b2c58, 0x08749c6e, 0x2b8f811d, 0x1770de2b, 0x0f312a10, 0x2c8f3ac5, 0xe297}}, - {{0x25e58ddb, 0x03ca5322, 0x1ed41416, 0x08f3aee1, 0x0d914912, 0x036eaee3, 0x370b4b48, 0x09483e32, 0xe137}}}, + {{{0x0db29f92, 0x0a956899, 0x11ecb162, 0x03a4e372, 0x18f811d2, 0x0e1bc575, 0x0c4a8417, 0x079d629e, 0xe297b2}}, + {{0x05e58ddb, 0x0794a645, 0x1b505058, 0x079d770b, 0x19149122, 0x0dd5dc66, 0x02d2d203, 0x041f196e, 0xe13725}}}, /* 7*16^5*G: */ - {{{0x0ad88c33, 0x3650edee, 0x1746bcaf, 0x06b8e536, 0x24da97d9, 0x1af24834, 0x394b66b0, 0x08ce3eca, 0x1cd2}}, - {{0x248fb1b2, 0x0a3a9e10, 0x2ca1e496, 0x3f944c57, 0x36bc2713, 0x21902ac4, 0x348b096c, 0x337e0e2a, 0xfc3a}}}, + {{{0x0ad88c33, 0x0ca1dbdc, 0x1d1af2bf, 0x15c729b2, 0x0da97d91, 0x1e490692, 0x12d9ac1a, 0x071f6572, 0x1cd223}}, + {{0x048fb1b2, 0x14753c21, 0x12879258, 0x1ca262bd, 0x0bc2713f, 0x1205589b, 0x02c25b21, 0x1f071569, 0xfc3acd}}}, /* 9*16^5*G: */ - {{{0x3b26aa73, 0x14eb2270, 0x063a0e0f, 0x3df846c3, 0x3b1ee0cd, 0x32b4c37f, 0x1fbbfcb1, 0x35eb6e7a, 0xf462}}, - {{0x38479e73, 0x117ab05d, 0x0502cca2, 0x3a3828c0, 0x333c7a49, 0x0ee929a1, 0x053140d5, 0x03469e0d, 0x406a}}}, + {{{0x1b26aa73, 0x09d644e1, 0x18e8383d, 0x0fc23618, 0x11ee0cdf, 0x16986ffd, 0x0eff2c72, 0x15b73d3f, 0xf462d7}}, + {{0x18479e73, 0x02f560bb, 0x140b3289, 0x11c14600, 0x13c7a49e, 0x1d253439, 0x0c50354e, 0x034f068a, 0x406a0d}}}, /* 11*16^5*G: */ - {{{0x3cd015e3, 0x3b8780aa, 0x26502273, 0x243a565f, 0x095168af, 0x36facf2a, 0x30caf75b, 0x224974fd, 0xe0f6}}, - {{0x12157cce, 0x2a89350b, 0x22936bbd, 0x2e2d4e47, 0x34c77c55, 0x09a5b1c9, 0x03aa9536, 0x078c4392, 0x0853}}}, + {{{0x1cd015e3, 0x170f0155, 0x194089cf, 0x01d2b2fc, 0x15168af9, 0x1f59e544, 0x12bdd6f6, 0x04ba7ee1, 0xe0f689}}, + {{0x12157cce, 0x15126a16, 0x0a4daef6, 0x116a723c, 0x0c77c55b, 0x14b6393a, 0x0aa54d89, 0x0621c907, 0x8531e}}}, /* 13*16^5*G: */ - {{{0x0bb76b12, 0x39b10c45, 0x21927691, 0x239d9dcf, 0x375a00ea, 0x20acc4ab, 0x3f57fc1d, 0x2b70554a, 0x28e4}}, - {{0x2c4747bd, 0x1f914e9f, 0x31628ff5, 0x282983c5, 0x1ea3f703, 0x12d96dae, 0x201b3f4e, 0x1313bf66, 0x14d7}}}, + {{{0x0bb76b12, 0x1362188a, 0x0649da47, 0x1cecee7c, 0x15a00ea8, 0x1598957b, 0x15ff0760, 0x182aa57e, 0x28e4ad}}, + {{0x0c4747bd, 0x1f229d3f, 0x058a3fd5, 0x014c1e2e, 0x0a3f703a, 0x1b2db5cf, 0x06cfd392, 0x09dfb340, 0x14d74c}}}, /* 15*16^5*G: */ - {{{0x276ff697, 0x2fd6007f, 0x20764628, 0x26da2194, 0x2097c636, 0x07b6aece, 0x2805ed27, 0x2e89e52e, 0x85a0}}, - {{0x12142721, 0x027b5369, 0x10a58b93, 0x3a5ffe9e, 0x2daa551d, 0x1e434f73, 0x3e24a554, 0x0b987ab0, 0xadf3}}} + {{{0x076ff697, 0x1fac00ff, 0x01d918a2, 0x16d10ca4, 0x097c6369, 0x16d5d9d0, 0x017b49c7, 0x04f29750, 0x85a0ba}}, + {{0x12142721, 0x04f6a6d2, 0x02962e4c, 0x12fff4f2, 0x1aa551de, 0x0869ee76, 0x0929551e, 0x0c3d587c, 0xadf32e}}} }, { /* 1*16^6*G: */ - {{{0x2392d805, 0x1c971773, 0x35405d43, 0x1ea01a61, 0x23449aa8, 0x1536abea, 0x293d7a4a, 0x3733d31a, 0xf8f5}}, - {{0x2cda02fa, 0x09986545, 0x12143ba0, 0x3cf69929, 0x21327351, 0x34f8cd91, 0x23054389, 0x1db3d9b5, 0xe581}}}, + {{{0x0392d805, 0x192e2ee7, 0x1501750d, 0x1500d30e, 0x1449aa87, 0x06d57d51, 0x0f5e9295, 0x19e98d52, 0xf8f5dc}}, + {{0x0cda02fa, 0x1330ca8b, 0x0850ee80, 0x07b4c94a, 0x1327351f, 0x1f19b230, 0x0150e274, 0x19ecdac6, 0xe58176}}}, /* 3*16^6*G: */ - {{{0x3fa046f7, 0x2752cc59, 0x207309d1, 0x0443ce40, 0x2e2d4517, 0x212b2251, 0x083a94e0, 0x2392a196, 0xe12c}}, - {{0x212646ad, 0x0e9568a2, 0x33119345, 0x03013844, 0x3126f6dd, 0x2cfb54e4, 0x1a2f3433, 0x011843f6, 0x7cec}}}, + {{{0x1fa046f7, 0x0ea598b3, 0x01cc2746, 0x021e7204, 0x02d45171, 0x05644a37, 0x0ea53821, 0x0950cb10, 0xe12c8e}}, + {{0x012646ad, 0x1d2ad145, 0x0c464d14, 0x1809c226, 0x126f6dd0, 0x1f6a9c98, 0x0bcd0cec, 0x0c21fb34, 0x7cec04}}}, /* 5*16^6*G: */ - {{{0x02853c43, 0x26c49fa3, 0x222e466b, 0x059b15eb, 0x11323648, 0x238bbf8f, 0x292093d0, 0x351d05e5, 0x394b}}, - {{0x2064469d, 0x05e0a332, 0x10fcf0cb, 0x0bd9c4b6, 0x160767d5, 0x38ff0bc7, 0x1c6b9207, 0x1b548547, 0x2b4d}}}, + {{{0x02853c43, 0x0d893f46, 0x08b919ae, 0x0cd8af5c, 0x13236481, 0x1177f1e8, 0x0824f423, 0x0e82f2d2, 0x394bd4}}, + {{0x0064469d, 0x0bc14665, 0x03f3c32c, 0x1ece25b2, 0x00767d52, 0x1fe178eb, 0x1ae481f8, 0x0a42a3b8, 0x2b4d6d}}}, /* 7*16^6*G: */ - {{{0x3c722e94, 0x30b75ce7, 0x1058961e, 0x36040e5b, 0x1404334e, 0x31995b16, 0x282e9445, 0x0e37ce37, 0xca85}}, - {{0x1049a527, 0x28298b7c, 0x08b26a43, 0x0254ea29, 0x3b9f12f2, 0x1cc49a87, 0x205c311e, 0x3f10bae7, 0x3b27}}}, + {{{0x1c722e94, 0x016eb9cf, 0x0162587b, 0x102072da, 0x004334ed, 0x132b62ca, 0x0ba51171, 0x1be71bd0, 0xca8538}}, + {{0x1049a527, 0x105316f8, 0x02c9a90e, 0x12a75149, 0x19f12f20, 0x189350fd, 0x170c479c, 0x085d73c0, 0x3b27fc}}}, /* 9*16^6*G: */ - {{{0x1cad6309, 0x1c5d18a7, 0x239ff488, 0x0687f0bc, 0x267b3dd3, 0x2dd18932, 0x17b75a1b, 0x06967c8d, 0x663e}}, - {{0x09981f28, 0x0ca1ae8e, 0x2eb52bd5, 0x01f51100, 0x1cf918b9, 0x0b060f2c, 0x2a8c3c10, 0x2dcee019, 0x292f}}}, + {{{0x1cad6309, 0x18ba314e, 0x0e7fd221, 0x143f85e4, 0x07b3dd31, 0x1a312653, 0x0dd686ed, 0x0b3e46af, 0x663e1a}}, + {{0x09981f28, 0x19435d1c, 0x1ad4af54, 0x0fa88805, 0x0f918b90, 0x00c1e58e, 0x030f040b, 0x07700cd5, 0x292fb7}}}, /* 11*16^6*G: */ - {{{0x22c23d03, 0x09d6c914, 0x3c7ff249, 0x286c1363, 0x3beeab3b, 0x0db08dc1, 0x3667096c, 0x3bf9cc18, 0xa2d9}}, - {{0x3085db74, 0x00b93013, 0x039df451, 0x0269fa56, 0x101b92ea, 0x0c10db1c, 0x01b8f155, 0x148a3321, 0x1cc8}}}, + {{{0x02c23d03, 0x13ad9229, 0x11ffc924, 0x03609b1f, 0x1eeab3ba, 0x1611b83d, 0x19c25b0d, 0x1ce60c6c, 0xa2d9ef}}, + {{0x1085db74, 0x01726027, 0x0e77d144, 0x134fd2b0, 0x01b92ea0, 0x021b6388, 0x0e3c554c, 0x05199083, 0x1cc852}}}, /* 13*16^6*G: */ - {{{0x07d4c6d1, 0x1d57e59c, 0x2d9fffb1, 0x18b35466, 0x3f35d0f6, 0x2442d49c, 0x1a9efe0b, 0x384ad22c, 0x5657}}, - {{0x0106bdec, 0x20c0fca6, 0x052c1418, 0x3e68d685, 0x2e6a0abf, 0x2ce43cce, 0x149f9acf, 0x2fbd2e37, 0x72b5}}}, + {{{0x07d4c6d1, 0x1aafcb38, 0x167ffec5, 0x059aa335, 0x135d0f66, 0x085a939f, 0x07bf82e4, 0x05691635, 0x5657e1}}, + {{0x0106bdec, 0x0181f94c, 0x14b05062, 0x1346b428, 0x06a0abff, 0x1c8799d7, 0x07e6b3ec, 0x1e971ba9, 0x72b5be}}}, /* 15*16^6*G: */ - {{{0x1933564a, 0x21953755, 0x1e3af44f, 0x1a2d3ebb, 0x2d8d2b7a, 0x13b7199d, 0x2e001086, 0x18857502, 0x5b68}}, - {{0x0204ef63, 0x2d7c1162, 0x078869f3, 0x0abb88a2, 0x1d95de39, 0x0c315346, 0x2264552d, 0x3a9a73ce, 0x76b5}}} + {{{0x1933564a, 0x032a6eaa, 0x18ebd13e, 0x1169f5db, 0x18d2b7a6, 0x16e333b6, 0x00042193, 0x02ba815c, 0x5b6862}}, + {{0x0204ef63, 0x1af822c4, 0x1e21a7ce, 0x15dc4510, 0x195de392, 0x062a68ce, 0x19154b4c, 0x0d39e744, 0x76b5ea}}} }, { /* 1*16^7*G: */ - {{{0x2f922dbd, 0x21288c5d, 0x399218f9, 0x298c4587, 0x0d71b91c, 0x17aab639, 0x1af313f8, 0x2dafff53, 0x6d28}}, - {{0x20ef3cff, 0x12affc0a, 0x04da2994, 0x093a7c2e, 0x0b4a1c4c, 0x2f869873, 0x1d2fa40f, 0x36414507, 0xaf39}}}, + {{{0x0f922dbd, 0x025118bb, 0x064863e6, 0x0c622c3f, 0x171b91ca, 0x1556c726, 0x1cc4fe17, 0x17ffa9b5, 0x6d28b6}}, + {{0x00ef3cff, 0x055ff815, 0x1368a651, 0x09d3e170, 0x14a1c4c2, 0x10d30e65, 0x0be903ef, 0x00a283ba, 0xaf39d9}}}, /* 3*16^7*G: */ - {{{0x1b168b64, 0x16437fe6, 0x186c840b, 0x14f40ab1, 0x14467ea1, 0x3c2417f0, 0x3e3ddd3d, 0x055e9fef, 0x7cd3}}, - {{0x1abbb16b, 0x15b034ad, 0x2e02e358, 0x2b1366dc, 0x1bfafb13, 0x1a39e2f3, 0x12c62205, 0x234845ca, 0x9ca0}}}, + {{{0x1b168b64, 0x0c86ffcc, 0x01b2102d, 0x07a0558b, 0x0467ea15, 0x0482fe0a, 0x0f774f7c, 0x0f4ff7fc, 0x7cd315}}, + {{0x1abbb16b, 0x0b60695a, 0x180b8d61, 0x189b36e5, 0x1fafb13a, 0x073c5e6d, 0x1188815a, 0x0422e525, 0x9ca08d}}}, /* 5*16^7*G: */ - {{{0x06ef29e8, 0x0ac71be8, 0x1d9aee3b, 0x371552c2, 0x05356264, 0x090c6675, 0x1f8c456b, 0x02f6d7cb, 0xed86}}, - {{0x39b90f8f, 0x00687126, 0x18daa335, 0x18c3d70b, 0x017bb1e7, 0x2fdacd01, 0x1a7fd7c6, 0x39d0dd75, 0xb837}}}, + {{{0x06ef29e8, 0x158e37d0, 0x166bb8ec, 0x18aa9613, 0x1356264d, 0x018ccea2, 0x03115ac9, 0x1b6be5bf, 0xed860b}}, + {{0x19b90f8f, 0x00d0e24d, 0x036a8cd4, 0x061eb85b, 0x17bb1e76, 0x1b59a020, 0x1ff5f1af, 0x086ebab4, 0xb837e7}}}, /* 7*16^7*G: */ - {{{0x3636e617, 0x37e462cf, 0x1f1cf599, 0x37340ef0, 0x272c9d47, 0x3870b9f8, 0x21243735, 0x3323f474, 0x6868}}, - {{0x3cbb3d27, 0x323773cf, 0x0384cd71, 0x3f8c3229, 0x313f0a60, 0x1640e1e4, 0x3f9e6b3c, 0x02296e46, 0xeed0}}}, + {{{0x1636e617, 0x0fc8c59f, 0x1c73d667, 0x19a07783, 0x12c9d47d, 0x0e173f13, 0x090dcd78, 0x11fa3a42, 0x6868cc}}, + {{0x1cbb3d27, 0x046ee79f, 0x0e1335c7, 0x1c619148, 0x13f0a60f, 0x081c3c98, 0x079acf16, 0x14b7237f, 0xeed008}}}, /* 9*16^7*G: */ - {{{0x113e2a34, 0x1e768a98, 0x23a11e2c, 0x074b9973, 0x2fd31829, 0x32d27c42, 0x0fe202c5, 0x2cd83ab2, 0xec03}}, - {{0x384566d6, 0x10890fba, 0x1a136b7a, 0x2a055b99, 0x2122728a, 0x3f788404, 0x058437be, 0x03fed828, 0x8602}}}, + {{{0x113e2a34, 0x1ced1530, 0x0e8478b1, 0x1a5ccb9c, 0x1d318291, 0x1a4f8857, 0x1880b172, 0x0c1d591f, 0xec03b3}}, + {{0x184566d6, 0x01121f75, 0x084dade9, 0x102adccb, 0x122728aa, 0x0f108090, 0x010defbf, 0x1f6c140b, 0x86020f}}}, /* 11*16^7*G: */ - {{{0x087c1b18, 0x3ab83397, 0x04991a25, 0x078b2d52, 0x1056fa10, 0x0c0d6964, 0x0b90de6a, 0x1928e79e, 0xa794}}, - {{0x3b94809a, 0x3ad61425, 0x1562821b, 0x2637a71c, 0x1a89f60d, 0x295e1e7a, 0x058cc249, 0x3d38fdca, 0x1361}}}, + {{{0x087c1b18, 0x1570672e, 0x12646897, 0x1c596a90, 0x056fa101, 0x01ad2c88, 0x04379a8c, 0x1473cf17, 0xa79464}}, + {{0x1b94809a, 0x15ac284b, 0x158a086f, 0x11bd38e2, 0x089f60d9, 0x0bc3cf4d, 0x03309269, 0x1c7ee50b, 0x1361f4}}}, /* 13*16^7*G: */ - {{{0x1ed10d26, 0x2538a31b, 0x1e595f65, 0x26afbe0a, 0x330ccc5a, 0x247eda53, 0x3bcc790e, 0x3ca02aa3, 0x544e}}, - {{0x36dafcc2, 0x3f093dc9, 0x22c06ae2, 0x0f5be5db, 0x0d70d368, 0x2c77fa36, 0x2c2ce9d6, 0x07277116, 0x95b9}}}, + {{{0x1ed10d26, 0x0a714636, 0x19657d96, 0x157df053, 0x10ccc5a9, 0x0fdb4a79, 0x131e43a4, 0x101551f7, 0x544ef2}}, + {{0x16dafcc2, 0x1e127b93, 0x0b01ab8b, 0x1adf2edc, 0x170d3683, 0x0eff46c6, 0x0b3a75ac, 0x13b88b58, 0x95b91c}}}, /* 15*16^7*G: */ - {{{0x37ad18e6, 0x1251e7e2, 0x13cad5e2, 0x2b4f9e63, 0x0aff9b57, 0x14f211ad, 0x0c6214de, 0x1b2217cd, 0xe2c2}}, - {{0x2554cfad, 0x36bf946a, 0x1981de4a, 0x3145729c, 0x17ba113b, 0x3899ba84, 0x0818851c, 0x06ca13d2, 0xb212}}} + {{{0x17ad18e6, 0x04a3cfc5, 0x0f2b5789, 0x1a7cf31a, 0x0ff9b57a, 0x1e4235a5, 0x18853794, 0x110be698, 0xe2c26c}}, + {{0x0554cfad, 0x0d7f28d5, 0x0607792b, 0x0a2b94e3, 0x1ba113bc, 0x1337508b, 0x06214738, 0x0509e910, 0xb2121b}}} }, { /* 1*16^8*G: */ - {{{0x185a5943, 0x296a7888, 0x065dfb63, 0x2e464d97, 0x2c71da1a, 0x15acc898, 0x2af89216, 0x1ad02bc8, 0x7fe3}}, - {{0x299ca101, 0x143454b1, 0x38af212d, 0x2cf5619e, 0x1ca6f174, 0x27d0101f, 0x236249f0, 0x3516096d, 0xe697}}}, + {{{0x185a5943, 0x12d4f110, 0x1977ed8e, 0x12326cb8, 0x071da1ab, 0x15991316, 0x1e248595, 0x0815e455, 0x7fe36b}}, + {{0x099ca101, 0x0868a963, 0x02bc84b5, 0x07ab0cf7, 0x0a6f174b, 0x1a0203ee, 0x18927c27, 0x0b04b6c6, 0xe697d4}}}, /* 3*16^8*G: */ - {{{0x1f0922a8, 0x1a9e0247, 0x05cf8d97, 0x243a7495, 0x2f8b808e, 0x09395808, 0x22d73809, 0x1a9016d3, 0x4b65}}, - {{0x199a80bb, 0x36b72b16, 0x1850f694, 0x1cee78ae, 0x18c4d6d4, 0x01330957, 0x3783920d, 0x28c744b9, 0xee1e}}}, + {{{0x1f0922a8, 0x153c048e, 0x173e365d, 0x01d3a4a8, 0x18b808e9, 0x072b0117, 0x15ce0249, 0x080b69c5, 0x4b656a}}, + {{0x199a80bb, 0x0d6e562c, 0x0143da53, 0x0773c573, 0x0c4d6d47, 0x06612aec, 0x00e48341, 0x03a25cef, 0xee1ea3}}}, /* 5*16^8*G: */ - {{{0x29d07e9e, 0x1413e221, 0x2a60c36b, 0x279f287d, 0x3d8e5ea0, 0x2caf83ec, 0x1e13d93d, 0x255baf59, 0x9d78}}, - {{0x03d8c8ee, 0x1375856b, 0x394c7b2f, 0x1828b68e, 0x3210ce74, 0x0aa27074, 0x2a8cd654, 0x279bbd23, 0xd514}}}, + {{{0x09d07e9e, 0x0827c443, 0x09830dad, 0x1cf943ed, 0x18e5ea09, 0x15f07d9e, 0x04f64f6c, 0x0dd7acbc, 0x9d7895}}, + {{0x03d8c8ee, 0x06eb0ad6, 0x0531ecbd, 0x0145b477, 0x010ce746, 0x144e0e99, 0x0335950a, 0x0dde91d5, 0xd5149e}}}, /* 7*16^8*G: */ - {{{0x3dc4950f, 0x19dd4219, 0x13942076, 0x106cab6f, 0x1b631657, 0x0da11b93, 0x13fa9572, 0x049cb84d, 0x4acb}}, - {{0x23d8b4df, 0x1b1b9111, 0x1866ac56, 0x2790a02d, 0x31e29fdf, 0x0a63db31, 0x3cdad8cf, 0x3483edd0, 0x726c}}}, + {{{0x1dc4950f, 0x13ba8433, 0x0e5081d9, 0x03655b7a, 0x16316574, 0x1423726d, 0x1ea55c8d, 0x0e5c26a7, 0x4acb12}}, + {{0x03d8b4df, 0x16372223, 0x019ab159, 0x1c85016b, 0x1e29fdf9, 0x0c7b6638, 0x16b633ca, 0x01f6e879, 0x726cd2}}}, /* 9*16^8*G: */ - {{{0x2d7e8cbd, 0x1031e9ef, 0x007d816f, 0x199fe2bc, 0x01464a2a, 0x114d5432, 0x317b4234, 0x17afc69a, 0x640c}}, - {{0x3ec5a5db, 0x1b8a40f2, 0x0ff9b020, 0x01a7ec63, 0x1eab9eba, 0x271badc0, 0x0fd2f2ae, 0x223f60a7, 0xd6ae}}}, + {{{0x0d7e8cbd, 0x0063d3df, 0x01f605bd, 0x0cff15e0, 0x1464a2a6, 0x09aa8640, 0x1ed08d11, 0x17e34d62, 0x640c5e}}, + {{0x1ec5a5db, 0x171481e5, 0x1fe6c081, 0x0d3f6319, 0x0ab9eba0, 0x0375b80f, 0x14bcaba7, 0x1fb0539f, 0xd6ae88}}}, /* 11*16^8*G: */ - {{{0x3e86bddc, 0x1c2812c1, 0x35ce3d5f, 0x349ae5e5, 0x1b6b9bf1, 0x158b2437, 0x04b32451, 0x012c6d0a, 0x8bba}}, - {{0x29e349c4, 0x088f1687, 0x0196e5f5, 0x2b3f793d, 0x19437ac6, 0x2fe4859a, 0x08ebf659, 0x26702708, 0xc340}}}, + {{{0x1e86bddc, 0x18502583, 0x1738f57d, 0x04d72f2e, 0x16b9bf1d, 0x116486ed, 0x0cc91455, 0x16368509, 0x8bba04}}, + {{0x09e349c4, 0x111e2d0f, 0x065b97d4, 0x19fbc9e8, 0x1437ac6a, 0x1c90b34c, 0x1afd966f, 0x18138411, 0xc34099}}}, /* 13*16^8*G: */ - {{{0x0257f582, 0x05c39e01, 0x2c3a258d, 0x26427ab7, 0x1a5fe41f, 0x1a50fdf1, 0x137e210a, 0x15d13fb3, 0x8b0a}}, - {{0x37372d4b, 0x205ffb7c, 0x31607664, 0x36d1ae9e, 0x237d4656, 0x285684df, 0x2c739662, 0x2913b035, 0x9e57}}}, + {{{0x0257f582, 0x0b873c02, 0x10e89634, 0x1213d5bd, 0x05fe41f9, 0x0a1fbe2d, 0x1f88429a, 0x089fd9a6, 0x8b0a57}}, + {{0x17372d4b, 0x00bff6f9, 0x0581d992, 0x168d74f6, 0x17d4656d, 0x0ad09bf1, 0x1ce598a8, 0x09d81ad8, 0x9e57a4}}}, /* 15*16^8*G: */ - {{{0x185e797e, 0x3c5127e6, 0x23c31683, 0x1b8893cb, 0x1678a6f0, 0x15bd24f6, 0x078971f8, 0x3fe5f099, 0x0a13}}, - {{0x139d666f, 0x0c9eae7d, 0x180c3928, 0x1fdbc29d, 0x21dc3ff2, 0x36063a3e, 0x083d5917, 0x2592c897, 0xeb1a}}} + {{{0x185e797e, 0x18a24fcc, 0x0f0c5a0f, 0x1c449e5c, 0x078a6f06, 0x17a49ecb, 0x025c7e15, 0x12f84c8f, 0xa13ff}}, + {{0x139d666f, 0x193d5cfa, 0x0030e4a0, 0x1ede14eb, 0x1dc3ff27, 0x00c747d0, 0x0f5645f6, 0x09644b90, 0xeb1a96}}} }, { /* 1*16^9*G: */ - {{{0x3dde3445, 0x2bfd3f87, 0x2aea7817, 0x2eea7768, 0x26519e76, 0x1c7f9ffc, 0x061e6853, 0x2d8e135c, 0x6965}}, - {{0x18855113, 0x3310e278, 0x25f99d97, 0x1f398146, 0x332dbef4, 0x392598e1, 0x02511325, 0x36b8e712, 0xd1bc}}}, + {{{0x1dde3445, 0x17fa7f0f, 0x0ba9e05e, 0x1753bb45, 0x0519e76b, 0x0ff3ff93, 0x079a14dc, 0x0709ae0c, 0x6965b6}}, + {{0x18855113, 0x0621c4f0, 0x17e6765f, 0x19cc0a34, 0x12dbef47, 0x04b31c39, 0x1444c979, 0x1c738904, 0xd1bcda}}}, /* 3*16^9*G: */ - {{{0x088acfc5, 0x17903e5a, 0x2689789f, 0x3bd626cd, 0x091a71b1, 0x39f76f50, 0x1c7da027, 0x3147779d, 0xe1cb}}, - {{0x2249a225, 0x2f17fb56, 0x2bfba523, 0x34ca4afb, 0x39e23ce7, 0x09d93ff6, 0x3daedb31, 0x20e5f379, 0xec67}}}, + {{{0x088acfc5, 0x0f207cb4, 0x1a25e27d, 0x1eb1366c, 0x11a71b1e, 0x1eedea04, 0x1f6809f9, 0x03bbceb8, 0xe1cbc5}}, + {{0x0249a225, 0x1e2ff6ad, 0x0fee948e, 0x065257dd, 0x1e23ce7d, 0x1b27fedc, 0x0bb6cc49, 0x12f9bcfb, 0xec6783}}}, /* 5*16^9*G: */ - {{{0x2107ccc6, 0x163a94ff, 0x03c82287, 0x0e25f855, 0x2900481d, 0x3a74a116, 0x38aa1731, 0x099e5c44, 0x9c3f}}, - {{0x3dea9152, 0x101e5334, 0x1f9b1868, 0x2a3f53a5, 0x3e6eca51, 0x0dd7d2fc, 0x11d9c8be, 0x0306d92d, 0xdaee}}}, + {{{0x0107ccc6, 0x0c7529ff, 0x0f208a1d, 0x112fc2a8, 0x100481d3, 0x0e9422d4, 0x0a85cc7a, 0x0f2e2271, 0x9c3f26}}, + {{0x1dea9152, 0x003ca669, 0x1e6c61a1, 0x11fa9d2b, 0x06eca51a, 0x1afa5f9f, 0x16722f8d, 0x036c96a3, 0xdaee0c}}}, /* 7*16^9*G: */ - {{{0x15a449e7, 0x0717ad0e, 0x13c2be42, 0x28a80d39, 0x00922b2f, 0x3eb05ec5, 0x32d72796, 0x3655df1a, 0x5c30}}, - {{0x2e2677d0, 0x1c3a9206, 0x3ce790e7, 0x179014f0, 0x0592d0b7, 0x2d97de67, 0x21b92164, 0x38ed6c23, 0x8025}}}, + {{{0x15a449e7, 0x0e2f5a1c, 0x0f0af908, 0x054069ca, 0x0922b2fa, 0x160bd8a0, 0x15c9e5be, 0x0aef8d65, 0x5c30d9}}, + {{0x0e2677d0, 0x1875240d, 0x139e439d, 0x1c80a787, 0x192d0b75, 0x12fbcce2, 0x0e48592d, 0x16b611c3, 0x8025e3}}}, /* 9*16^9*G: */ - {{{0x0b8ceb07, 0x2956300a, 0x3ee271cf, 0x1e494aff, 0x28d99553, 0x138ac1fa, 0x29682afe, 0x2fc8c323, 0xaa3b}}, - {{0x1fd83984, 0x26a118ba, 0x2b3f9eb9, 0x1c6caf1e, 0x1162ec3b, 0x32c3f932, 0x2c26844d, 0x032c2707, 0xe632}}}, + {{{0x0b8ceb07, 0x12ac6014, 0x1b89c73e, 0x124a57ff, 0x0d995537, 0x11583f54, 0x1a0abf93, 0x046191d2, 0xaa3bbf}}, + {{0x1fd83984, 0x0d423174, 0x0cfe7ae6, 0x036578f5, 0x162ec3b7, 0x187f2648, 0x09a11372, 0x161383d8, 0xe6320c}}}, /* 11*16^9*G: */ - {{{0x03bfd1f1, 0x103a9556, 0x1d65732e, 0x0db70d45, 0x0001943a, 0x183f2645, 0x3418179e, 0x0c9444cc, 0xab4a}}, - {{0x08e1c233, 0x044e5843, 0x39e98cf2, 0x1f64c909, 0x2fe057a5, 0x2cef4104, 0x08668b4e, 0x192ec0db, 0xea6c}}}, + {{{0x03bfd1f1, 0x00752aac, 0x1595ccb9, 0x0db86a2b, 0x001943a3, 0x07e4c8a0, 0x0605e798, 0x0a226668, 0xab4a32}}, + {{0x08e1c233, 0x089cb086, 0x07a633c8, 0x1b26484f, 0x1e057a57, 0x1de82097, 0x19a2d3ac, 0x17606d90, 0xea6c64}}}, /* 13*16^9*G: */ - {{{0x0b1d6d3f, 0x2101b5e0, 0x2eebb890, 0x0dd9a293, 0x25a8105f, 0x0dfd7362, 0x15d77f73, 0x2c96777b, 0xdba9}}, - {{0x09cd8133, 0x10ba4a0a, 0x12bd93cc, 0x2f66f114, 0x2b871448, 0x2a653d3f, 0x35b7b5ac, 0x0b4fd5d4, 0xb386}}}, + {{{0x0b1d6d3f, 0x02036bc0, 0x1baee242, 0x0ecd149d, 0x1a8105f3, 0x1fae6c52, 0x15dfdccd, 0x0b3bbdab, 0xdba9b2}}, + {{0x09cd8133, 0x01749414, 0x0af64f31, 0x1b3788a2, 0x1871448b, 0x0ca7a7f5, 0x0ded6b2a, 0x07eaea6b, 0xb3862d}}}, /* 15*16^9*G: */ - {{{0x31fa2a6a, 0x1e680e00, 0x30e4b256, 0x3f075616, 0x23cdfe34, 0x375d0ac6, 0x0274507a, 0x3d310ba6, 0x1998}}, - {{0x06415142, 0x01fb6d2f, 0x37258b56, 0x1b008e1e, 0x38a1e94c, 0x03e0022d, 0x2fa10970, 0x105b4642, 0x2ebb}}} + {{{0x11fa2a6a, 0x1cd01c01, 0x0392c959, 0x183ab0b6, 0x1cdfe34f, 0x0ba158d1, 0x1d141eb7, 0x1885d304, 0x1998f4}}, + {{0x06415142, 0x03f6da5e, 0x1c962d58, 0x180470f6, 0x0a1e94c6, 0x1c0045bc, 0x08425c03, 0x0da3215f, 0x2ebb41}}} }, { /* 1*16^10*G: */ - {{{0x0d9aefbd, 0x163f29b1, 0x3b957752, 0x3f91ec9c, 0x3c43dc1e, 0x2a7c3506, 0x29d7632c, 0x0d072319, 0x0fbc}}, - {{0x13e71ca0, 0x34edbaa7, 0x00a9ff1e, 0x02c1a788, 0x17d3d395, 0x052c7525, 0x20e3fe40, 0x0898cbcd, 0xbd80}}}, + {{{0x0d9aefbd, 0x0c7e5362, 0x0e55dd49, 0x1c8f64e7, 0x043dc1ef, 0x0f86a0de, 0x15d8cb2a, 0x03918cd3, 0xfbc34}}, + {{0x13e71ca0, 0x09db754e, 0x02a7fc7b, 0x160d3c40, 0x1d3d3950, 0x058ea4ab, 0x18ff9005, 0x0c65e6c1, 0xbd8022}}}, /* 3*16^10*G: */ - {{{0x29434837, 0x1e5b7ffb, 0x220c1bb8, 0x2cc502e1, 0x0fb06dad, 0x1071bfed, 0x07aedb13, 0x062af12a, 0xd76d}}, - {{0x3b215b4c, 0x3ea813e6, 0x1b7ccc24, 0x291639dd, 0x2b933290, 0x390853de, 0x16644de0, 0x1368cbb6, 0xf6bc}}}, + {{{0x09434837, 0x1cb6fff7, 0x08306ee1, 0x0628170c, 0x1b06dadb, 0x0e37fda7, 0x0bb6c4d0, 0x1578950f, 0xd76d18}}, + {{0x1b215b4c, 0x1d5027cd, 0x0df33093, 0x08b1ceeb, 0x1933290a, 0x010a7bd5, 0x19137839, 0x1465db2c, 0xf6bc4d}}}, /* 5*16^10*G: */ - {{{0x1c07f222, 0x0ba27c86, 0x060fe7d0, 0x388718eb, 0x1753d1c5, 0x2074687c, 0x3ff604f4, 0x31941859, 0xd5c0}}, - {{0x0c6ffd57, 0x0bbda478, 0x0813a86e, 0x3cfd469e, 0x1f75b9ba, 0x3831dfd2, 0x3b8850cd, 0x02e18205, 0x15a3}}}, + {{{0x1c07f222, 0x1744f90c, 0x183f9f40, 0x0438c758, 0x153d1c5e, 0x0e8d0f8b, 0x1d813d20, 0x0a0c2cff, 0xd5c0c6}}, + {{0x0c6ffd57, 0x177b48f0, 0x004ea1b8, 0x07ea34f1, 0x175b9baf, 0x063bfa4f, 0x02143378, 0x10c102f7, 0x15a30b}}}, /* 7*16^10*G: */ - {{{0x0e93bfa6, 0x291c5a89, 0x1a1362a4, 0x274a5682, 0x0c9fe0d3, 0x272e99ad, 0x2f62ce54, 0x0d939291, 0x734c}}, - {{0x18d10774, 0x31be9e66, 0x10297c4f, 0x284d8822, 0x0c5f48ec, 0x26078d48, 0x39d049de, 0x0540eaa9, 0x0995}}}, + {{{0x0e93bfa6, 0x1238b512, 0x084d8a92, 0x1a52b413, 0x09fe0d39, 0x05d335a6, 0x18b39527, 0x09c948de, 0x734c36}}, + {{0x18d10774, 0x037d3ccc, 0x00a5f13f, 0x026c4112, 0x05f48eca, 0x00f1a906, 0x141277a6, 0x007554f3, 0x99515}}}, /* 9*16^10*G: */ - {{{0x1fa194ae, 0x03ad45fd, 0x2054aecf, 0x100a4766, 0x1eb14906, 0x1d7674aa, 0x26a89011, 0x367681ed, 0x79a3}}, - {{0x1fcf634b, 0x3f197a72, 0x379bc4d4, 0x35097ccb, 0x2f03d86b, 0x19c6e162, 0x0b1b34b3, 0x36f29c95, 0x84e1}}}, + {{{0x1fa194ae, 0x075a8bfa, 0x0152bb3c, 0x00523b34, 0x0b149064, 0x0ece954f, 0x0a24045d, 0x1b40f6cd, 0x79a3d9}}, + {{0x1fcf634b, 0x1e32f4e4, 0x1e6f1353, 0x084be65e, 0x103d86bd, 0x18dc2c57, 0x06cd2cd9, 0x194e4a96, 0x84e1db}}}, /* 11*16^10*G: */ - {{{0x21e8b7fe, 0x2b241800, 0x385b26a6, 0x3438b85d, 0x3c98e05d, 0x3932ab73, 0x305828a3, 0x3f425356, 0x3393}}, - {{0x023c6821, 0x30509108, 0x29b94b70, 0x15acc2a2, 0x1a668d8e, 0x3fabb671, 0x3beb82ea, 0x0defb219, 0x1304}}}, + {{{0x01e8b7fe, 0x16483001, 0x016c9a9a, 0x01c5c2ef, 0x098e05dd, 0x06556e7e, 0x160a28f9, 0x0129ab60, 0x3393fd}}, + {{0x023c6821, 0x00a12210, 0x06e52dc3, 0x0d661515, 0x0668d8e5, 0x1576ce2d, 0x1ae0babf, 0x17d90cf7, 0x130437}}}, /* 13*16^10*G: */ - {{{0x21528cf6, 0x0255e755, 0x250694ea, 0x280942bd, 0x1b0a52e6, 0x2d161bb9, 0x227e15e1, 0x0a2184d1, 0xa16b}}, - {{0x3ce93f3b, 0x02e483e7, 0x3cc80138, 0x24fef204, 0x1150f434, 0x33b5e760, 0x3ad99913, 0x262ba14d, 0xf405}}}, + {{{0x01528cf6, 0x04abceab, 0x141a53a8, 0x004a15ec, 0x10a52e6a, 0x02c3772d, 0x1f85786d, 0x10c268c4, 0xa16b28}}, + {{0x1ce93f3b, 0x05c907cf, 0x132004e0, 0x07f79027, 0x150f4349, 0x16bcec08, 0x166644f3, 0x15d0a6f5, 0xf40598}}}, /* 15*16^10*G: */ - {{{0x0c8db2e0, 0x144299ae, 0x30d73583, 0x0f2f7057, 0x1a74f647, 0x3226aea5, 0x3474cbf6, 0x33880638, 0xd317}}, - {{0x274bc9a9, 0x16cd28ac, 0x2b860f3a, 0x289d3408, 0x179136ca, 0x0b0fa38e, 0x3844b99c, 0x0842a424, 0xd61a}}} + {{{0x0c8db2e0, 0x0885335c, 0x035cd60d, 0x197b82be, 0x074f6473, 0x04d5d4ad, 0x1d32fdb2, 0x04031c68, 0xd317ce}}, + {{0x074bc9a9, 0x0d9a5159, 0x0e183ce9, 0x04e9a045, 0x19136caa, 0x01f471cb, 0x112e670b, 0x01521270, 0xd61a21}}} }, { /* 1*16^11*G: */ - {{{0x23fe67b2, 0x1b8c65ea, 0x22e3338c, 0x2a2ff9c2, 0x3323b234, 0x19ae6ea5, 0x085dcbc6, 0x3090ddcf, 0x6608}}, - {{0x25b47a28, 0x248ff973, 0x0c543081, 0x0ac567d0, 0x06e03fc2, 0x3d90369d, 0x1c168846, 0x05afb148, 0xa1a9}}}, + {{{0x03fe67b2, 0x1718cbd5, 0x0b8cce31, 0x117fce14, 0x123b234a, 0x15cdd4b9, 0x1772f199, 0x086ee790, 0x6608c2}}, + {{0x05b47a28, 0x091ff2e7, 0x1150c206, 0x162b3e81, 0x0e03fc22, 0x1206d3a3, 0x05a211bd, 0x17d8a438, 0xa1a916}}}, /* 3*16^11*G: */ - {{{0x2bc73e02, 0x0f9baab4, 0x365312c1, 0x259853ba, 0x17863184, 0x2a6045f5, 0x1dc23206, 0x1ab8a9b1, 0xf095}}, - {{0x0611219d, 0x34b3da66, 0x3ae94572, 0x0b41236e, 0x03935667, 0x08162bca, 0x0e03c76e, 0x39980451, 0x433f}}}, + {{{0x0bc73e02, 0x1f375569, 0x194c4b04, 0x0cc29dd6, 0x18631849, 0x0c08beab, 0x108c81aa, 0x1c54d8bb, 0xf0956a}}, + {{0x0611219d, 0x0967b4cc, 0x0ba515cb, 0x1a091b77, 0x19356672, 0x02c57941, 0x00f1db88, 0x0c02289c, 0x433fe6}}}, /* 5*16^11*G: */ - {{{0x1c5fe45c, 0x3788b794, 0x07c0f597, 0x2ca06a0e, 0x37283488, 0x3c9275f3, 0x2a60ca52, 0x3afa8f28, 0xdb98}}, - {{0x3ef45a22, 0x129c0710, 0x2480e1c4, 0x20c813ea, 0x112c8ce9, 0x144a7762, 0x185a2de1, 0x3cc2dd6f, 0xe0c0}}}, + {{{0x1c5fe45c, 0x0f116f28, 0x1f03d65f, 0x05035070, 0x1283488b, 0x124ebe7b, 0x183294bc, 0x1d479454, 0xdb98eb}}, + {{0x1ef45a22, 0x05380e21, 0x12038711, 0x06409f54, 0x12c8ce98, 0x094eec48, 0x168b7854, 0x016eb7b0, 0xe0c0f3}}}, /* 7*16^11*G: */ - {{{0x22128eac, 0x3d679837, 0x0af1ccba, 0x11d63573, 0x2a51690c, 0x29acedf5, 0x1a5f421b, 0x300582b7, 0x0a73}}, - {{0x24f1180d, 0x2164a475, 0x355d9ca3, 0x0dd67c5d, 0x350a7c79, 0x32db7653, 0x2838ca55, 0x36958113, 0x443f}}}, + {{{0x02128eac, 0x1acf306f, 0x0bc732eb, 0x0eb1ab99, 0x051690c4, 0x159dbeb5, 0x17d086e9, 0x02c15bb4, 0xa73c0}}, + {{0x04f1180d, 0x02c948eb, 0x1576728e, 0x0eb3e2ee, 0x10a7c793, 0x1b6eca7a, 0x0e329572, 0x0ac089d0, 0x443fda}}}, /* 9*16^11*G: */ - {{{0x23ccbc30, 0x196a4cc5, 0x1349618c, 0x37f97487, 0x0997249e, 0x34dd99e8, 0x34f2370e, 0x0830d1f2, 0x3787}}, - {{0x1315729e, 0x2880c9fc, 0x1348f846, 0x2f3e5574, 0x279b6d16, 0x062b02aa, 0x2538c931, 0x376e73dc, 0x8f1b}}}, + {{{0x03ccbc30, 0x12d4998b, 0x0d258631, 0x1fcba43a, 0x197249ed, 0x1bb33d04, 0x1c8dc3b4, 0x1868f969, 0x378720}}, + {{0x1315729e, 0x110193f8, 0x0d23e11a, 0x19f2aba2, 0x19b6d16b, 0x05605553, 0x0e324c46, 0x1739ee4a, 0x8f1bdd}}}, /* 11*16^11*G: */ - {{{0x03bb1b6b, 0x192a3795, 0x07c2bfaa, 0x17fbccbd, 0x15a62157, 0x20463041, 0x31a619d9, 0x34876de2, 0xfe8f}}, - {{0x30eaaf93, 0x1ed766e8, 0x0abf8899, 0x053773fc, 0x2d13c00f, 0x0a3a57d6, 0x16e3769e, 0x08abb0c9, 0x791e}}}, + {{{0x03bb1b6b, 0x12546f2a, 0x1f0afea9, 0x1fde65e8, 0x1a621575, 0x08c6082a, 0x09867660, 0x03b6f163, 0xfe8fd2}}, + {{0x10eaaf93, 0x1daecdd1, 0x0afe2265, 0x09bb9fe1, 0x113c00f1, 0x074afad6, 0x18dda78a, 0x15d864ad, 0x791e22}}}, /* 13*16^11*G: */ - {{{0x344b7cea, 0x20156672, 0x16cf87de, 0x111a5024, 0x33dcca47, 0x010089e2, 0x37e2ee82, 0x07f55e7e, 0x2c33}}, - {{0x15d1c9c2, 0x3f0ad1ab, 0x13094077, 0x249447fc, 0x3dd65061, 0x0fcf630e, 0x21e76fcf, 0x1ec73381, 0x2056}}}, + {{{0x144b7cea, 0x002acce5, 0x1b3e1f7a, 0x08d28122, 0x1dcca474, 0x00113c59, 0x18bba081, 0x1aaf3f6f, 0x2c331f}}, + {{0x15d1c9c2, 0x1e15a356, 0x0c2501df, 0x04a23fe2, 0x1d650619, 0x19ec61de, 0x19dbf3cf, 0x0399c0c3, 0x20567b}}}, /* 15*16^11*G: */ - {{{0x0112278c, 0x3e4a6cde, 0x28d9a158, 0x00592742, 0x044b66dd, 0x22d321fe, 0x1a320a34, 0x301b1194, 0x509b}}, - {{0x0e178f66, 0x321d7262, 0x335f945e, 0x197fa1b9, 0x0f64570f, 0x03d3c5ee, 0x246ec176, 0x1a30adc8, 0xb4b1}}} + {{{0x0112278c, 0x1c94d9bc, 0x03668563, 0x02c93a15, 0x04b66dd0, 0x1a643fc2, 0x0c828d22, 0x0d88ca34, 0x509bc0}}, + {{0x0e178f66, 0x043ae4c4, 0x0d7e517b, 0x0bfd0dce, 0x164570f6, 0x1a78bdc7, 0x1bb05d83, 0x1856e448, 0xb4b168}}} }, { /* 1*16^12*G: */ - {{{0x17e55104, 0x0baebe00, 0x38e9c71c, 0x0ea0d7ee, 0x0b561cf7, 0x3a4f0d36, 0x3873763d, 0x1d9489ed, 0xd8de}}, - {{0x252e08cd, 0x280bbe03, 0x140db1b2, 0x3dcff386, 0x1cf924c2, 0x318a2b47, 0x3f2d15c4, 0x25196f84, 0x2fd2}}}, + {{{0x17e55104, 0x175d7c00, 0x03a71c70, 0x1506bf77, 0x1561cf73, 0x09e1a6c5, 0x1cdd8f7a, 0x0a44f6f0, 0xd8de76}}, + {{0x052e08cd, 0x10177c07, 0x1036c6ca, 0x0e7f9c32, 0x0f924c2f, 0x114568ee, 0x0b457131, 0x0cb7c27e, 0x2fd294}}}, /* 3*16^12*G: */ - {{{0x2987bfd3, 0x24e70b1f, 0x0c4284c6, 0x3151cbfd, 0x1dd19187, 0x37efabeb, 0x18e33551, 0x1e1bef54, 0xe3a5}}, - {{0x0cc23e7d, 0x3b4c6db2, 0x128e0817, 0x373cbb36, 0x18210ca3, 0x1ee7fd2b, 0x040e6847, 0x2b4254d6, 0xf74b}}}, + {{{0x0987bfd3, 0x09ce163f, 0x110a131a, 0x0a8e5fe9, 0x1d19187c, 0x1df57d6e, 0x18cd5477, 0x0df7aa31, 0xe3a578}}, + {{0x0cc23e7d, 0x1698db64, 0x0a38205f, 0x19e5d9b2, 0x0210ca3d, 0x1cffa56c, 0x039a11de, 0x012a6b08, 0xf74bad}}}, /* 5*16^12*G: */ - {{{0x22d5056e, 0x19e54748, 0x247a07cb, 0x372d69f8, 0x2e5e480e, 0x097ff3a5, 0x120d4115, 0x1c107b29, 0x42a9}}, - {{0x30f7db11, 0x21053722, 0x29fd1fd4, 0x13920f5b, 0x163b26b6, 0x0db749ad, 0x087066ec, 0x1fd9b3c0, 0xf2fc}}}, + {{{0x02d5056e, 0x13ca8e91, 0x11e81f2d, 0x196b4fc4, 0x05e480ed, 0x0ffe74b7, 0x03504549, 0x083d94a4, 0x42a970}}, + {{0x10f7db11, 0x020a6e45, 0x07f47f52, 0x1c907add, 0x03b26b64, 0x16e935ab, 0x1c19bb0d, 0x0cd9e010, 0xf2fc7f}}}, /* 7*16^12*G: */ - {{{0x13dafd3b, 0x19d17e47, 0x1cb3956c, 0x2e267c0b, 0x1379d66f, 0x0cb0bb59, 0x3964cfe2, 0x29c6c709, 0x0d6c}}, - {{0x1a6fe6e8, 0x1ab7c508, 0x288771ad, 0x08922afb, 0x07de58a0, 0x1252809c, 0x2293d9fe, 0x0c2ce3f7, 0xa851}}}, + {{{0x13dafd3b, 0x13a2fc8e, 0x12ce55b1, 0x1133e05b, 0x179d66fb, 0x16176b29, 0x1933f88c, 0x036384f2, 0xd6ca7}}, + {{0x1a6fe6e8, 0x156f8a10, 0x021dc6b5, 0x049157dd, 0x1de58a02, 0x0a501383, 0x04f67f92, 0x1671fbc5, 0xa85130}}}, /* 9*16^12*G: */ - {{{0x31131f8b, 0x1afe71ff, 0x3a20d4df, 0x191a5833, 0x031fb469, 0x308b7e71, 0x1a3d97d4, 0x329eb619, 0x05ed}}, - {{0x3a6f779f, 0x3b3c2c66, 0x0e89d490, 0x1494017c, 0x0271be33, 0x275c6d7c, 0x086bc01c, 0x2207923a, 0x9e58}}}, + {{{0x11131f8b, 0x15fce3ff, 0x0883537d, 0x08d2c19f, 0x11fb4696, 0x116fce21, 0x0f65f530, 0x0f5b0cb4, 0x5edca}}, + {{0x1a6f779f, 0x167858cd, 0x1a275243, 0x04a00be1, 0x071be335, 0x0b8daf81, 0x1af00727, 0x03c91d10, 0x9e5888}}}, /* 11*16^12*G: */ - {{{0x2b597e4d, 0x323e7d07, 0x37d1a319, 0x1d3cc979, 0x371c1149, 0x2d168ced, 0x3a0a4121, 0x301582f1, 0x5a13}}, - {{0x241856e0, 0x3df921a7, 0x1136664a, 0x37a1ead6, 0x2d73ce7b, 0x346283c8, 0x397ff51f, 0x0f04e243, 0xc9e7}}}, + {{{0x0b597e4d, 0x047cfa0f, 0x1f468c67, 0x09e64bce, 0x11c11497, 0x02d19dbb, 0x0290486d, 0x0ac178f4, 0x5a13c0}}, + {{0x041856e0, 0x1bf2434f, 0x04d9992b, 0x1d0f56b2, 0x173ce7bd, 0x0c507916, 0x1ffd47f4, 0x027121f2, 0xc9e73c}}}, /* 13*16^12*G: */ - {{{0x0260faf0, 0x2a9e2585, 0x3e95935d, 0x2ef4d165, 0x0f272ea2, 0x113869a0, 0x36e75431, 0x1595805e, 0x96b2}}, - {{0x2366d412, 0x03909483, 0x07d4f5ac, 0x02efe61c, 0x3f99e189, 0x36395cce, 0x37cac00a, 0x29a8006c, 0xdcf8}}}, + {{{0x0260faf0, 0x153c4b0a, 0x1a564d76, 0x17a68b2f, 0x1272ea2b, 0x070d3407, 0x19d50c51, 0x0ac02f6d, 0x96b256}}, + {{0x0366d412, 0x07212907, 0x1f53d6b0, 0x177f30e0, 0x199e1890, 0x072b99df, 0x12b002b6, 0x1400366f, 0xdcf8a6}}}, /* 15*16^12*G: */ - {{{0x2ad13276, 0x12686f92, 0x1c043c7a, 0x18d43aba, 0x3771a3ca, 0x04acace1, 0x0de2426f, 0x06443107, 0x0b97}}, - {{0x0a84dadb, 0x0ce3cd08, 0x270fae3b, 0x0f5e4a60, 0x36811f59, 0x0b916cef, 0x2eefbd4e, 0x121bbc01, 0xac28}}} + {{{0x0ad13276, 0x04d0df25, 0x1010f1e9, 0x06a1d5d3, 0x171a3ca6, 0x15959c3b, 0x18909bc4, 0x0218839b, 0xb9719}}, + {{0x0a84dadb, 0x19c79a10, 0x1c3eb8ec, 0x1af25304, 0x0811f593, 0x122d9dfb, 0x1bef538b, 0x0dde00dd, 0xac2848}}} }, { /* 1*16^13*G: */ - {{{0x071e5c83, 0x3a9af248, 0x142a0bee, 0x349fc661, 0x18e5b18b, 0x2116dca9, 0x2d73f20a, 0x32505409, 0x54cc}}, - {{0x140916a1, 0x3f423bdc, 0x18ee496c, 0x2782f317, 0x12bf2292, 0x3e1c576b, 0x145323a8, 0x0fd16d14, 0x1c43}}}, + {{{0x071e5c83, 0x1535e490, 0x10a82fbb, 0x04fe330a, 0x0e5b18bd, 0x02db952c, 0x1cfc82a1, 0x082a04da, 0x54ccc9}}, + {{0x140916a1, 0x1e8477b8, 0x03b925b3, 0x1c1798bb, 0x0bf22929, 0x038aed69, 0x14c8ea3e, 0x08b68a28, 0x1c433f}}}, /* 3*16^13*G: */ - {{{0x2f76167c, 0x3178d88a, 0x07467394, 0x0bd08b31, 0x0cd9f22f, 0x08b1a4b7, 0x2ff9539c, 0x0bb72dcf, 0x8758}}, - {{0x2f4d7ff6, 0x31beed85, 0x3197be86, 0x00a3c19d, 0x3236a888, 0x040b0f0d, 0x24a7bfde, 0x250d42b5, 0x075b}}}, + {{{0x0f76167c, 0x02f1b115, 0x1d19ce53, 0x1e845988, 0x0d9f22f2, 0x163496e6, 0x1e54e708, 0x1b96e7df, 0x87582e}}, + {{0x0f4d7ff6, 0x037ddb0b, 0x065efa1b, 0x051e0cee, 0x036a8880, 0x0161e1b9, 0x09eff784, 0x06a15ac9, 0x75b94}}}, /* 5*16^13*G: */ - {{{0x34de6611, 0x19c8fba1, 0x3821fb04, 0x3d95ce52, 0x26f11e33, 0x16dcd8d5, 0x336db1c2, 0x1eb287c9, 0x4a10}}, - {{0x18a805fe, 0x0d63afb9, 0x02132ac0, 0x17551e97, 0x00052e07, 0x3993a3dc, 0x3ef3934c, 0x09944018, 0x809b}}}, + {{{0x14de6611, 0x1391f743, 0x0087ec11, 0x0cae7297, 0x0f11e33f, 0x1b9b1ab3, 0x1b6c7096, 0x1943e4e6, 0x4a107a}}, + {{0x18a805fe, 0x1ac75f72, 0x084cab00, 0x1aa8f4b8, 0x0052e075, 0x12747b80, 0x1ce4d339, 0x0a200c7d, 0x809b26}}}, /* 7*16^13*G: */ - {{{0x2dcfecb0, 0x32e93b41, 0x0a8d846f, 0x20ff474c, 0x3f49f6e9, 0x28383526, 0x2dfc9654, 0x0bacdcaa, 0xfd40}}, - {{0x2da08de8, 0x0164fcf7, 0x1e65e791, 0x12d3092f, 0x2ba86b1a, 0x1898e26e, 0x23a22e9a, 0x100c3769, 0xd6b3}}}, + {{{0x0dcfecb0, 0x05d27683, 0x0a3611bf, 0x07fa3a61, 0x149f6e98, 0x0706a4df, 0x1f259528, 0x166e555b, 0xfd402e}}, + {{0x0da08de8, 0x02c9f9ef, 0x19979e44, 0x1698497b, 0x1a86b1a4, 0x131c4dd5, 0x088ba698, 0x061bb4c7, 0xd6b340}}}, /* 9*16^13*G: */ - {{{0x154659ed, 0x2d37583d, 0x15d966e5, 0x2b8f4886, 0x09d0a07f, 0x2e381ffb, 0x075155df, 0x2cd19186, 0x467b}}, - {{0x2800cf83, 0x2c81f42c, 0x1013e009, 0x06f04373, 0x382cd370, 0x0b3561b6, 0x178e8a1f, 0x3ff416aa, 0xd01e}}}, + {{{0x154659ed, 0x1a6eb07a, 0x17659b96, 0x1c7a4432, 0x1d0a07fa, 0x0703ff64, 0x145577ee, 0x08c8c30e, 0x467bb3}}, + {{0x0800cf83, 0x1903e859, 0x004f8026, 0x17821b9a, 0x02cd3701, 0x06ac36dc, 0x03a287cb, 0x1a0b552f, 0xd01eff}}}, /* 11*16^13*G: */ - {{{0x1c97e515, 0x3992612b, 0x1885a5fe, 0x0535b0ce, 0x1ec7e569, 0x1e6d8c3a, 0x1c0e46c8, 0x2e63e337, 0xcf66}}, - {{0x006c8a51, 0x160853aa, 0x190033a9, 0x3c1d1636, 0x2c6a7b33, 0x16d040d3, 0x061211c2, 0x1c5ee411, 0x0a70}}}, + {{{0x1c97e515, 0x1324c256, 0x021697fb, 0x09ad8673, 0x0c7e5691, 0x0db1874f, 0x0391b21e, 0x11f19bb8, 0xcf66b9}}, + {{0x006c8a51, 0x0c10a754, 0x0400cea5, 0x00e8b1b3, 0x06a7b33f, 0x1a081a76, 0x04847096, 0x0f72088c, 0xa7071}}}, /* 13*16^13*G: */ - {{{0x186154e5, 0x2e94a840, 0x2afa0dd3, 0x100a99a6, 0x08677086, 0x32254eb5, 0x3aa34751, 0x14b183ef, 0x3d92}}, - {{0x1603a8a2, 0x1ff24fda, 0x07dd7077, 0x287edf5f, 0x2b4cf3ae, 0x24cd0a25, 0x29d7fc44, 0x007734be, 0x3d0d}}}, + {{{0x186154e5, 0x1d295080, 0x0be8374e, 0x0054cd35, 0x06770864, 0x04a9d6a4, 0x08d1d472, 0x18c1f7f5, 0x3d9252}}, + {{0x1603a8a2, 0x1fe49fb4, 0x1f75c1dd, 0x03f6faf8, 0x14cf3aea, 0x19a144b5, 0x15ff1124, 0x1b9a5f53, 0x3d0d01}}}, /* 15*16^13*G: */ - {{{0x2a4a8daa, 0x0ed8ed8a, 0x28a5ca3d, 0x041803bc, 0x0a968ce5, 0x3ad6d23d, 0x1769c760, 0x0e2c9a22, 0x2bbe}}, - {{0x1236e49b, 0x3821dd3a, 0x3eb6e7d7, 0x00ace938, 0x16085099, 0x33fbe47e, 0x3b36f5e2, 0x01fd8034, 0xf857}}} + {{{0x0a4a8daa, 0x1db1db15, 0x029728f4, 0x00c01de5, 0x0968ce51, 0x1ada47a5, 0x1a71d83a, 0x164d112e, 0x2bbe38}}, + {{0x1236e49b, 0x1043ba74, 0x1adb9f5f, 0x056749c7, 0x00850990, 0x1f7c8fcb, 0x0dbd78b3, 0x1ec01a76, 0xf85707}}} }, { /* 1*16^14*G: */ - {{{0x22d32936, 0x0c3eddc4, 0x2847f01c, 0x03340b8c, 0x3d7f38e4, 0x331f4544, 0x0a47d9f6, 0x03165e05, 0xc544}}, - {{0x07cabfd4, 0x290be8dd, 0x1e41e5d9, 0x29b4a18c, 0x2cf4acd8, 0x3078748f, 0x21fa72ed, 0x3a6e8e0f, 0xd27e}}}, + {{{0x02d32936, 0x187dbb89, 0x011fc070, 0x19a05c65, 0x17f38e40, 0x03e8a89e, 0x11f67db3, 0x0b2f0294, 0xc5440c}}, + {{0x07cabfd4, 0x1217d1ba, 0x19079766, 0x0da50c63, 0x0f4acd8a, 0x0f0e91f6, 0x1e9cbb70, 0x174707c3, 0xd27ee9}}}, /* 3*16^14*G: */ - {{{0x3989a8e1, 0x361407b1, 0x0ee4bdd7, 0x0765bcdd, 0x1cfe0a7c, 0x03811e6e, 0x3a79b750, 0x00f11737, 0x3e4d}}, - {{0x041c240a, 0x21e44e21, 0x3bd67409, 0x2bc6357c, 0x0aa719ff, 0x045f2b5f, 0x26475aac, 0x11342056, 0x12f7}}}, + {{{0x1989a8e1, 0x0c280f63, 0x1b92f75f, 0x1b2de6e9, 0x0fe0a7c1, 0x1023cdce, 0x1e6dd403, 0x188b9bf4, 0x3e4d03}}, + {{0x041c240a, 0x03c89c42, 0x0f59d026, 0x1e31abe7, 0x0a719ffa, 0x0be56be5, 0x11d6ab04, 0x1a102b4c, 0x12f744}}}, /* 5*16^14*G: */ - {{{0x19bb7902, 0x24e6a343, 0x2b7c73f6, 0x309b1ca1, 0x085e9fd8, 0x28927a51, 0x210359a9, 0x21126cf5, 0x01b6}}, - {{0x203ee653, 0x35fd12c7, 0x1836682c, 0x3ac9811c, 0x2d1581fc, 0x0663970d, 0x39c3e0bf, 0x18e87a4d, 0xe590}}}, + {{{0x19bb7902, 0x09cd4686, 0x0df1cfda, 0x04d8e50d, 0x05e9fd8c, 0x124f4a24, 0x00d66a68, 0x09367ac2, 0x1b684}}, + {{0x003ee653, 0x0bfa258f, 0x00d9a0b3, 0x164c08e3, 0x11581fce, 0x0c72e1b6, 0x10f82fc6, 0x143d26f3, 0xe59063}}}, /* 7*16^14*G: */ - {{{0x0371d9fe, 0x0a6d5b53, 0x199d6bbc, 0x12cd5b06, 0x2b3a4cf0, 0x25569f0e, 0x09ca2335, 0x0f2c6b33, 0x952c}}, - {{0x0189a13f, 0x1db39b49, 0x008c75ed, 0x11193c46, 0x2ce5d066, 0x3e44dbdb, 0x22f06a7d, 0x2151bdf5, 0x59b9}}}, + {{{0x0371d9fe, 0x14dab6a6, 0x0675aef0, 0x166ad833, 0x13a4cf04, 0x0ad3e1d5, 0x1288cd65, 0x16359993, 0x952c3c}}, + {{0x0189a13f, 0x1b673692, 0x0231d7b5, 0x08c9e230, 0x0e5d0664, 0x089b7b76, 0x1c1a9f7e, 0x08defac5, 0x59b985}}}, /* 9*16^14*G: */ - {{{0x0bc2c885, 0x11fff1da, 0x264e57c8, 0x147b9dd4, 0x17cde515, 0x2601142e, 0x26eac858, 0x13b856c5, 0xdfcb}}, - {{0x1345d92e, 0x1752990c, 0x3abe9757, 0x1dce251e, 0x2c0f411c, 0x13f09b20, 0x213a153c, 0x08e55541, 0x536a}}}, + {{{0x0bc2c885, 0x03ffe3b4, 0x19395f21, 0x03dceea4, 0x1cde5155, 0x002285cb, 0x1ab21626, 0x1c2b62cd, 0xdfcb4e}}, + {{0x1345d92e, 0x0ea53218, 0x0afa5d5d, 0x0e7128f7, 0x00f411c7, 0x1e136416, 0x0e854f13, 0x12aaa0c2, 0x536a23}}}, /* 11*16^14*G: */ - {{{0x3510208e, 0x0e2e14af, 0x0d794387, 0x23338b61, 0x3c97bbdb, 0x1ebce811, 0x2500c8a8, 0x19b026f9, 0x1579}}, - {{0x0d207357, 0x183bb894, 0x2da43dfd, 0x23f1910c, 0x0cbe0700, 0x3fdedeee, 0x2264eabd, 0x1b56adc4, 0x4044}}}, + {{{0x1510208e, 0x1c5c295f, 0x15e50e1c, 0x199c5b09, 0x097bbdb8, 0x179d023e, 0x00322a1e, 0x18137cca, 0x157966}}, + {{0x0d207357, 0x10777128, 0x1690f7f5, 0x1f8c8865, 0x0be07008, 0x1bdbddc6, 0x193aaf7f, 0x0b56e244, 0x40446d}}}, /* 13*16^14*G: */ - {{{0x0b96fe13, 0x327f32fa, 0x0852ea81, 0x2492b4ed, 0x3f6e23e4, 0x06a3fe04, 0x2990ad6e, 0x078f12c7, 0xc6b2}}, - {{0x37bb1417, 0x001ae5ab, 0x1e6d2d6a, 0x1954245e, 0x2b28a2ff, 0x2de078d3, 0x34d48e54, 0x337630cc, 0x335b}}}, + {{{0x0b96fe13, 0x04fe65f4, 0x014baa07, 0x0495a769, 0x16e23e49, 0x147fc09f, 0x042b5b86, 0x078963d3, 0xc6b21e}}, + {{0x17bb1417, 0x0035cb57, 0x19b4b5a8, 0x0aa122f3, 0x128a2ff6, 0x1c0f1a75, 0x1523952d, 0x1b186669, 0x335bcd}}}, /* 15*16^14*G: */ - {{{0x03936565, 0x0d96066b, 0x37fa4c7c, 0x29ecdb65, 0x1522d997, 0x2f2a754e, 0x3296f0b4, 0x39311e31, 0xa231}}, - {{0x35ec5f19, 0x2b95a818, 0x2f154268, 0x295b8025, 0x03cf942b, 0x253b1a20, 0x3be91c0d, 0x3262fb1f, 0x80e0}}} + {{{0x03936565, 0x1b2c0cd6, 0x1fe931f0, 0x0f66db2e, 0x122d997a, 0x054ea9ca, 0x05bc2d2f, 0x188f18e5, 0xa231e4}}, + {{0x15ec5f19, 0x172b5031, 0x1c5509a2, 0x0adc012d, 0x1cf942ba, 0x07634401, 0x1a470365, 0x117d8ff7, 0x80e0c9}}} }, { /* 1*16^15*G: */ - {{{0x3066fd48, 0x3e7d05ca, 0x0971583b, 0x0dc4072e, 0x3adca61c, 0x1e6e5e9a, 0x3f1c506c, 0x159e9089, 0x241c}}, - {{0x12857b08, 0x3df4b19e, 0x2a366057, 0x2a1c4e2b, 0x3203a48e, 0x0e05f010, 0x02d4b936, 0x0b64f50c, 0x40a6}}}, + {{{0x1066fd48, 0x1cfa0b95, 0x05c560ef, 0x0e203971, 0x0dca61c3, 0x0dcbd35d, 0x07141b1e, 0x0f4844fe, 0x241c56}}, + {{0x12857b08, 0x1be9633c, 0x08d9815f, 0x10e2715d, 0x003a48ea, 0x00be0219, 0x152e4d8e, 0x127a8605, 0x40a62d}}}, /* 3*16^15*G: */ - {{{0x0df9591d, 0x187df6e4, 0x2b4c82a8, 0x3b0eb090, 0x327218dc, 0x034f12ac, 0x178e9cba, 0x348ee09a, 0xde2f}}, - {{0x0457ad84, 0x13865cf4, 0x0c036a4b, 0x26a287e2, 0x392ebbda, 0x32dfb212, 0x243f305e, 0x1c44ced8, 0x400d}}}, + {{{0x0df9591d, 0x10fbedc8, 0x0d320aa1, 0x18758485, 0x07218dce, 0x09e25599, 0x03a72e83, 0x07704d2f, 0xde2fd2}}, + {{0x0457ad84, 0x070cb9e8, 0x100da92d, 0x15143f11, 0x12ebbda9, 0x1bf6425c, 0x0fcc17b2, 0x02676c48, 0x400d71}}}, /* 5*16^15*G: */ - {{{0x3562282c, 0x3aa0952b, 0x0fbc3772, 0x0bcebe4e, 0x211340f0, 0x2522c093, 0x0cbdd993, 0x226c0c13, 0x8df8}}, - {{0x21d195cd, 0x095aaf65, 0x2f9bb157, 0x1fdc1133, 0x0af35e24, 0x10798c62, 0x1ceed6c7, 0x16d9cc81, 0x7452}}}, + {{{0x1562282c, 0x15412a57, 0x1ef0ddcb, 0x1e75f271, 0x11340f02, 0x04581270, 0x0f7664e5, 0x16060999, 0x8df889}}, + {{0x01d195cd, 0x12b55ecb, 0x1e6ec55c, 0x1ee0899d, 0x0f35e247, 0x0f318c45, 0x1bb5b1d0, 0x0ce640b9, 0x74525b}}}, /* 7*16^15*G: */ - {{{0x0dddb2dd, 0x2754a254, 0x02c0da6f, 0x22193373, 0x12f24507, 0x3ee033c5, 0x380f8001, 0x1d633662, 0xa0fd}}, - {{0x33ede6b2, 0x3f653fe1, 0x1409a7c7, 0x233a5be2, 0x308f311c, 0x247f4c4e, 0x368d5f86, 0x360d704c, 0x53e5}}}, + {{{0x0dddb2dd, 0x0ea944a8, 0x0b0369be, 0x10c99b98, 0x0f245078, 0x1c0678a9, 0x03e0007e, 0x119b3170, 0xa0fd75}}, + {{0x13ede6b2, 0x1eca7fc3, 0x10269f1f, 0x19d2df12, 0x08f311c8, 0x0fe989d8, 0x0357e1a4, 0x06b8266d, 0x53e5d8}}}, /* 9*16^15*G: */ - {{{0x0f542e36, 0x0232ea81, 0x13415c2e, 0x08bfebe8, 0x2335d84e, 0x16499e51, 0x1a0f67de, 0x31611cb4, 0x3170}}, - {{0x363288b5, 0x1b11d6bb, 0x199be1bc, 0x1bdd5a56, 0x39773d00, 0x05424ffa, 0x27fe2375, 0x0d84bf0e, 0xb208}}}, + {{{0x0f542e36, 0x0465d502, 0x0d0570b8, 0x05ff5f42, 0x135d84e2, 0x0933ca31, 0x03d9f796, 0x108e5a34, 0x3170c5}}, + {{0x163288b5, 0x1623ad77, 0x066f86f1, 0x1eead2b3, 0x1773d006, 0x0849ff5c, 0x1f88dd45, 0x025f874f, 0xb20836}}}, /* 11*16^15*G: */ - {{{0x1c7548e9, 0x266c8e97, 0x092d54c7, 0x376a01c2, 0x063fe5d8, 0x1205a53c, 0x13e029db, 0x2c2a428b, 0x92fa}}, - {{0x0917758f, 0x31c4b341, 0x32d08488, 0x28371a3b, 0x2679ffc8, 0x05c53830, 0x246bcf43, 0x2d1a032c, 0x55e7}}}, + {{{0x1c7548e9, 0x0cd91d2e, 0x04b5531e, 0x1b500e11, 0x03fe5d8d, 0x00b4a783, 0x180a76d2, 0x152145a7, 0x92fab0}}, + {{0x0917758f, 0x03896682, 0x0b421223, 0x01b8d1de, 0x079ffc8a, 0x18a70613, 0x1af3d0c5, 0x0d019648, 0x55e7b4}}}, /* 13*16^15*G: */ - {{{0x1498f7f8, 0x0360142e, 0x2411622e, 0x37d9f4c9, 0x2c8712c4, 0x2f846c64, 0x355179d0, 0x196f8600, 0x91b0}}, - {{0x3f23195b, 0x31d03678, 0x389639e3, 0x0b1ed095, 0x17e264df, 0x3fcd2400, 0x31620ff9, 0x1bddfed9, 0x035b}}}, + {{{0x1498f7f8, 0x06c0285c, 0x104588b8, 0x1ecfa64c, 0x08712c4d, 0x108d8c96, 0x145e742f, 0x17c3006a, 0x91b065}}, + {{0x1f23195b, 0x03a06cf1, 0x0258e78f, 0x18f684af, 0x1e264df2, 0x19a4800b, 0x1883fe7f, 0x0eff6ce2, 0x35b6f}}}, /* 15*16^15*G: */ - {{{0x0060e322, 0x0772fb89, 0x1c4d14b5, 0x3371cdea, 0x1ab9923e, 0x241a5d22, 0x1cb3a9c3, 0x07d332b2, 0x8e4a}}, - {{0x104619d7, 0x38860f36, 0x14fbfe04, 0x002a6365, 0x2e7bc4fb, 0x017b4901, 0x0d7752fb, 0x2dd7acca, 0x4936}}} + {{{0x0060e322, 0x0ee5f712, 0x113452d4, 0x1b8e6f53, 0x0b9923ec, 0x034ba44d, 0x0cea70e4, 0x09995939, 0x8e4a1f}}, + {{0x104619d7, 0x110c1e6c, 0x13eff813, 0x01531b2a, 0x07bc4fb0, 0x0f692037, 0x1dd4bec1, 0x0bd6651a, 0x4936b7}}} }, { /* 1*16^16*G: */ - {{{0x0e14db63, 0x039d72d2, 0x1651f7e9, 0x124eeaab, 0x2e25de29, 0x0964b8c9, 0x1aaa5849, 0x08af0a04, 0x0fa8}}, - {{0x1f462ee7, 0x10449151, 0x0fe82f5e, 0x2c699414, 0x1f188b34, 0x2b52f2cf, 0x3a80d6f4, 0x12ba3d76, 0xbff4}}}, + {{{0x0e14db63, 0x073ae5a4, 0x1947dfa4, 0x1277555a, 0x025de294, 0x0c971937, 0x0a961249, 0x17850235, 0xfa822}}, + {{0x1f462ee7, 0x008922a2, 0x1fa0bd79, 0x034ca0a1, 0x1188b34b, 0x0a5e59ef, 0x0035bd2b, 0x1d1ebb75, 0xbff44a}}}, /* 3*16^16*G: */ - {{{0x3db3cdec, 0x14b114fd, 0x228ebf57, 0x3bce84ac, 0x2a4bc8db, 0x199179ef, 0x12f5ce59, 0x30193fe4, 0x85b2}}, - {{0x0a03f81f, 0x3d342081, 0x24cf8e08, 0x2602cd39, 0x0c6d00dc, 0x1fe8b4bf, 0x1153663c, 0x09e3ce74, 0xf64b}}}, + {{{0x1db3cdec, 0x096229fb, 0x0a3afd5d, 0x1e742564, 0x04bc8dbe, 0x122f3df5, 0x1d739659, 0x0c9ff225, 0x85b2c0}}, + {{0x0a03f81f, 0x1a684102, 0x133e3823, 0x101669cc, 0x06d00dc9, 0x1d1697e6, 0x14d98f1f, 0x11e73a22, 0xf64b27}}}, /* 5*16^16*G: */ - {{{0x0607b030, 0x22296b92, 0x184d6732, 0x36bfd8f9, 0x16f29c24, 0x07eeb3b0, 0x21467785, 0x00ddb100, 0x110b}}, - {{0x33617c3a, 0x10ea844a, 0x3298749f, 0x2f8555be, 0x21c70c87, 0x3ae27e11, 0x2e6734c6, 0x0ae14c63, 0x8443}}}, + {{{0x0607b030, 0x0452d724, 0x01359cca, 0x15fec7cb, 0x0f29c24d, 0x1dd6760b, 0x119de147, 0x0ed88042, 0x110b03}}, + {{0x13617c3a, 0x01d50895, 0x0a61d27d, 0x1c2aadf6, 0x1c70c87b, 0x1c4fc230, 0x19cd31ba, 0x10a631dc, 0x84432b}}}, /* 7*16^16*G: */ - {{{0x35a76f08, 0x13b76071, 0x3bbed4e5, 0x257c94e2, 0x1caaf832, 0x1b8490ac, 0x071d714f, 0x139127d9, 0x1878}}, - {{0x2b824993, 0x2ce58175, 0x20a25320, 0x275d29e9, 0x31e671fc, 0x1ea3f6b1, 0x21ae7177, 0x3b5fd287, 0x8d76}}}, + {{{0x15a76f08, 0x076ec0e3, 0x0efb5395, 0x0be4a717, 0x0aaf8329, 0x1092158e, 0x075c53db, 0x0893ec8e, 0x18784e}}, + {{0x0b824993, 0x19cb02eb, 0x02894c82, 0x1ae94f4c, 0x1e671fc9, 0x147ed638, 0x0b9c5dde, 0x0fe943c3, 0x8d76ed}}}, /* 9*16^16*G: */ - {{{0x3a6fad81, 0x3a38cf27, 0x00cb03ec, 0x0cd95d23, 0x3a037d9c, 0x15b75dc0, 0x1e6b9aef, 0x3e781f41, 0x58a2}}, - {{0x3b109594, 0x10018578, 0x1300b825, 0x22ecb4cb, 0x3fa6bd79, 0x1a0be1c5, 0x160e0c1b, 0x19316b15, 0x06ab}}}, + {{{0x1a6fad81, 0x14719e4f, 0x032c0fb3, 0x06cae918, 0x0037d9c3, 0x16ebb81d, 0x1ae6bbd5, 0x1c0fa0bc, 0x58a2f9}}, + {{0x1b109594, 0x00030af1, 0x0c02e095, 0x1765a65a, 0x1a6bd798, 0x017c38bf, 0x038306da, 0x18b58aac, 0x6ab64}}}, /* 11*16^16*G: */ - {{{0x1eb52583, 0x2c8bc47e, 0x10cc13af, 0x22a673b0, 0x0f676fea, 0x39b6ec9e, 0x2bba240e, 0x0837339f, 0x1ef0}}, - {{0x3a3f17ae, 0x16c9e065, 0x012d4cb5, 0x30c03e5c, 0x1695306a, 0x3db03d2e, 0x214b0097, 0x1dac969e, 0x5944}}}, + {{{0x1eb52583, 0x191788fc, 0x03304ebe, 0x15339d82, 0x1676fea8, 0x16dd93c7, 0x0e8903b9, 0x1b99cfd7, 0x1ef020}}, + {{0x1a3f17ae, 0x0d93c0cb, 0x04b532d5, 0x0601f2e0, 0x095306ac, 0x1607a5cb, 0x12c025fd, 0x164b4f42, 0x594476}}}, /* 13*16^16*G: */ - {{{0x30a1958f, 0x1708fb07, 0x3b56643b, 0x0e6d491b, 0x3fa32c4f, 0x345133ea, 0x2a21395d, 0x2058f075, 0x4e4a}}, - {{0x08636f8a, 0x10ecfd45, 0x2c43d66a, 0x010217ec, 0x1c6fa840, 0x3d28fb8a, 0x0c8d1033, 0x2916de7a, 0x2574}}}, + {{{0x10a1958f, 0x0e11f60f, 0x0d5990ed, 0x136a48df, 0x1a32c4f3, 0x0a267d5f, 0x084e5774, 0x0c783ad4, 0x4e4a81}}, + {{0x08636f8a, 0x01d9fa8a, 0x110f59a9, 0x0810bf65, 0x06fa8400, 0x051f714e, 0x03440cfd, 0x0b6f3d19, 0x2574a4}}}, /* 15*16^16*G: */ - {{{0x24935db5, 0x209d6a11, 0x06bdb0ee, 0x05e60987, 0x14519e28, 0x09f83b56, 0x21104e33, 0x1a85ab75, 0xf696}}, - {{0x1d166838, 0x28d20db0, 0x001bf013, 0x1d14e8d1, 0x3c755e2d, 0x17b95cb0, 0x31db2c1a, 0x38c1ea40, 0xba0d}}} + {{{0x04935db5, 0x013ad423, 0x1af6c3ba, 0x0f304c38, 0x0519e281, 0x1f076aca, 0x04138cc9, 0x02d5bac2, 0xf6966a}}, + {{0x1d166838, 0x11a41b60, 0x006fc04e, 0x08a74688, 0x0755e2d7, 0x172b961e, 0x16cb0697, 0x00f52063, 0xba0de3}}} }, { /* 1*16^17*G: */ - {{{0x376a6987, 0x23d04c16, 0x3da43ff6, 0x1206ad10, 0x2e1b3f2b, 0x31a6235f, 0x099547dd, 0x0635ea66, 0x54bc}}, - {{0x1b9aae49, 0x3915f341, 0x373b119f, 0x3ae3b52e, 0x33e2fd52, 0x06e146e9, 0x2eaf3739, 0x23048479, 0x4b2c}}}, + {{{0x176a6987, 0x07a0982d, 0x1690ffda, 0x10356887, 0x01b3f2b4, 0x14c46bf7, 0x0551f771, 0x1af53313, 0x54bc18}}, + {{0x1b9aae49, 0x122be682, 0x1cec467f, 0x171da976, 0x1e2fd52e, 0x1c28dd39, 0x0bcdce46, 0x02423cdd, 0x4b2c8c}}}, /* 3*16^17*G: */ - {{{0x3d1fd820, 0x22fd1fd7, 0x07675003, 0x21e15192, 0x31271b78, 0x0d40898a, 0x1c52aa86, 0x2f3da030, 0xbafb}}, - {{0x1bf074f0, 0x2bb6b548, 0x31fcad6e, 0x070d2848, 0x1bc0fde8, 0x1efd6b22, 0x0dd812ce, 0x265f276d, 0x1487}}}, + {{{0x1d1fd820, 0x05fa3faf, 0x1d9d400e, 0x0f0a8c90, 0x1271b788, 0x08113158, 0x14aaa18d, 0x1ed01838, 0xbafbbc}}, + {{0x1bf074f0, 0x176d6a90, 0x07f2b5ba, 0x18694246, 0x1c0fde81, 0x1fad644d, 0x1604b39e, 0x0f93b69b, 0x148799}}}, /* 5*16^17*G: */ - {{{0x14299b7e, 0x245c204a, 0x186e0d0e, 0x39e7cb42, 0x0220ec24, 0x30eff1d7, 0x389fe2a3, 0x0e3dc40c, 0x9b19}}, - {{0x047b84de, 0x15eca15d, 0x06b8232c, 0x337a147e, 0x2a3ec90a, 0x03a63872, 0x10283314, 0x2a9bbc5c, 0xfb12}}}, + {{{0x14299b7e, 0x08b84094, 0x01b8343a, 0x0f3e5a13, 0x020ec24e, 0x1dfe3ae1, 0x07f8a8f0, 0x1ee20671, 0x9b1938}}, + {{0x047b84de, 0x0bd942ba, 0x1ae08cb1, 0x1bd0a3f0, 0x03ec90ac, 0x14c70e55, 0x0a0cc503, 0x0dde2e20, 0xfb12aa}}}, /* 7*16^17*G: */ - {{{0x110cc4c4, 0x35041d03, 0x0a53da0f, 0x074d68b1, 0x361b2cb7, 0x207f7019, 0x175907c3, 0x06617300, 0xa677}}, - {{0x3c976570, 0x083cec8d, 0x2ff3094c, 0x1d15dce9, 0x1d9c3dbc, 0x2f598079, 0x0dd98f29, 0x18617dd4, 0x8550}}}, + {{{0x110cc4c4, 0x0a083a06, 0x094f683f, 0x1a6b4589, 0x01b2cb71, 0x0fee033b, 0x1641f0e0, 0x10b9802e, 0xa67719}}, + {{0x1c976570, 0x1079d91b, 0x1fcc2530, 0x08aee74d, 0x19c3dbc7, 0x0b300f2e, 0x1663ca6f, 0x10beea1b, 0x855061}}}, /* 9*16^17*G: */ - {{{0x14242a28, 0x104200b5, 0x13ca7715, 0x16f2c849, 0x374eca45, 0x22bde12d, 0x2afc109e, 0x3b54dac3, 0x88b7}}, - {{0x394ed8ce, 0x2e5a07b1, 0x383e347f, 0x0d9a8723, 0x07bd934e, 0x2fe774d6, 0x1345e47f, 0x14c81891, 0x22b0}}}, + {{{0x14242a28, 0x0084016a, 0x0f29dc55, 0x1796424a, 0x14eca455, 0x17bc25bb, 0x1f0427a2, 0x0a6d61d5, 0x88b7ed}}, + {{0x194ed8ce, 0x1cb40f63, 0x00f8d1fe, 0x0cd4391f, 0x1bd934e3, 0x1cee9ac3, 0x11791fef, 0x040c48a6, 0x22b053}}}, /* 11*16^17*G: */ - {{{0x1bc1a94c, 0x058513b2, 0x271daf80, 0x19c74acf, 0x1e875751, 0x35cac089, 0x2b3d2052, 0x05004aa1, 0x0371}}, - {{0x2fc2073c, 0x30302db3, 0x2c424838, 0x14630d8a, 0x105335c8, 0x3086952b, 0x17390ef8, 0x1a4f5477, 0x4d1d}}}, + {{{0x1bc1a94c, 0x0b0a2764, 0x1c76be00, 0x0e3a567c, 0x08757516, 0x1958112f, 0x0f4814b5, 0x002550d6, 0x37114}}, + {{0x0fc2073c, 0x00605b67, 0x110920e3, 0x03186c55, 0x05335c85, 0x10d2a568, 0x0e43be30, 0x07aa3bae, 0x4d1d69}}}, /* 13*16^17*G: */ - {{{0x077f88ba, 0x3ef47826, 0x29bed36e, 0x2601de7b, 0x2a2cc350, 0x168cba13, 0x0293e34b, 0x08532261, 0xcc98}}, - {{0x07885278, 0x2918bbf2, 0x3354c4e0, 0x3d839fbb, 0x3d63abef, 0x3129919d, 0x1afa9114, 0x2d3a3949, 0x04eb}}}, + {{{0x077f88ba, 0x1de8f04c, 0x06fb4dbb, 0x100ef3dd, 0x02cc3509, 0x11974275, 0x04f8d2d6, 0x09913085, 0xcc9821}}, + {{0x07885278, 0x123177e4, 0x0d531382, 0x0c1cfdde, 0x163abeff, 0x053233be, 0x1ea44531, 0x1d1ca4b5, 0x4ebb4}}}, /* 15*16^17*G: */ - {{{0x3d70187c, 0x15cc6537, 0x3640c7f1, 0x06b218a6, 0x0f5bf875, 0x139780a4, 0x2a10f981, 0x2b80a690, 0x0ad3}}, - {{0x3fc775a7, 0x37ff3d2c, 0x262a0f67, 0x0d3ec205, 0x2bb33dd0, 0x3157c17e, 0x046e3785, 0x10351d62, 0x2af0}}} + {{{0x1d70187c, 0x0b98ca6f, 0x19031fc5, 0x1590c536, 0x15bf8751, 0x12f01487, 0x043e6053, 0x00534854, 0xad3ae}}, + {{0x1fc775a7, 0x0ffe7a59, 0x18a83d9f, 0x09f6102c, 0x1b33dd03, 0x0af82fd5, 0x1b8de171, 0x1a8eb108, 0x2af040}}} }, { /* 1*16^18*G: */ - {{{0x30aae231, 0x02abeb45, 0x1f96b7c6, 0x252e149e, 0x27756f51, 0x09208e49, 0x1e3f285f, 0x325a65d8, 0x1d35}}, - {{0x0cd6ac71, 0x219c18eb, 0x29a66f15, 0x3d62a91c, 0x2bf810ed, 0x182ad88b, 0x208231d6, 0x1b2d8b7d, 0xc722}}}, + {{{0x10aae231, 0x0557d68b, 0x1e5adf18, 0x0970a4f3, 0x1756f519, 0x0411c933, 0x0fca17c9, 0x0d32ec3c, 0x1d35c9}}, + {{0x0cd6ac71, 0x033831d6, 0x0699bc56, 0x0b1548e5, 0x1f810edf, 0x055b1175, 0x008c7598, 0x16c5bec1, 0xc7226c}}}, /* 3*16^18*G: */ - {{{0x0cfa3fac, 0x3834ff86, 0x32b8193c, 0x2b61a7f0, 0x0d803023, 0x3aed1758, 0x2234ce2c, 0x1011e9b4, 0xdf3d}}, - {{0x0fc7d419, 0x1189b64e, 0x2882975f, 0x358f3925, 0x0f9dbfaf, 0x2887ca70, 0x140db24a, 0x1bd48a7f, 0x48fa}}}, + {{{0x0cfa3fac, 0x1069ff0c, 0x0ae064f3, 0x1b0d3f86, 0x1803023a, 0x1da2eb06, 0x0d338b3a, 0x08f4da44, 0xdf3d40}}, + {{0x0fc7d419, 0x03136c9c, 0x020a5d7d, 0x0c79c92d, 0x19dbfafd, 0x10f94e07, 0x036c92a8, 0x0a453fa8, 0x48fa6f}}}, /* 5*16^18*G: */ - {{{0x1f1322d4, 0x3b6496b8, 0x2ccdcbba, 0x029a5012, 0x11f822cb, 0x39b1328c, 0x16144ea1, 0x2bdaac7e, 0xdbb2}}, - {{0x0a8c5311, 0x2924ad3d, 0x37e3a5fa, 0x27f25e1e, 0x033f9d9a, 0x18347b59, 0x3561aa1b, 0x1d6e4bc4, 0xebae}}}, + {{{0x1f1322d4, 0x16c92d70, 0x13372eeb, 0x14d28095, 0x1f822cb0, 0x16265188, 0x0513a879, 0x0d563f2c, 0xdbb2af}}, + {{0x0a8c5311, 0x12495a7a, 0x1f8e97ea, 0x1f92f0f6, 0x13f9d9a9, 0x068f6b21, 0x186a86d8, 0x1725e26a, 0xebae75}}}, /* 7*16^18*G: */ - {{{0x21138f7b, 0x01a68cf2, 0x1f2e8f2f, 0x30724f8b, 0x1b5f0bc4, 0x2a2899fe, 0x21fd4caf, 0x1ed65fc9, 0x1dba}}, - {{0x239bf268, 0x320b631e, 0x18232c0d, 0x0db9ade6, 0x0007f581, 0x06401aee, 0x3efc63ae, 0x1f4f9779, 0x6aaf}}}, + {{{0x01138f7b, 0x034d19e5, 0x1cba3cbc, 0x03927c5b, 0x15f0bc4c, 0x05133fcd, 0x1f532bea, 0x0b2fe4c3, 0x1dba7b}}, + {{0x039bf268, 0x0416c63d, 0x008cb037, 0x0dcd6f33, 0x007f5813, 0x08035dc0, 0x1f18eb86, 0x07cbbcfd, 0x6aaf7d}}}, /* 9*16^18*G: */ - {{{0x179a70af, 0x36a1ddc0, 0x364df288, 0x2750a6a6, 0x1305c6ec, 0x2fa0b57d, 0x2919d31b, 0x0b910989, 0x348a}}, - {{0x07b66e82, 0x2a121852, 0x3e13e5ac, 0x29f0b16d, 0x230105b2, 0x11ef3800, 0x23e808c7, 0x3e9e7d56, 0xa1b9}}}, + {{{0x179a70af, 0x0d43bb80, 0x1937ca23, 0x1a853536, 0x105c6ec9, 0x1416afa9, 0x0674c6ef, 0x0884c4d2, 0x348a2e}}, + {{0x07b66e82, 0x142430a4, 0x184f96b2, 0x0f858b6f, 0x10105b2a, 0x1de70011, 0x1a0231d1, 0x0f3eab47, 0xa1b9fa}}}, /* 11*16^18*G: */ - {{{0x04d3a201, 0x1d1db5db, 0x19b9eefc, 0x3a49a93f, 0x1adf5f36, 0x293efe4c, 0x09e1ca86, 0x32146667, 0x3a4e}}, - {{0x28635f89, 0x36165bdd, 0x33cd55bd, 0x34c796bd, 0x374a8b27, 0x00f04691, 0x262de69e, 0x0bbe0bd8, 0xc99a}}}, + {{{0x04d3a201, 0x1a3b6bb6, 0x06e7bbf1, 0x124d49fb, 0x0df5f36e, 0x07dfc98d, 0x1872a1a9, 0x0a333393, 0x3a4ec8}}, + {{0x08635f89, 0x0c2cb7bb, 0x0f3556f7, 0x063cb5ee, 0x14a8b27d, 0x1e08d23b, 0x0b79a780, 0x1f05ec4c, 0xc99a2e}}}, /* 13*16^18*G: */ - {{{0x1c978567, 0x3beb9cbf, 0x0dc1f981, 0x1769a210, 0x31f60be1, 0x24d758bf, 0x0d45784e, 0x14b620cd, 0xb1ba}}, - {{0x362dc291, 0x1fe920a8, 0x2fcd40a7, 0x291b2c2e, 0x1bb78fd9, 0x3df3dc4f, 0x143a77c5, 0x2bb1ea1a, 0xa46b}}}, + {{{0x1c978567, 0x17d7397e, 0x1707e607, 0x1b4d1081, 0x1f60be15, 0x1aeb17f8, 0x115e13a4, 0x1b10669a, 0xb1ba52}}, + {{0x162dc291, 0x1fd24151, 0x1f35029d, 0x08d96175, 0x1b78fd9a, 0x1e7b89ed, 0x0e9df17d, 0x18f50d28, 0xa46bae}}}, /* 15*16^18*G: */ - {{{0x12350da1, 0x08a3ba94, 0x175f043d, 0x10531df0, 0x212c2f19, 0x22dee5a5, 0x2aafd271, 0x3acf63bc, 0x0ae6}}, - {{0x30a14bc3, 0x1cf827cd, 0x143da4bc, 0x351a3c3b, 0x0189b566, 0x00d3dff1, 0x06cae2dd, 0x3ba7ed80, 0x99cd}}} + {{{0x12350da1, 0x11477528, 0x1d7c10f4, 0x0298ef82, 0x12c2f194, 0x1bdcb4b0, 0x0bf49c62, 0x07b1de55, 0xae6eb}}, + {{0x10a14bc3, 0x19f04f9b, 0x10f692f1, 0x08d1e1da, 0x189b566d, 0x1a7bfe20, 0x12b8b740, 0x13f6c00d, 0x99cdee}}} }, { /* 1*16^19*G: */ - {{{0x350e4f5f, 0x15cabaa1, 0x167e0e65, 0x3d72a6a9, 0x02f29acb, 0x3fc3dea8, 0x35aef388, 0x2a566112, 0x55d9}}, - {{0x3ca97db0, 0x2163adda, 0x3ad1b15c, 0x2604318c, 0x08ec524c, 0x355d3ef3, 0x2d203766, 0x1fe6a976, 0x69cb}}}, + {{{0x150e4f5f, 0x0b957543, 0x19f83995, 0x0b95354a, 0x0f29acbf, 0x187bd501, 0x0bbce23f, 0x0b30896b, 0x55d9a9}}, + {{0x1ca97db0, 0x02c75bb5, 0x0b46c572, 0x10218c67, 0x0ec524c9, 0x0ba7de64, 0x080dd9b5, 0x1354bb5a, 0x69cb7f}}}, /* 3*16^19*G: */ - {{{0x3eb142e9, 0x01aa621f, 0x207fcfbc, 0x1dbac191, 0x2ed480c1, 0x361a0e3e, 0x33e11794, 0x10faf91b, 0x4b00}}, - {{0x22c68552, 0x12cb14b5, 0x21258880, 0x08ca43ce, 0x222d870f, 0x1e2118d8, 0x1ac1adb1, 0x33c8e8c3, 0x173c}}}, + {{{0x1eb142e9, 0x0354c43f, 0x01ff3ef0, 0x0dd60c8c, 0x0d480c17, 0x0341c7d7, 0x1845e536, 0x1d7c8de7, 0x4b0043}}, + {{0x02c68552, 0x0596296b, 0x04962201, 0x06521e74, 0x02d870f2, 0x04231b11, 0x106b6c5e, 0x047461b5, 0x173ccf}}}, /* 5*16^19*G: */ - {{{0x17f1aa96, 0x1b752b9c, 0x0ff6481f, 0x35e97dcd, 0x3463c513, 0x0a372edc, 0x16fc2327, 0x349e64ab, 0x79ea}}, - {{0x0b0a3fb7, 0x02e9c739, 0x1b3955a8, 0x2135c444, 0x256542de, 0x390e4d58, 0x2dabf1a6, 0x3a73feea, 0xa95d}}}, + {{{0x17f1aa96, 0x16ea5738, 0x1fd9207d, 0x0f4bee69, 0x063c513d, 0x06e5db9a, 0x1f08c9ca, 0x0f3255ad, 0x79ead2}}, + {{0x0b0a3fb7, 0x05d38e72, 0x0ce556a0, 0x09ae2223, 0x16542de8, 0x01c9ab12, 0x0afc69b9, 0x19ff755b, 0xa95de9}}}, /* 7*16^19*G: */ - {{{0x393a9ae6, 0x201729cb, 0x077f8adc, 0x382a8167, 0x2d743f8e, 0x1e78d8c6, 0x1a1ceb52, 0x00143c93, 0x318e}}, - {{0x1c447d79, 0x212d5a53, 0x2d3a8ee1, 0x14dbf6eb, 0x104bd094, 0x05f29479, 0x29299f4d, 0x3b844673, 0x2792}}}, + {{{0x193a9ae6, 0x002e5397, 0x1dfe2b72, 0x01540b38, 0x1743f8ee, 0x0f1b18d6, 0x073ad49e, 0x0a1e49b4, 0x318e00}}, + {{0x1c447d79, 0x025ab4a6, 0x14ea3b86, 0x06dfb75d, 0x04bd0945, 0x1e528f28, 0x0a67d345, 0x022339d2, 0x2792ee}}}, /* 9*16^19*G: */ - {{{0x1d30585a, 0x0de516d3, 0x35014951, 0x3fe286a8, 0x00a4b495, 0x00cbd243, 0x1e43bb88, 0x151c74bc, 0x6bbc}}, - {{0x348b05f3, 0x2be5fbbc, 0x2f9ead96, 0x3c10a040, 0x2226be09, 0x3b8ac57c, 0x129f04a9, 0x0626c305, 0x467b}}}, + {{{0x1d30585a, 0x1bca2da6, 0x14052544, 0x1f143546, 0x0a4b495f, 0x197a4860, 0x10eee200, 0x0e3a5e3c, 0x6bbc54}}, + {{0x148b05f3, 0x17cbf779, 0x1e7ab65a, 0x00850205, 0x026be09f, 0x1158af91, 0x07c12a7b, 0x136182a5, 0x467b18}}}, /* 11*16^19*G: */ - {{{0x00136275, 0x1893e023, 0x38775352, 0x11f0005c, 0x360d78a6, 0x146a43dd, 0x1fd1189b, 0x12318430, 0x9401}}, - {{0x1997aa47, 0x358e8445, 0x04e1a425, 0x12ceb958, 0x05d6695d, 0x09312ad4, 0x3a4f77aa, 0x3e57c4d9, 0x6967}}}, + {{{0x00136275, 0x1127c046, 0x01dd4d49, 0x0f8002e7, 0x00d78a64, 0x0d487bbb, 0x144626d4, 0x18c2183f, 0x940148}}, + {{0x1997aa47, 0x0b1d088a, 0x13869097, 0x1675cac0, 0x1d6695d4, 0x06255a82, 0x13ddea89, 0x0be26cf4, 0x6967f9}}}, /* 13*16^19*G: */ - {{{0x1f0fe850, 0x0e84f74e, 0x111a7bdc, 0x1348c2f9, 0x25f98e86, 0x15b24a36, 0x1b49c91b, 0x0ce4980e, 0xc418}}, - {{0x3d38666d, 0x0d63d11a, 0x01a0af01, 0x169fb278, 0x2fd55806, 0x0257509a, 0x00f7aeb8, 0x3fb27235, 0x3537}}}, + {{{0x1f0fe850, 0x1d09ee9c, 0x0469ef70, 0x1a4617ca, 0x1f98e864, 0x164946d2, 0x127246d5, 0x124c0736, 0xc41833}}, + {{0x1d38666d, 0x1ac7a235, 0x0682bc04, 0x14fd93c0, 0x1d558065, 0x0aea1357, 0x1debae02, 0x19391a81, 0x3537fe}}}, /* 15*16^19*G: */ - {{{0x34937fbe, 0x3f9104dd, 0x051ba6ec, 0x2c13777c, 0x16f546c0, 0x050006be, 0x27d70e0c, 0x28fd89f1, 0x2bab}}, - {{0x173a1df4, 0x0e43955d, 0x0ac81109, 0x0b712c64, 0x0eabc9ec, 0x0ec33649, 0x08b88d78, 0x31d96c88, 0x77e5}}} + {{{0x14937fbe, 0x1f2209bb, 0x146e9bb3, 0x009bbbe0, 0x0f546c0b, 0x0000d7cb, 0x15c38305, 0x1ec4f8cf, 0x2baba3}}, + {{0x173a1df4, 0x1c872aba, 0x0b204424, 0x1b896321, 0x0abc9ec2, 0x1866c927, 0x0e235e0e, 0x0cb64411, 0x77e5c7}}} }, { /* 1*16^20*G: */ - {{{0x0351964c, 0x134f4b79, 0x35412c1d, 0x1a490ddb, 0x355c0834, 0x2af28615, 0x0c47fae5, 0x3e566f8a, 0x6e29}}, - {{0x163fd88f, 0x062092f5, 0x20bfb631, 0x1903149e, 0x04246def, 0x0bb1b306, 0x332f6505, 0x1767d403, 0x3456}}}, + {{{0x0351964c, 0x069e96f2, 0x1504b075, 0x12486ede, 0x15c08346, 0x1e50c2ba, 0x11feb96a, 0x0b37c518, 0x6e29f9}}, + {{0x163fd88f, 0x0c4125ea, 0x02fed8c4, 0x0818a4f4, 0x0246def6, 0x163660c2, 0x0bd9414b, 0x13ea01e6, 0x34565d}}}, /* 3*16^20*G: */ - {{{0x0c0e49cc, 0x3e54040e, 0x3c5400d3, 0x08cb6a16, 0x3740ed41, 0x0a237b2e, 0x30f6edd8, 0x352a5e25, 0xd691}}, - {{0x100f4152, 0x342ed307, 0x2d043f2d, 0x16f8740a, 0x3e0c52ac, 0x2ef6d5d8, 0x0f397f7f, 0x39e1d2de, 0x7a79}}}, + {{{0x0c0e49cc, 0x1ca8081c, 0x1150034f, 0x065b50b7, 0x140ed412, 0x046f65db, 0x1dbb760a, 0x152f12e1, 0xd691d4}}, + {{0x100f4152, 0x085da60e, 0x1410fcb7, 0x17c3a055, 0x00c52ac5, 0x1edabb1f, 0x0e5fdfee, 0x10e96f1e, 0x7a79e7}}}, /* 5*16^20*G: */ - {{{0x2b9b930a, 0x361dae7c, 0x130f58f3, 0x2c4d4a91, 0x3bbc49de, 0x16df7de9, 0x0d7c5dee, 0x1a11a8b8, 0x2a5d}}, - {{0x3b2caeca, 0x1bfcd17c, 0x22716858, 0x16dcd0d7, 0x04ab58ea, 0x33c0e40f, 0x2476de5c, 0x1f025a1d, 0xdc3d}}}, + {{{0x0b9b930a, 0x0c3b5cf9, 0x0c3d63cf, 0x026a548a, 0x1bc49deb, 0x1befbd3d, 0x1f177b96, 0x08d45c1a, 0x2a5d68}}, + {{0x1b2caeca, 0x17f9a2f9, 0x09c5a161, 0x16e686bc, 0x0ab58ea5, 0x181c81e2, 0x1db79733, 0x012d0ec8, 0xdc3d7c}}}, /* 7*16^20*G: */ - {{{0x016959ef, 0x29f72f4a, 0x01db59af, 0x1e74159d, 0x275df876, 0x10c504b8, 0x3b5262f0, 0x125a8e26, 0x8764}}, - {{0x20cd5010, 0x180c472f, 0x2f9e3f16, 0x15ab505c, 0x2d961f28, 0x2d049e5b, 0x02ffd9e0, 0x1a758740, 0x599b}}}, + {{{0x016959ef, 0x13ee5e94, 0x076d66be, 0x13a0ace8, 0x15df8767, 0x18a09713, 0x1498bc10, 0x0d471376, 0x876449}}, + {{0x00cd5010, 0x10188e5f, 0x1e78fc59, 0x0d5a82e5, 0x1961f285, 0x0093cb76, 0x1ff6782d, 0x1ac3a005, 0x599b69}}}, /* 9*16^20*G: */ - {{{0x3aef0f84, 0x0e502738, 0x31c75b96, 0x2ed41aa1, 0x2db8cab0, 0x38feb05e, 0x071b133d, 0x24ef2049, 0x94d3}}, - {{0x378ba7c1, 0x16b986e4, 0x0acf12a8, 0x0fd00994, 0x239a07dd, 0x32f0e1ac, 0x363f21e1, 0x1aad3ad2, 0x5a82}}}, + {{{0x1aef0f84, 0x1ca04e71, 0x071d6e58, 0x16a0d50e, 0x1b8cab0b, 0x1fd60bd6, 0x06c4cf78, 0x1790248e, 0x94d393}}, + {{0x178ba7c1, 0x0d730dc9, 0x0b3c4aa1, 0x1e804ca1, 0x19a07dd3, 0x1e1c3591, 0x0fc87872, 0x169d696c, 0x5a826a}}}, /* 11*16^20*G: */ - {{{0x2ffed1b7, 0x35155e13, 0x24aa3b4e, 0x36f44995, 0x34bd2ee2, 0x1425c0b4, 0x24e2dd17, 0x2d682227, 0x4a72}}, - {{0x1601dc5f, 0x17ca7f62, 0x34d9845b, 0x3992e3b1, 0x08ea9685, 0x0cff011f, 0x120e2c8c, 0x39ba9287, 0x3531}}}, + {{{0x0ffed1b7, 0x0a2abc27, 0x12a8ed3b, 0x17a24cac, 0x0bd2ee2d, 0x04b8169a, 0x18b745d4, 0x141113c9, 0x4a72b5}}, + {{0x1601dc5f, 0x0f94fec4, 0x1366116d, 0x0c971d8e, 0x0ea9685e, 0x1fe023e4, 0x038b230c, 0x1d4943a4, 0x3531e6}}}, /* 13*16^20*G: */ - {{{0x10467317, 0x0810fc97, 0x0d9186a0, 0x10771076, 0x1e790091, 0x199bcbeb, 0x31e15a78, 0x073f168d, 0xd7f0}}, - {{0x0f7d014e, 0x32e55f57, 0x17fbd895, 0x2805d0da, 0x15ef5728, 0x0d8501b0, 0x26c26ec7, 0x2ef661dc, 0x888d}}}, + {{{0x10467317, 0x1021f92e, 0x16461a80, 0x03b883b1, 0x07900914, 0x13797d6f, 0x18569e19, 0x1f8b46e3, 0xd7f01c}}, + {{0x0f7d014e, 0x05cabeae, 0x1fef6257, 0x002e86d2, 0x1ef5728a, 0x10a0360a, 0x109bb1cd, 0x1b30ee4d, 0x888dbb}}}, /* 15*16^20*G: */ - {{{0x3dea02c1, 0x2f5d6429, 0x374087c3, 0x3eee6df1, 0x231206e4, 0x02fe7647, 0x0371bbe8, 0x282e7ddf, 0x7e50}}, - {{0x2d45c201, 0x0f251b7f, 0x18e1b283, 0x08e4d3c5, 0x0b951774, 0x31bc776e, 0x3e29c616, 0x174f1383, 0xc340}}} + {{{0x1dea02c1, 0x1ebac853, 0x1d021f0e, 0x17736f8e, 0x11206e4f, 0x1fcec8f1, 0x1c6efa02, 0x173eef86, 0x7e50a0}}, + {{0x0d45c201, 0x1e4a36ff, 0x0386ca0c, 0x07269e2b, 0x19517742, 0x178eedc5, 0x0a7185b1, 0x0789c1fc, 0xc3405d}}} }, { /* 1*16^21*G: */ - {{{0x0cb71280, 0x229f5044, 0x04563112, 0x1070966a, 0x2f458ec1, 0x3cbbc1e5, 0x3eed9c00, 0x1aa7acaf, 0xff04}}, - {{0x1ec33919, 0x3b0c9c7d, 0x128487a7, 0x0adb9baf, 0x0cfcc901, 0x07b76f75, 0x13a170a0, 0x156b3025, 0x432f}}}, + {{{0x0cb71280, 0x053ea088, 0x1158c44a, 0x0384b350, 0x1458ec14, 0x17783cb7, 0x1b67003c, 0x13d657fd, 0xff046a}}, + {{0x1ec33919, 0x161938fa, 0x0a121e9f, 0x16dcdd7a, 0x0fcc9012, 0x16edeea6, 0x085c2807, 0x159812a7, 0x432f55}}}, /* 3*16^21*G: */ - {{{0x33ca3ce3, 0x3c9e0aa8, 0x36a77e25, 0x0ac6196a, 0x12231fef, 0x16f07d4c, 0x3dcd31a9, 0x31174534, 0xf717}}, - {{0x10ed88e9, 0x2253336d, 0x0176df06, 0x14f8af77, 0x2dee55af, 0x2d53b42a, 0x1512dca9, 0x101da326, 0x422c}}}, + {{{0x13ca3ce3, 0x193c1551, 0x1a9df897, 0x1630cb56, 0x0231fef2, 0x1e0fa989, 0x134c6a56, 0x0ba29a7b, 0xf717c4}}, + {{0x10ed88e9, 0x04a666da, 0x05db7c1a, 0x07c57bb8, 0x1ee55af5, 0x0a768556, 0x04b72a6d, 0x0ed1932a, 0x422c40}}}, /* 5*16^21*G: */ - {{{0x1b28cd88, 0x0da10c35, 0x2a9bd9ac, 0x23825d40, 0x11b32c73, 0x3ad589fe, 0x30b20c2f, 0x1a6d3ccd, 0x60e2}}, - {{0x2be2066c, 0x0a6ea290, 0x2c846b0e, 0x11584e31, 0x28df7602, 0x0846225c, 0x1f0a9609, 0x05d6995e, 0xfe00}}}, + {{{0x1b28cd88, 0x1b42186a, 0x0a6f66b0, 0x1c12ea05, 0x1b32c738, 0x1ab13fc8, 0x0c830bfa, 0x169e66e1, 0x60e269}}, + {{0x0be2066c, 0x14dd4521, 0x1211ac38, 0x0ac2718d, 0x0df76024, 0x08c44b94, 0x02a58248, 0x0b4caf3e, 0xfe0017}}}, /* 7*16^21*G: */ - {{{0x061cc594, 0x14ec64ca, 0x0d0536b1, 0x12f745c1, 0x34685596, 0x16e817f2, 0x399490aa, 0x25e8799c, 0x7992}}, - {{0x0f8d309e, 0x3a444248, 0x3ac6e909, 0x36a1ab82, 0x1fe50127, 0x1a4461e2, 0x3c9b0e10, 0x3c633548, 0x132f}}}, + {{{0x061cc594, 0x09d8c994, 0x1414dac5, 0x17ba2e09, 0x06855964, 0x1d02fe5a, 0x05242a96, 0x143cce73, 0x799297}}, + {{0x0f8d309e, 0x14888490, 0x0b1ba427, 0x150d5c17, 0x1e50127d, 0x088c3c4f, 0x06c3841a, 0x119aa479, 0x132ff1}}}, /* 9*16^21*G: */ - {{{0x172d0aba, 0x32311e89, 0x37e1b16d, 0x34642b71, 0x01241dd8, 0x383bad54, 0x2807079e, 0x3a53bf90, 0x2d9b}}, - {{0x31fa0876, 0x23dcc7ec, 0x0b710e6f, 0x34719e62, 0x19d91bba, 0x3be4d2d8, 0x098a2295, 0x236d7a7a, 0xa970}}}, + {{{0x172d0aba, 0x04623d12, 0x1f86c5b7, 0x03215b8e, 0x1241dd8d, 0x0775aa80, 0x01c1e7b8, 0x09dfc850, 0x2d9be9}}, + {{0x11fa0876, 0x07b98fd9, 0x0dc439be, 0x038cf311, 0x1d91bbad, 0x1c9a5b0c, 0x0288a57b, 0x16bd3d13, 0xa9708d}}}, /* 11*16^21*G: */ - {{{0x355e8732, 0x0301ed20, 0x06d1e31e, 0x298bb794, 0x12c243cf, 0x2f194c52, 0x2421660c, 0x00e7b220, 0x2127}}, - {{0x20cacc07, 0x1648d7d1, 0x2d7bd68d, 0x24fcfcee, 0x3f0a5cd6, 0x12e76eed, 0x235aa019, 0x271bc8eb, 0x8521}}}, + {{{0x155e8732, 0x0603da41, 0x1b478c78, 0x0c5dbca0, 0x0c243cfa, 0x03298a49, 0x0859832f, 0x13d91048, 0x212703}}, + {{0x00cacc07, 0x0c91afa3, 0x15ef5a35, 0x07e7e775, 0x10a5cd69, 0x1cedddbf, 0x16a80652, 0x0de475c6, 0x85219c}}}, /* 13*16^21*G: */ - {{{0x32083347, 0x0244d033, 0x31a53226, 0x06b8f99d, 0x02b42b9e, 0x343d6ae8, 0x0e0eb97a, 0x2d52caf6, 0xfab5}}, - {{0x3d38fd2f, 0x33327360, 0x2a69afa9, 0x178de985, 0x0a3eafc0, 0x1eabc898, 0x141503c8, 0x3445861b, 0x5758}}}, + {{{0x12083347, 0x0489a067, 0x0694c898, 0x15c7ccee, 0x0b42b9e1, 0x07ad5d01, 0x03ae5eb4, 0x09657b1c, 0xfab5b5}}, + {{0x1d38fd2f, 0x0664e6c1, 0x09a6bea7, 0x1c6f4c2d, 0x03eafc05, 0x15791305, 0x0540f21e, 0x02c30da8, 0x5758d1}}}, /* 15*16^21*G: */ - {{{0x3f572554, 0x3d9c9853, 0x0f4dab73, 0x210b91c6, 0x3ea56ff3, 0x0259dc2d, 0x31fca579, 0x09d5c9e5, 0x685d}}, - {{0x20979e03, 0x1c6bdb42, 0x0f4cca4b, 0x22aa8ab0, 0x20377cc5, 0x0e720107, 0x345fc06e, 0x2270882a, 0xa82f}}} + {{{0x1f572554, 0x1b3930a7, 0x1d36adcf, 0x085c8e31, 0x0a56ff38, 0x0b3b85bf, 0x1f295e42, 0x0ae4f2e3, 0x685d27}}, + {{0x00979e03, 0x18d7b685, 0x1d33292d, 0x15545581, 0x0377cc58, 0x0e4020f0, 0x17f01b8e, 0x18441568, 0xa82f89}}} }, { /* 1*16^22*G: */ - {{{0x05852e50, 0x1f42c933, 0x3570cc5c, 0x0b1f98f3, 0x2e7eff8b, 0x26a88d27, 0x3b058c1f, 0x31f7ffaa, 0xe486}}, - {{0x2ecf107d, 0x1ae8f2b6, 0x392ebd86, 0x1118f58c, 0x11e05a69, 0x2229727d, 0x2a12e9ee, 0x1d7b5581, 0x51fd}}}, + {{{0x05852e50, 0x1e859266, 0x15c33171, 0x18fcc79e, 0x07eff8b2, 0x1511a4f7, 0x016307e6, 0x1bffd576, 0xe486c7}}, + {{0x0ecf107d, 0x15d1e56d, 0x04baf619, 0x08c7ac67, 0x1e05a694, 0x052e4fa8, 0x04ba7ba2, 0x1daac0d4, 0x51fd75}}}, /* 3*16^22*G: */ - {{{0x1c881907, 0x19aa9915, 0x300b1dac, 0x0b219cd6, 0x2e041514, 0x0417319a, 0x3fb7c964, 0x112ee38b, 0x4acf}}, - {{0x363cdafc, 0x249ad15b, 0x0d84b252, 0x0d4acbdf, 0x0a545799, 0x10a16b44, 0x1587b354, 0x2a3f83ff, 0xad99}}}, + {{{0x1c881907, 0x1355322a, 0x002c76b1, 0x190ce6b6, 0x00415142, 0x02e63357, 0x0df25904, 0x1771c5ff, 0x4acf44}}, + {{0x163cdafc, 0x0935a2b7, 0x1612c94a, 0x0a565ef9, 0x05457993, 0x142d6885, 0x01ecd510, 0x1fc1ffab, 0xad99a8}}}, /* 5*16^22*G: */ - {{{0x3439383f, 0x0aeb81a5, 0x201a2aa8, 0x3fe958ad, 0x234eec34, 0x2a8a4b20, 0x0a649dd7, 0x08a0d062, 0x4ddf}}, - {{0x23d52337, 0x0cbea060, 0x31f82696, 0x35741144, 0x0c0c6b3d, 0x2eba5f4e, 0x1883d74a, 0x189ec364, 0xe71c}}}, + {{{0x1439383f, 0x15d7034b, 0x0068aaa0, 0x1f4ac56c, 0x14eec34f, 0x11496411, 0x192775ea, 0x10683114, 0x4ddf22}}, + {{0x03d52337, 0x197d40c1, 0x07e09a58, 0x0ba08a26, 0x00c6b3dd, 0x174be9c6, 0x00f5d2ae, 0x0f61b231, 0xe71c62}}}, /* 7*16^22*G: */ - {{{0x1822b4f4, 0x1b722055, 0x065df8f2, 0x0d4ebf3e, 0x3bf39ba5, 0x13a781e5, 0x1879e133, 0x195e44de, 0x58b0}}, - {{0x0c60fbca, 0x181ea084, 0x04e52596, 0x29281dbf, 0x22836c1c, 0x32957c09, 0x22c37027, 0x22a90516, 0x55a9}}}, + {{{0x1822b4f4, 0x16e440aa, 0x1977e3c9, 0x0a75f9f0, 0x1f39ba53, 0x14f03cbd, 0x1e784cd3, 0x0f226f30, 0x58b065}}, + {{0x0c60fbca, 0x103d4108, 0x13949659, 0x0940edf8, 0x0836c1ca, 0x12af8131, 0x10dc09f2, 0x14828b45, 0x55a98a}}}, /* 9*16^22*G: */ - {{{0x34fe39b0, 0x2caf4430, 0x0b4ded14, 0x0c5cf35d, 0x381f358a, 0x2910708c, 0x33529763, 0x38162992, 0xa345}}, - {{0x2baf79dc, 0x1c25202e, 0x3369df53, 0x231a9d6a, 0x39d949ce, 0x02156ca3, 0x2a70f91f, 0x3569b572, 0x7c6d}}}, + {{{0x14fe39b0, 0x195e8861, 0x0d37b452, 0x02e79ae9, 0x01f358a3, 0x020e119c, 0x14a5d8e9, 0x0b14c966, 0xa345e0}}, + {{0x0baf79dc, 0x184a405d, 0x0da77d4d, 0x18d4eb56, 0x1d949ce8, 0x02ad947c, 0x1c3e47c2, 0x14dab954, 0x7c6dd5}}}, /* 11*16^22*G: */ - {{{0x126695fb, 0x3ef81ee6, 0x03adee13, 0x342ee7f9, 0x16ccb6af, 0x2b2e1d1b, 0x0a2c8201, 0x2fe0c064, 0x3a10}}, - {{0x24eb7e47, 0x1571caca, 0x3d452887, 0x23fa9b10, 0x0a65c5f2, 0x00e121a2, 0x22715762, 0x216cfb06, 0xb5d5}}}, + {{{0x126695fb, 0x1df03dcc, 0x0eb7b84f, 0x01773fc8, 0x0ccb6afd, 0x05c3a36b, 0x0b20806b, 0x10603214, 0x3a10bf}}, + {{0x04eb7e47, 0x0ae39595, 0x1514a21d, 0x1fd4d887, 0x065c5f28, 0x1c243445, 0x1c55d880, 0x167d8344, 0xb5d585}}}, /* 13*16^22*G: */ - {{{0x3d2c8614, 0x106a3a59, 0x05845962, 0x2c258298, 0x112876a7, 0x33d6b0c2, 0x10433ca5, 0x377eb240, 0x12fb}}, - {{0x18b0b174, 0x01def075, 0x019f495f, 0x109608e7, 0x12cfb54d, 0x36450a33, 0x3806833f, 0x0834a409, 0xa5ff}}}, + {{{0x1d2c8614, 0x00d474b3, 0x16116589, 0x012c14c0, 0x12876a7b, 0x1ad61848, 0x10cf2973, 0x1f592020, 0x12fbdd}}, + {{0x18b0b174, 0x03bde0ea, 0x067d257c, 0x04b04738, 0x0cfb54d4, 0x08a14669, 0x01a0cff6, 0x1a5204f0, 0xa5ff20}}}, /* 15*16^22*G: */ - {{{0x2d9aeeaf, 0x0fdd90c0, 0x05afc865, 0x341e5328, 0x399a3005, 0x2b8e87eb, 0x178777b8, 0x3a1668ae, 0x8bec}}, - {{0x05f9eb5e, 0x168368f2, 0x38980f75, 0x0880e3db, 0x3fc368bb, 0x22442c3b, 0x251fcfbb, 0x0cf13141, 0x35f9}}} + {{{0x0d9aeeaf, 0x1fbb2181, 0x16bf2194, 0x00f29940, 0x19a3005d, 0x11d0fd7c, 0x01ddee2b, 0x0b34572f, 0x8bece8}}, + {{0x05f9eb5e, 0x0d06d1e4, 0x02603dd5, 0x04071edf, 0x1c368bb2, 0x0885877f, 0x07f3eee2, 0x1898a0ca, 0x35f933}}} }, { /* 1*16^23*G: */ - {{{0x2b519178, 0x12dae3b0, 0x03d1fc58, 0x0ee66629, 0x22ee0ab6, 0x0233e2d7, 0x10430cfe, 0x1fd2ed79, 0xf41d}}, - {{0x0a6a3551, 0x1e859977, 0x119e1f9a, 0x126b30da, 0x282347ab, 0x11b78fea, 0x2f8d6f10, 0x1a6faf66, 0xe6a6}}}, + {{{0x0b519178, 0x05b5c761, 0x0f47f161, 0x17333148, 0x0ee0ab63, 0x067c5af1, 0x10c33f82, 0x0976bca0, 0xf41d7f}}, + {{0x0a6a3551, 0x1d0b32ee, 0x06787e69, 0x135986d2, 0x02347ab4, 0x16f1fd54, 0x035bc411, 0x17d7b35f, 0xe6a669}}}, /* 3*16^23*G: */ - {{{0x1e3501d9, 0x29c4c4f8, 0x361fc8b1, 0x3a0b386e, 0x2d3e611b, 0x0b5a4758, 0x14e7f333, 0x209fb58b, 0xd65f}}, - {{0x2b55759e, 0x2e511b1b, 0x1730be1a, 0x304eab57, 0x2b87fc61, 0x2df29459, 0x290fe537, 0x183f3c26, 0xf24b}}}, + {{{0x1e3501d9, 0x138989f0, 0x187f22c6, 0x1059c376, 0x13e611be, 0x0b48eb16, 0x19fccccb, 0x0fdac5a9, 0xd65f82}}, + {{0x0b55759e, 0x1ca23637, 0x1cc2f86a, 0x02755aba, 0x187fc61c, 0x1e528b35, 0x03f94ded, 0x1f9e1352, 0xf24b60}}}, /* 5*16^23*G: */ - {{{0x0f2ed84e, 0x2d8bf890, 0x3e2ea12c, 0x26537cd7, 0x2cc0ade7, 0x1b22d5e0, 0x05c385ee, 0x2d6db7ac, 0x55a9}}, - {{0x146495a3, 0x1e771541, 0x2a0d8f05, 0x3fed35c4, 0x17f43ae8, 0x1d34643b, 0x319ab291, 0x0865ab27, 0xc4f2}}}, + {{{0x0f2ed84e, 0x1b17f120, 0x18ba84b2, 0x129be6bf, 0x0c0ade79, 0x045abc16, 0x10e17b9b, 0x16dbd60b, 0x55a9b5}}, + {{0x146495a3, 0x1cee2a82, 0x08363c15, 0x1f69ae25, 0x1f43ae8f, 0x068c876b, 0x06aca45d, 0x12d593e3, 0xc4f221}}}, /* 7*16^23*G: */ - {{{0x075495a2, 0x2f4b3e1c, 0x0bc00b29, 0x3787ad92, 0x148bc49f, 0x3b582989, 0x371da1f7, 0x15db71f6, 0x79de}}, - {{0x2aec6fb8, 0x00b231aa, 0x093a7468, 0x053d4259, 0x1c79c683, 0x39b6b91f, 0x06a02785, 0x0f439ac6, 0x3b2d}}}, + {{{0x075495a2, 0x1e967c38, 0x0f002ca6, 0x1c3d6c91, 0x08bc49fd, 0x0b05312a, 0x07687dfb, 0x0db8fb6e, 0x79de57}}, + {{0x0aec6fb8, 0x01646355, 0x04e9d1a0, 0x09ea12c9, 0x079c6831, 0x16d723ee, 0x0809e179, 0x01cd630d, 0x3b2d3d}}}, /* 9*16^23*G: */ - {{{0x02d1e7bb, 0x3ba4ab32, 0x111964ce, 0x30ffe40d, 0x17e55524, 0x12cda565, 0x004b6e26, 0x138c8589, 0x8fe0}}, - {{0x1a62e84f, 0x29d66b43, 0x3046a8cd, 0x2459191b, 0x0db34e5b, 0x1b3a95ea, 0x2358fe5d, 0x36d408bd, 0x3987}}}, + {{{0x02d1e7bb, 0x17495664, 0x0465933b, 0x07ff206a, 0x1e55524c, 0x19b4acab, 0x12db8992, 0x0642c480, 0x8fe04e}}, + {{0x1a62e84f, 0x13acd686, 0x011aa336, 0x02c8c8de, 0x1b34e5b9, 0x0752bd46, 0x163f975b, 0x0a045ec6, 0x3987db}}}, /* 11*16^23*G: */ - {{{0x29f7c360, 0x00692bb1, 0x08085c21, 0x3f355df9, 0x1224e24e, 0x25298da3, 0x1f8f150a, 0x264255fb, 0x3af4}}, - {{0x287d7a7b, 0x0e770aa9, 0x360895cd, 0x15537589, 0x333c3348, 0x3e1920b9, 0x1d91d531, 0x180c34ec, 0xd170}}}, + {{{0x09f7c360, 0x00d25763, 0x00217084, 0x19aaefc9, 0x024e24ef, 0x0531b469, 0x03c542a5, 0x012afdbf, 0x3af499}}, + {{0x087d7a7b, 0x1cee1553, 0x18225734, 0x0a9bac4e, 0x13c33485, 0x03241739, 0x04754c7e, 0x061a763b, 0xd17060}}}, /* 13*16^23*G: */ - {{{0x370373be, 0x26948eb9, 0x263d3b53, 0x0f418884, 0x227c4e21, 0x160bcff8, 0x08076c1a, 0x3817188f, 0x31a7}}, - {{0x290950a8, 0x3b5e1e43, 0x1a254308, 0x3a0ae654, 0x23db1e8c, 0x2c2ab8d0, 0x1de67021, 0x0bbcfe34, 0xc23d}}}, + {{{0x170373be, 0x0d291d73, 0x18f4ed4e, 0x1a0c4424, 0x07c4e213, 0x0179ff11, 0x01db0696, 0x0b8c4790, 0x31a7e0}}, + {{0x090950a8, 0x16bc3c87, 0x08950c23, 0x105732a3, 0x1db1e8ce, 0x05571a11, 0x199c086c, 0x1e7f1a3b, 0xc23d2e}}}, /* 15*16^23*G: */ - {{{0x0b923b45, 0x109843b7, 0x13e24bdb, 0x0ea7effc, 0x198458a3, 0x144d18b7, 0x2d23ed15, 0x199204d5, 0x740a}}, - {{0x11ecaa5f, 0x2304f8e1, 0x3c8480ba, 0x25e64e41, 0x1606cfa8, 0x391e229d, 0x1523f2f4, 0x01230973, 0x7f6d}}} + {{{0x0b923b45, 0x0130876e, 0x0f892f6d, 0x153f7fe2, 0x18458a33, 0x09a316ec, 0x08fb4554, 0x09026ada, 0x740a66}}, + {{0x11ecaa5f, 0x0609f1c2, 0x121202ea, 0x0f32720f, 0x006cfa89, 0x03c453ab, 0x08fcbd39, 0x1184b9aa, 0x7f6d04}}} }, { /* 1*16^24*G: */ - {{{0x3512218e, 0x212aa4e5, 0x0ca0141a, 0x29486c1d, 0x22e902e9, 0x202ce862, 0x277a6578, 0x141984a9, 0x4a5b}}, - {{0x0c4f3840, 0x2fab69e9, 0x1e26d9d0, 0x1b6c5506, 0x227d4062, 0x1813ef85, 0x089f1c42, 0x11873ab0, 0xeb13}}}, + {{{0x1512218e, 0x025549cb, 0x1280506a, 0x0a4360e9, 0x0e902e9a, 0x059d0c51, 0x1e995e20, 0x0cc254ce, 0x4a5b50}}, + {{0x0c4f3840, 0x1f56d3d2, 0x189b6742, 0x1b62a833, 0x07d40626, 0x027df0b1, 0x07c71098, 0x039d5811, 0xeb1346}}}, /* 3*16^24*G: */ - {{{0x118473fd, 0x0bbd0389, 0x29733915, 0x2e409af1, 0x28a9e3bb, 0x24aae65c, 0x18ba0852, 0x018c8ccc, 0x1064}}, - {{0x385cf805, 0x3e9858b9, 0x021d039a, 0x2f864343, 0x05883ccf, 0x1e0a7996, 0x3a2d8c8e, 0x0ca08ee2, 0x9c68}}}, + {{{0x118473fd, 0x177a0712, 0x05cce454, 0x1204d78d, 0x0a9e3bbb, 0x155ccb94, 0x0e8214a4, 0x06466631, 0x106406}}, + {{0x185cf805, 0x1d30b173, 0x08740e6b, 0x1c321a18, 0x1883ccfb, 0x014f32c2, 0x0b63239e, 0x10477174, 0x9c6832}}}, /* 5*16^24*G: */ - {{{0x253f30f3, 0x159fbb21, 0x1a238dd3, 0x108fb4bb, 0x083f212b, 0x29043550, 0x327bf5ed, 0x2b63fc17, 0x38c8}}, - {{0x2be9217b, 0x01839d27, 0x159df37a, 0x20fea60a, 0x3d641f65, 0x02595376, 0x0b116f39, 0x185e1db7, 0x83c2}}}, + {{{0x053f30f3, 0x0b3f7643, 0x088e374d, 0x047da5db, 0x03f212b4, 0x0086aa04, 0x1efd7b69, 0x11fe0be4, 0x38c8ad}}, + {{0x0be9217b, 0x03073a4f, 0x1677cde8, 0x07f53052, 0x1641f658, 0x0b2a6ede, 0x045bce42, 0x0f0edb96, 0x83c261}}}, /* 7*16^24*G: */ - {{{0x36ef1584, 0x10f9a446, 0x3920cbf5, 0x2a68a8e3, 0x35184277, 0x23ef8ff4, 0x0bb09585, 0x232f3a18, 0x6fcb}}, - {{0x1d3110f2, 0x0f27df08, 0x28a4325c, 0x24bdb5a4, 0x30459d59, 0x30208eb0, 0x21d76d54, 0x2a0f62dc, 0xa8f1}}}, + {{{0x16ef1584, 0x01f3488d, 0x04832fd5, 0x1345471f, 0x1184277a, 0x1df1fe9a, 0x0c256163, 0x179d0c17, 0x6fcb8c}}, + {{0x1d3110f2, 0x1e4fbe10, 0x0290c970, 0x05edad25, 0x0459d599, 0x0411d618, 0x15db5530, 0x07b16e43, 0xa8f1a8}}}, /* 9*16^24*G: */ - {{{0x062255ef, 0x23d44d01, 0x364078ce, 0x35c74d19, 0x05b0ee50, 0x05724379, 0x2e2bd735, 0x342e4fdd, 0x7811}}, - {{0x1be3252e, 0x162fbe6c, 0x2d43768a, 0x07b4144e, 0x385132f5, 0x00ba5006, 0x1ac7a54c, 0x1d8dc2ed, 0x99bb}}}, + {{{0x062255ef, 0x07a89a02, 0x1901e33a, 0x0e3a68ce, 0x1b0ee50d, 0x0e486f22, 0x0af5cd45, 0x1727eedc, 0x7811d0}}, + {{0x1be3252e, 0x0c5f7cd8, 0x150dda29, 0x1da0a275, 0x05132f51, 0x174a00dc, 0x11e95300, 0x06e176b5, 0x99bb76}}}, /* 11*16^24*G: */ - {{{0x353d2ea7, 0x0f8443c4, 0x3fa86509, 0x3b4208e8, 0x016f2a9e, 0x2dca757e, 0x350ce0c7, 0x0f6512a2, 0xc358}}, - {{0x0b667bbd, 0x2c60fa78, 0x15f1c432, 0x32496994, 0x1fcccdd6, 0x1189fbe2, 0x1e90f596, 0x1eb024e4, 0x5396}}}, + {{{0x153d2ea7, 0x1f088789, 0x1ea19424, 0x1a104747, 0x16f2a9ee, 0x194eafc0, 0x033831ed, 0x1289516a, 0xc3583d}}, + {{0x0b667bbd, 0x18c1f4f0, 0x17c710ca, 0x124b4ca2, 0x1cccdd6c, 0x113f7c4f, 0x043d6591, 0x1812723d, 0x53967a}}}, /* 13*16^24*G: */ - {{{0x102e3099, 0x3b77c381, 0x28401658, 0x3c84e998, 0x3ad00d53, 0x03c062ed, 0x2e501f3a, 0x33ca0f37, 0xd591}}, - {{0x055ac5af, 0x0ef09d95, 0x3116fd63, 0x3cbbfe22, 0x0bc5825c, 0x04cc34d4, 0x0e6e44e5, 0x3973f11e, 0x87eb}}}, + {{{0x102e3099, 0x16ef8702, 0x01005963, 0x04274cc5, 0x0d00d53f, 0x180c5dbd, 0x1407ce83, 0x05079bdc, 0xd591cf}}, + {{0x055ac5af, 0x1de13b2a, 0x045bf58c, 0x05dff116, 0x1c5825cf, 0x19869a85, 0x1b913944, 0x19f88f1c, 0x87ebe5}}}, /* 15*16^24*G: */ - {{{0x32a940a5, 0x2c995918, 0x014e6b12, 0x10d7ad69, 0x39e8714a, 0x09078693, 0x235c4c01, 0x03584bcc, 0xa0aa}}, - {{0x0b950422, 0x0fe20a9a, 0x3d1bf939, 0x1a473769, 0x181f3e6c, 0x0d33e680, 0x3642819b, 0x03ae9dbd, 0x2234}}} + {{{0x12a940a5, 0x1932b231, 0x0539ac4a, 0x06bd6b48, 0x1e8714a4, 0x00f0d27c, 0x17130049, 0x0c25e646, 0xa0aa0d}}, + {{0x0b950422, 0x1fc41534, 0x146fe4e4, 0x1239bb4f, 0x01f3e6c6, 0x067cd00c, 0x10a066cd, 0x174edeec, 0x22340e}}} }, { /* 1*16^25*G: */ - {{{0x008e2df0, 0x18a360dc, 0x328e5f76, 0x30ec95d0, 0x3e0f5032, 0x30a77e2e, 0x2b995012, 0x2442f78a, 0x2eb3}}, - {{0x1274eaae, 0x2443313b, 0x0f65f490, 0x1034483b, 0x24999f95, 0x0df4d236, 0x34b3a77d, 0x3008cdd1, 0x3f29}}}, + {{{0x008e2df0, 0x1146c1b8, 0x0a397dd9, 0x0764ae86, 0x00f5032c, 0x14efc5df, 0x065404b0, 0x017bc557, 0x2eb391}}, + {{0x1274eaae, 0x08866276, 0x1d97d242, 0x01a241d9, 0x0999f954, 0x1e9a46d2, 0x0ce9df4d, 0x0466e8e9, 0x3f29c0}}}, /* 3*16^25*G: */ - {{{0x282867f0, 0x3c0ae12d, 0x3190a39b, 0x0509b886, 0x0900f0a2, 0x2f45a9e0, 0x07ce22aa, 0x36e23993, 0xf6e9}}, - {{0x0f1861ea, 0x1d6cebc4, 0x170b6234, 0x0106e97e, 0x00d5b127, 0x24eddba3, 0x2ab7481d, 0x1e42deb4, 0x53ca}}}, + {{{0x082867f0, 0x1815c25b, 0x06428e6f, 0x084dc436, 0x100f0a21, 0x08b53c04, 0x1388aaaf, 0x111cc98f, 0xf6e9db}}, + {{0x0f1861ea, 0x1ad9d788, 0x1c2d88d1, 0x08374bf2, 0x0d5b1270, 0x1dbb7460, 0x0dd20764, 0x016f5a55, 0x53ca79}}}, /* 5*16^25*G: */ - {{{0x320d6102, 0x2b7410e3, 0x34539409, 0x1b54de28, 0x199a5ef0, 0x3056e6d8, 0x2449d785, 0x36ce1d83, 0xfd1d}}, - {{0x2e003b7c, 0x28299246, 0x1513983d, 0x0f864484, 0x03b70016, 0x287c7de2, 0x0638aeda, 0x2e1ce414, 0xcb54}}}, + {{{0x120d6102, 0x16e821c7, 0x114e5026, 0x1aa6f146, 0x19a5ef06, 0x0adcdb0c, 0x1275e170, 0x070ec1c8, 0xfd1ddb}}, + {{0x0e003b7c, 0x1053248d, 0x144e60f6, 0x1c322422, 0x1b700163, 0x0f8fbc41, 0x0e2bb6a8, 0x0e720a0c, 0xcb54b8}}}, /* 7*16^25*G: */ - {{{0x02c77cb7, 0x0fdcd077, 0x2dc15b6f, 0x1b650240, 0x2e698fef, 0x129cf997, 0x1901d9fe, 0x1cf08966, 0x61a2}}, - {{0x1ddb25ed, 0x151847e0, 0x0ae1f748, 0x316b669c, 0x2b0cc9c5, 0x28867d7b, 0x2d3d3f4e, 0x334cd34e, 0x5bba}}}, + {{{0x02c77cb7, 0x1fb9a0ee, 0x17056dbc, 0x1b281205, 0x0698fef6, 0x139f32f7, 0x00767f92, 0x1844b332, 0x61a273}}, + {{0x1ddb25ed, 0x0a308fc0, 0x0b87dd21, 0x0b5b34e1, 0x10cc9c5c, 0x10cfaf75, 0x0f4fd3a8, 0x0669a75a, 0x5bbacd}}}, /* 9*16^25*G: */ - {{{0x377d8976, 0x266355b8, 0x30f292db, 0x05ce8e38, 0x1d04b55e, 0x00b2608a, 0x201b64cb, 0x23997bdd, 0xcd2e}}, - {{0x0867bc22, 0x05a5bd07, 0x1428c051, 0x03b783cd, 0x06ff68f6, 0x073a3cb5, 0x2a31ffc3, 0x2b4d88d0, 0xf58e}}}, + {{{0x177d8976, 0x0cc6ab71, 0x03ca4b6e, 0x0e7471c6, 0x104b55e1, 0x164c114e, 0x06d932c0, 0x0cbdeec0, 0xcd2e8e}}, + {{0x0867bc22, 0x0b4b7a0e, 0x10a30144, 0x1dbc1e6a, 0x0ff68f60, 0x074796a3, 0x0c7ff0c7, 0x06c46854, 0xf58ead}}}, /* 11*16^25*G: */ - {{{0x2c67c998, 0x026cc1b0, 0x3cf1b866, 0x26c1faa8, 0x304c259a, 0x097aa290, 0x23efb402, 0x07e70e08, 0x9bd6}}, - {{0x28199514, 0x0d02be70, 0x0424b18c, 0x1f6707a4, 0x1450fa92, 0x3c825a5a, 0x06f5c5c8, 0x0102645b, 0x77b2}}}, + {{{0x0c67c998, 0x04d98361, 0x13c6e198, 0x160fd547, 0x04c259a9, 0x0f545218, 0x1bed0089, 0x13870447, 0x9bd61f}}, + {{0x08199514, 0x1a057ce1, 0x1092c630, 0x1b383d20, 0x050fa927, 0x104b4b4a, 0x1d71723c, 0x01322d8d, 0x77b204}}}, /* 13*16^25*G: */ - {{{0x2aafa568, 0x291785ef, 0x01e22766, 0x335ea5dc, 0x17a016b4, 0x389e9044, 0x0777512a, 0x3ad3de5c, 0x7afa}}, - {{0x01c1f2df, 0x3b54e8be, 0x1d390233, 0x0b9a50ca, 0x01365a97, 0x34504d41, 0x3d27d895, 0x39864cfe, 0xc6ef}}}, + {{{0x0aafa568, 0x122f0bdf, 0x07889d9a, 0x1af52ee0, 0x1a016b4c, 0x13d2088b, 0x1dd44ab8, 0x09ef2e0e, 0x7afaeb}}, + {{0x01c1f2df, 0x16a9d17c, 0x14e408cf, 0x1cd28653, 0x1365a972, 0x0a09a820, 0x09f62574, 0x03267f7a, 0xc6efe6}}}, /* 15*16^25*G: */ - {{{0x0e59ddeb, 0x1f9c0f94, 0x11e98a8b, 0x0f98a72b, 0x2b0c3b48, 0x36530525, 0x012f9061, 0x00889f89, 0xd9a0}}, - {{0x0f0af5a4, 0x3ce4ffe0, 0x35f18ce5, 0x18aa2f2a, 0x27058185, 0x183e290d, 0x2022c43c, 0x2cbe4ede, 0x975e}}} + {{{0x0e59ddeb, 0x1f381f28, 0x07a62a2d, 0x1cc5395a, 0x10c3b483, 0x0a60a4b5, 0x0be41876, 0x044fc482, 0xd9a002}}, + {{0x0f0af5a4, 0x19c9ffc0, 0x17c63397, 0x05517956, 0x10581856, 0x07c521b3, 0x08b10f18, 0x1f276f40, 0x975eb2}}} }, { /* 1*16^26*G: */ - {{{0x3ecca7e0, 0x1ce697a8, 0x343333ec, 0x34b263d9, 0x0d9428a7, 0x3d8cd489, 0x12a0c0fe, 0x3b8f171e, 0x7ef2}}, - {{0x152ac094, 0x00ac8b75, 0x3bd3d203, 0x2c851437, 0x2609db81, 0x19fd4757, 0x0c011a4f, 0x2189cc2b, 0xafb6}}}, + {{{0x1ecca7e0, 0x19cd2f51, 0x10cccfb1, 0x05931ece, 0x19428a7d, 0x119a9126, 0x08303fbd, 0x078b8f25, 0x7ef2ee}}, + {{0x152ac094, 0x015916ea, 0x0f4f480c, 0x0428a1bf, 0x009db81b, 0x1fa8eaf3, 0x004693d9, 0x04e61598, 0xafb686}}}, /* 3*16^26*G: */ - {{{0x233f0ffa, 0x0bcd60f6, 0x1807a417, 0x3932b184, 0x19c641ca, 0x1295db27, 0x07acd762, 0x15c9c5a2, 0x3704}}, - {{0x20fa35ac, 0x3fb4ff19, 0x28bf2fc5, 0x2e8fadea, 0x15ff4c57, 0x2ed2ee22, 0x1e74f841, 0x0231869c, 0x5c64}}}, + {{{0x033f0ffa, 0x179ac1ed, 0x001e905c, 0x09958c23, 0x1c641cae, 0x12bb64ec, 0x0b35d892, 0x04e2d10f, 0x370457}}, + {{0x00fa35ac, 0x1f69fe33, 0x02fcbf17, 0x147d6f55, 0x1ff4c57b, 0x1a5dc44a, 0x1d3e106e, 0x18c34e3c, 0x5c6408}}}, /* 5*16^26*G: */ - {{{0x32603513, 0x31be6194, 0x14a00953, 0x319371a0, 0x0bb697f6, 0x3aa90b02, 0x0db722d1, 0x1e7950a6, 0xc2a9}}, - {{0x3c3505b9, 0x15d56cb0, 0x01514499, 0x3199b7d2, 0x1bce7e8c, 0x1e02064d, 0x2b5c8542, 0x35d2879b, 0xef9d}}}, + {{{0x12603513, 0x037cc329, 0x1280254f, 0x0c9b8d02, 0x1b697f6c, 0x15216045, 0x0dc8b47a, 0x1ca8531b, 0xc2a979}}, + {{0x1c3505b9, 0x0baad961, 0x05451265, 0x0ccdbe90, 0x1ce7e8cc, 0x0040c9ad, 0x1721509e, 0x0943cdd6, 0xef9dd7}}}, /* 7*16^26*G: */ - {{{0x19fdee3e, 0x191bfec7, 0x0302e01e, 0x07e5dc5b, 0x17afb968, 0x2ec5736c, 0x059e1172, 0x061aac7f, 0xc9f4}}, - {{0x0ced22e7, 0x0799b317, 0x358df4f5, 0x3854c71e, 0x03214344, 0x1cc50ae2, 0x3a3410df, 0x029fcf2c, 0x0942}}}, + {{{0x19fdee3e, 0x1237fd8e, 0x0c0b8079, 0x1f2ee2d8, 0x1afb9681, 0x18ae6d8b, 0x07845cae, 0x0d563f8b, 0xc9f418}}, + {{0x0ced22e7, 0x0f33662e, 0x1637d3d4, 0x02a638f6, 0x1214344e, 0x18a15c41, 0x0d0437dc, 0x0fe79674, 0x9420a}}}, /* 9*16^26*G: */ - {{{0x0814f217, 0x032cf99d, 0x356cffaf, 0x368fdee1, 0x3bb6a4a9, 0x280093e0, 0x00256b08, 0x3d56e012, 0x27dc}}, - {{0x0cf2ed4c, 0x13252d62, 0x11fc3bf1, 0x13a3eac6, 0x202a380a, 0x22eac252, 0x15dee0bc, 0x3d53d523, 0xbe18}}}, + {{{0x0814f217, 0x0659f33a, 0x15b3febc, 0x147ef70e, 0x1b6a4a9d, 0x00127c1d, 0x095ac228, 0x0b700900, 0x27dcf5}}, + {{0x0cf2ed4c, 0x064a5ac4, 0x07f0efc5, 0x1d1f5632, 0x02a380a4, 0x1d584a50, 0x17b82f22, 0x09ea91ab, 0xbe18f5}}}, /* 11*16^26*G: */ - {{{0x1b9e310c, 0x168a93f5, 0x04cfd4a7, 0x0f396e6e, 0x15918731, 0x3492b0ce, 0x2ea4b9c8, 0x0080ec95, 0x3b8b}}, - {{0x2d19fc9b, 0x25059816, 0x2b305839, 0x3fe012e0, 0x0117a6a8, 0x1db8ddf1, 0x3615bd61, 0x1f13ac0c, 0x9111}}}, + {{{0x1b9e310c, 0x0d1527ea, 0x133f529d, 0x19cb7370, 0x19187313, 0x125619ca, 0x092e7234, 0x00764add, 0x3b8b02}}, + {{0x0d19fc9b, 0x0a0b302d, 0x0cc160e6, 0x1f009705, 0x117a6a8f, 0x171bbe20, 0x056f585d, 0x09d6066c, 0x91117c}}}, /* 13*16^26*G: */ - {{{0x27615b36, 0x3c7878ae, 0x3f3c15f8, 0x13fc7a31, 0x14c3372a, 0x30901be4, 0x0103a105, 0x0e6316f3, 0xa5e7}}, - {{0x09136d80, 0x3660b8e5, 0x0b613c04, 0x3ff064dc, 0x15f8c547, 0x0e37bca8, 0x0e4ce464, 0x3d63725d, 0x1f3f}}}, + {{{0x07615b36, 0x18f0f15d, 0x1cf057e3, 0x1fe3d18f, 0x0c3372a4, 0x12037c8a, 0x00e84170, 0x118b7982, 0xa5e739}}, + {{0x09136d80, 0x0cc171ca, 0x0d84f013, 0x1f8326e1, 0x1f8c547f, 0x06f7950a, 0x1339190e, 0x11b92e9c, 0x1f3ff5}}}, /* 15*16^26*G: */ - {{{0x2d3e10db, 0x2dec10cb, 0x0b87159b, 0x1ccb86b2, 0x2b61fa47, 0x0110ffd3, 0x1532bdee, 0x060d56b2, 0xaad2}}, - {{0x2fa05fb3, 0x0d4d6af5, 0x31cba276, 0x00c9dcac, 0x1f8b4a72, 0x3778a3f5, 0x02e3b3a7, 0x07bbaebe, 0x793b}}} + {{{0x0d3e10db, 0x1bd82197, 0x0e1c566e, 0x065c3591, 0x161fa477, 0x021ffa75, 0x0caf7b81, 0x06ab592a, 0xaad218}}, + {{0x0fa05fb3, 0x1a9ad5eb, 0x072e89d8, 0x064ee566, 0x18b4a720, 0x0f147eaf, 0x18ece9f7, 0x1dd75f05, 0x793b1e}}} }, { /* 1*16^27*G: */ - {{{0x2c49e853, 0x1c07c243, 0x175e04a6, 0x32d4d4a6, 0x1fa77aa9, 0x009553ad, 0x00aeb578, 0x10590859, 0x0e51}}, - {{0x36405cb2, 0x0db8f44d, 0x0c9ee363, 0x1a0e5064, 0x11030df5, 0x3ad294ea, 0x05469278, 0x073a9964, 0xcf33}}}, + {{{0x0c49e853, 0x180f8487, 0x1d781299, 0x16a6a532, 0x1a77aa9c, 0x12aa75af, 0x0bad5e00, 0x0c842c81, 0xe5141}}, + {{0x16405cb2, 0x1b71e89b, 0x127b8d8c, 0x10728321, 0x1030df56, 0x1a529d48, 0x11a49e3a, 0x1d4cb20a, 0xcf331c}}}, /* 3*16^27*G: */ - {{{0x1dc6afad, 0x1288fc70, 0x1f80f46c, 0x34f648a5, 0x00c6771b, 0x3b497d93, 0x2cf25de8, 0x2819d972, 0x977b}}, - {{0x1d7faa09, 0x358b3714, 0x1da1a154, 0x1d684907, 0x01d9992f, 0x0fea8342, 0x38fa2883, 0x2f10ebb6, 0x1bc3}}}, + {{{0x1dc6afad, 0x0511f8e0, 0x1e03d1b1, 0x07b2452b, 0x0c6771bd, 0x092fb260, 0x1c977a3b, 0x0cecb959, 0x977ba0}}, + {{0x1d7faa09, 0x0b166e28, 0x16868553, 0x0b42483b, 0x1d9992f7, 0x1d506840, 0x1e8a20cf, 0x0875db71, 0x1bc3bc}}}, /* 5*16^27*G: */ - {{{0x1d81983b, 0x17dd175f, 0x38eab786, 0x0883f40b, 0x3ffacc10, 0x32d81dc7, 0x23abe4c3, 0x0a184a84, 0x3bc3}}, - {{0x11a637b6, 0x3667ca14, 0x3bb848db, 0x0d2216a3, 0x300a7f43, 0x2cc172ab, 0x08a20250, 0x209b7b43, 0xa6b5}}}, + {{{0x1d81983b, 0x0fba2ebe, 0x03aade19, 0x041fa05f, 0x1facc102, 0x1b03b8ff, 0x0af930f2, 0x0c254247, 0x3bc328}}, + {{0x11a637b6, 0x0ccf9428, 0x0ee1236f, 0x0910b51f, 0x00a7f433, 0x182e5578, 0x0880942c, 0x0dbda191, 0xa6b582}}}, /* 7*16^27*G: */ - {{{0x37c8537b, 0x17ddb07f, 0x01f80617, 0x232b2dd1, 0x396c21ca, 0x2bbf872b, 0x004ac51b, 0x293a3a7b, 0x67cb}}, - {{0x385726da, 0x33ad415c, 0x0403f6e1, 0x37c10fb4, 0x31cc047b, 0x07187cbe, 0x08984a1e, 0x3b7b7a87, 0x5b65}}}, + {{{0x17c8537b, 0x0fbb60ff, 0x07e0185d, 0x19596e88, 0x16c21ca8, 0x17f0e57c, 0x12b146eb, 0x1d1d3d80, 0x67cba4}}, + {{0x185726da, 0x075a82b9, 0x100fdb87, 0x1e087da0, 0x1cc047bd, 0x030f97d8, 0x06128787, 0x1dbd4391, 0x5b65ed}}}, /* 9*16^27*G: */ - {{{0x0b6a1226, 0x1a08a339, 0x35465393, 0x3e7a722a, 0x28f3922a, 0x1cf5a191, 0x099931a0, 0x23a9b55d, 0xc595}}, - {{0x066961d4, 0x30401a23, 0x22108b91, 0x21db6fae, 0x05bd8296, 0x3865c675, 0x37dd7ecb, 0x2a20bdc3, 0xa031}}}, + {{{0x0b6a1226, 0x14114672, 0x15194e4d, 0x13d39156, 0x0f3922af, 0x1eb43234, 0x064c681c, 0x14daae93, 0xc5958e}}, + {{0x066961d4, 0x00803446, 0x08422e47, 0x0edb7d74, 0x1bd82968, 0x0cb8cea2, 0x175fb2f8, 0x105ee1ef, 0xa031a8}}}, /* 11*16^27*G: */ - {{{0x33713a52, 0x1378fe16, 0x03c5417e, 0x31d6e31a, 0x0a5fa025, 0x33030f1d, 0x25ca7c1f, 0x1efe0b90, 0x83f0}}, - {{0x1fb0ffb6, 0x04449cfe, 0x1fb45d2a, 0x2d6dd838, 0x07d3cfca, 0x1e53244b, 0x38bb9049, 0x13c42896, 0xf2ec}}}, + {{{0x13713a52, 0x06f1fc2d, 0x0f1505f9, 0x0eb718d0, 0x05fa025c, 0x0061e3a5, 0x129f07f3, 0x1f05c84b, 0x83f07b}}, + {{0x1fb0ffb6, 0x088939fc, 0x1ed174a8, 0x0b6ec1c3, 0x1d3cfcab, 0x0a648963, 0x0ee4125e, 0x02144b71, 0xf2ec4f}}}, /* 13*16^27*G: */ - {{{0x21ba21b0, 0x2b668244, 0x0c265539, 0x15763480, 0x2e0076d8, 0x1a01a1ba, 0x242d4e6f, 0x2e93e6d6, 0x938d}}, - {{0x0d5b4325, 0x1d366579, 0x32b697c3, 0x3c6efb8f, 0x36b90bcb, 0x2ab6f744, 0x356566e9, 0x302a26bd, 0x48af}}}, + {{{0x01ba21b0, 0x16cd0489, 0x109954e6, 0x0bb1a401, 0x00076d85, 0x00343757, 0x0b539bda, 0x09f36b48, 0x938dba}}, + {{0x0d5b4325, 0x1a6ccaf2, 0x0ada5f0d, 0x0377dc7e, 0x0b90bcbf, 0x16dee89b, 0x1959ba6a, 0x15135eea, 0x48afc0}}}, /* 15*16^27*G: */ - {{{0x3f2b24f1, 0x14f92698, 0x3e76bcfb, 0x2bb193d7, 0x349779cf, 0x076ab3ce, 0x031e73a8, 0x226ddb28, 0x7efa}}, - {{0x2f8e4b83, 0x19771752, 0x154a455d, 0x2eb7ceb1, 0x16ab211d, 0x3b488bf0, 0x0aeff78c, 0x3cfb187d, 0xa99f}}} + {{{0x1f2b24f1, 0x09f24d31, 0x19daf3ed, 0x1d8c9ebf, 0x09779cfa, 0x0d5679da, 0x079cea07, 0x16ed9406, 0x7efa89}}, + {{0x0f8e4b83, 0x12ee2ea5, 0x15291575, 0x15be758a, 0x0ab211db, 0x09117e0b, 0x1bfde33b, 0x1d8c3e95, 0xa99ff3}}} }, { /* 1*16^28*G: */ - {{{0x22f2b734, 0x01a66fe7, 0x101d267f, 0x30eed6d5, 0x16445779, 0x129e1bc4, 0x0c99a063, 0x008a67bb, 0x224a}}, - {{0x11ec7fdf, 0x103d6152, 0x3c7afd08, 0x2dc12d9c, 0x1d7fff07, 0x2822b61c, 0x122b4149, 0x2a34a6db, 0xfa41}}}, + {{{0x02f2b734, 0x034cdfcf, 0x007499fc, 0x0776b6aa, 0x0445779c, 0x13c3788b, 0x066818d2, 0x0533dd99, 0x224a02}}, + {{0x11ec7fdf, 0x007ac2a4, 0x11ebf421, 0x0e096ce7, 0x17fff07b, 0x0456c38e, 0x0ad05268, 0x1a536da4, 0xfa41a8}}}, /* 3*16^28*G: */ - {{{0x1d254033, 0x27a4bd1d, 0x2a4707ac, 0x0da0a030, 0x36f24078, 0x2b7e9a22, 0x0ec59fcd, 0x00bb854f, 0xe635}}, - {{0x28f05e3f, 0x3a2aa225, 0x3fcf3607, 0x24568312, 0x09ce482c, 0x13a03c1c, 0x21e11ad7, 0x20dec7d8, 0xa7c5}}}, + {{{0x1d254033, 0x0f497a3a, 0x091c1eb2, 0x0d050185, 0x0f240783, 0x0fd3445b, 0x1167f36b, 0x1dc2a79d, 0xe63502}}, + {{0x08f05e3f, 0x1455444b, 0x1f3cd81f, 0x02b41897, 0x1ce482c9, 0x14078384, 0x1846b5d3, 0x0f63ec43, 0xa7c583}}}, /* 5*16^28*G: */ - {{{0x21e08f33, 0x2e5826bf, 0x3982cca2, 0x3f58c772, 0x3000e2b1, 0x2d1714cf, 0x3968712a, 0x37b09cba, 0x5648}}, - {{0x0269f1c9, 0x1bbb66b1, 0x01179512, 0x1caefcb8, 0x37a2693e, 0x23d71935, 0x37043f47, 0x371c1c23, 0x95fd}}}, + {{{0x01e08f33, 0x1cb04d7f, 0x060b328a, 0x1ac63b97, 0x000e2b1f, 0x02e299f8, 0x1a1c4aad, 0x184e5d72, 0x5648de}}, + {{0x0269f1c9, 0x1776cd62, 0x045e5449, 0x0577e5c0, 0x1a2693e7, 0x1ae326bb, 0x010fd1e3, 0x0e0e11ee, 0x95fddc}}}, /* 7*16^28*G: */ - {{{0x3ab98c43, 0x0ee0802f, 0x23e8aa4e, 0x2e95dd5f, 0x2c8f03c5, 0x14be3b2f, 0x0ed26951, 0x3067cce0, 0x1941}}, - {{0x22abe217, 0x3e884368, 0x0df56398, 0x3d8b4f6e, 0x3b8c53d8, 0x1b6ca923, 0x1b2b6e2b, 0x2e0d1657, 0x8e66}}}, + {{{0x1ab98c43, 0x1dc1005f, 0x0fa2a938, 0x14aeeafc, 0x08f03c5b, 0x17c765f6, 0x149a5454, 0x13e6701d, 0x1941c1}}, + {{0x02abe217, 0x1d1086d1, 0x17d58e63, 0x0c5a7b71, 0x18c53d8f, 0x0d95247d, 0x0adb8adb, 0x068b2bb6, 0x8e66b8}}}, /* 9*16^28*G: */ - {{{0x02d8c2f4, 0x199c3441, 0x39c0189e, 0x0cc86e7d, 0x0d8a0bd7, 0x1cef78d9, 0x34bd67fa, 0x190c7442, 0xfc58}}, - {{0x3cfd274a, 0x0463223f, 0x3c338b40, 0x38b2c17a, 0x3db4ab29, 0x0f09e79a, 0x2d9564a3, 0x3794b3a2, 0x99fa}}}, + {{{0x02d8c2f4, 0x13386882, 0x07006279, 0x064373ef, 0x18a0bd73, 0x1def1b26, 0x0f59fe9c, 0x063a2169, 0xfc5864}}, + {{0x1cfd274a, 0x08c6447f, 0x10ce2d00, 0x05960bd7, 0x1b4ab29e, 0x013cf35e, 0x055928cf, 0x0a59d15b, 0x99fade}}}, /* 11*16^28*G: */ - {{{0x11ff0f18, 0x0ac1dfc7, 0x149a42d1, 0x382f39c1, 0x32d6c207, 0x3eeb3e6b, 0x0f1dea9b, 0x0ee9ac31, 0xee99}}, - {{0x250782ad, 0x004e1db2, 0x30f2cb18, 0x0d72037d, 0x05bcfeb4, 0x3175633a, 0x0db2c1f6, 0x3536515e, 0xd87f}}}, + {{{0x11ff0f18, 0x1583bf8e, 0x12690b44, 0x0179ce0a, 0x0d6c207e, 0x1d67cd79, 0x077aa6fe, 0x14d6189e, 0xee993b}}, + {{0x050782ad, 0x009c3b65, 0x03cb2c60, 0x0b901bee, 0x1bcfeb43, 0x0eac6742, 0x0cb07db1, 0x1b28af1b, 0xd87fd4}}}, /* 13*16^28*G: */ - {{{0x0fdde3fc, 0x11e9fdd5, 0x1628cc9e, 0x2a222781, 0x2f31fbe5, 0x03710694, 0x3e2428da, 0x145eaba7, 0xba49}}, - {{0x2fcb7d01, 0x0fbf48cb, 0x3292caaa, 0x37872078, 0x13359adf, 0x3b90dd80, 0x055950b4, 0x2db872a5, 0xa88f}}}, + {{{0x0fdde3fc, 0x03d3fbaa, 0x18a33279, 0x11113c0a, 0x131fbe5a, 0x0e20d297, 0x090a3683, 0x0f55d3fc, 0xba4951}}, + {{0x0fcb7d01, 0x1f7e9197, 0x0a4b2aa8, 0x1c3903c6, 0x1359adfd, 0x121bb009, 0x16542d3b, 0x1c39528a, 0xa88fb6}}}, /* 15*16^28*G: */ - {{{0x3d14da68, 0x2224a8bd, 0x1d201737, 0x19307e13, 0x3612b54a, 0x0b3e09cd, 0x2f1ba4de, 0x23c5d08a, 0xd339}}, - {{0x15a90e3d, 0x3c1d8c6d, 0x141453a3, 0x31e9e48b, 0x22b020af, 0x094b47a2, 0x13d60eb7, 0x3535347f, 0xa34a}}} + {{{0x1d14da68, 0x0449517b, 0x14805cde, 0x0983f09b, 0x012b54a6, 0x07c139bb, 0x06e9378b, 0x02e8455e, 0xd3398f}}, + {{0x15a90e3d, 0x183b18da, 0x10514e8f, 0x0f4f245a, 0x0b020afc, 0x0968f451, 0x1583adc9, 0x1a9a3fa7, 0xa34ad4}}} }, { /* 1*16^29*G: */ - {{{0x3789b84d, 0x298196b5, 0x1041ce2e, 0x1f57b934, 0x2493fe16, 0x174446d5, 0x34b4ccdb, 0x298515cd, 0x4a89}}, - {{0x018e3ea8, 0x3e6df5fc, 0x0711999e, 0x0b8a018d, 0x2677e6a7, 0x0baa5e7f, 0x00d5c08c, 0x13a1fb52, 0x45b0}}}, + {{{0x1789b84d, 0x13032d6b, 0x010738ba, 0x1abdc9a2, 0x093fe167, 0x0888dab2, 0x0d3336d7, 0x028ae6e9, 0x4a89a6}}, + {{0x018e3ea8, 0x1cdbebf8, 0x1c46667b, 0x1c500c68, 0x077e6a72, 0x154bcff3, 0x1570230b, 0x10fda901, 0x45b04e}}}, /* 3*16^29*G: */ - {{{0x02e14c34, 0x39dac8dd, 0x33275936, 0x1317af81, 0x1377c983, 0x26cc39e0, 0x0ef92a2a, 0x25922a1c, 0xcc9f}}, - {{0x14be556b, 0x224855ea, 0x28c7e058, 0x2645fc60, 0x2689db29, 0x0598cf6f, 0x0c96f431, 0x3fcb2d7e, 0x829b}}}, + {{{0x02e14c34, 0x13b591ba, 0x0c9d64db, 0x18bd7c0e, 0x177c9834, 0x19873c09, 0x1e4a8aa6, 0x09150e1d, 0xcc9f96}}, + {{0x14be556b, 0x0490abd4, 0x031f8162, 0x122fe305, 0x089db299, 0x1319edf3, 0x05bd0c45, 0x0596bf19, 0x829bff}}}, /* 5*16^29*G: */ - {{{0x15de4837, 0x1f79b216, 0x1e5e74e8, 0x10a1b20b, 0x198a758d, 0x1630742b, 0x1041af4f, 0x23687eab, 0x5c61}}, - {{0x234a7dee, 0x02e160ed, 0x02278cac, 0x34d99259, 0x3d9671ec, 0x2038e127, 0x3a19d88b, 0x2445ef3c, 0x4c71}}}, + {{{0x15de4837, 0x1ef3642c, 0x1979d3a1, 0x050d905b, 0x18a758d4, 0x060e856c, 0x106bd3d6, 0x143f55a0, 0x5c618d}}, + {{0x034a7dee, 0x05c2c1db, 0x089e32b0, 0x06cc92c8, 0x19671ecd, 0x071c24fe, 0x067622e0, 0x02f79e74, 0x4c7191}}}, /* 7*16^29*G: */ - {{{0x16635396, 0x1624d099, 0x28a6c0c2, 0x32b8568d, 0x31c11ef2, 0x178b7799, 0x206a2e58, 0x221aa456, 0xab8a}}, - {{0x3fc92c23, 0x38e3e9a8, 0x3d2d6ad7, 0x0d8160fd, 0x3cd5abb9, 0x23fe0922, 0x04319566, 0x33df1f6a, 0xe773}}}, + {{{0x16635396, 0x0c49a132, 0x029b0309, 0x15c2b46d, 0x1c11ef2c, 0x116ef338, 0x1a8b9617, 0x0d522b40, 0xab8a88}}, + {{0x1fc92c23, 0x11c7d351, 0x14b5ab5f, 0x0c0b07ef, 0x0d5abb93, 0x1fc1245e, 0x0c6559a3, 0x0f8fb508, 0xe773cf}}}, /* 9*16^29*G: */ - {{{0x01df49c3, 0x3090f962, 0x1069a35a, 0x3a24219b, 0x15604aa9, 0x1992e2da, 0x1838cdec, 0x32145090, 0x62b7}}, - {{0x36341c21, 0x2f8da03f, 0x07cb5509, 0x2d4ed84e, 0x0922db8f, 0x225aba35, 0x20335594, 0x358854ab, 0xa71e}}}, + {{{0x01df49c3, 0x0121f2c4, 0x01a68d6b, 0x11210cda, 0x1604aa9e, 0x125c5b4a, 0x0e337b19, 0x0a284830, 0x62b7c8}}, + {{0x16341c21, 0x1f1b407f, 0x1f2d5426, 0x0a76c270, 0x122db8fb, 0x0b5746a4, 0x0cd56522, 0x042a55c0, 0xa71ed6}}}, /* 11*16^29*G: */ - {{{0x244f47d0, 0x2bc51b8b, 0x09f002f3, 0x167d77a5, 0x1fc9791b, 0x147c21a7, 0x089c5f97, 0x2f6fe917, 0x4897}}, - {{0x0e1320bf, 0x079406ab, 0x0f011958, 0x1b68006a, 0x3b093f52, 0x23b2a505, 0x0138c34e, 0x3083debf, 0xe77d}}}, + {{{0x044f47d0, 0x178a3717, 0x07c00bce, 0x13ebbd29, 0x1c9791b5, 0x0f8434ef, 0x0717e5d4, 0x17f48b91, 0x4897bd}}, + {{0x0e1320bf, 0x0f280d56, 0x1c046560, 0x1b400351, 0x1093f526, 0x1654a0bd, 0x0e30d3a3, 0x01ef5f82, 0xe77dc2}}}, /* 13*16^29*G: */ - {{{0x31581bd3, 0x186f3a6d, 0x2190786e, 0x3e8c637d, 0x322f2ecb, 0x0781ef69, 0x06576c45, 0x3f2d5592, 0xeb1c}}, - {{0x1cd98a09, 0x2f3a3661, 0x1bd1a645, 0x273cc671, 0x0d6e3cb3, 0x10017af9, 0x14d20504, 0x339d5c7e, 0xfd47}}}, + {{{0x11581bd3, 0x10de74db, 0x0641e1b9, 0x14631bec, 0x02f2ecbf, 0x103ded39, 0x15db1147, 0x16aac90c, 0xeb1cfc}}, + {{0x1cd98a09, 0x1e746cc2, 0x0f469916, 0x19e6338b, 0x16e3cb39, 0x002f5f26, 0x14814110, 0x0eae3f29, 0xfd47ce}}}, /* 15*16^29*G: */ - {{{0x273a3111, 0x0048af6d, 0x34c818f9, 0x2e0b905e, 0x2576a018, 0x152b0b9c, 0x21e09c0d, 0x22eef923, 0xa1fd}}, - {{0x38c704ef, 0x221f9942, 0x3d51169b, 0x3b12516f, 0x0916c0c7, 0x1df81ef0, 0x308569bd, 0x17628d28, 0xad21}}} + {{{0x073a3111, 0x00915edb, 0x132063e4, 0x105c82f6, 0x176a018b, 0x05617392, 0x18270355, 0x177c91c3, 0xa1fd8b}}, + {{0x18c704ef, 0x043f3285, 0x15445a6e, 0x18928b7f, 0x116c0c7e, 0x1f03de04, 0x015a6f5d, 0x11469461, 0xad215d}}} }, { /* 1*16^30*G: */ - {{{0x32bd05a0, 0x10e32129, 0x31fc80d3, 0x208cdf42, 0x2d1f90ba, 0x0be657cd, 0x1885cedc, 0x248d8e8c, 0xe5e8}}, - {{0x21a69f5d, 0x24db78af, 0x0d099aec, 0x1ce656e7, 0x1b5c3eca, 0x07ac079e, 0x387d2130, 0x27793686, 0x7743}}}, + {{{0x12bd05a0, 0x01c64253, 0x07f2034d, 0x0466fa16, 0x11f90ba8, 0x1ccaf9b6, 0x0173b70b, 0x06c74631, 0xe5e892}}, + {{0x01a69f5d, 0x09b6f15f, 0x14266bb2, 0x0732b739, 0x15c3eca7, 0x1580f3cd, 0x1f484c07, 0x1c9b4370, 0x77439d}}}, /* 3*16^30*G: */ - {{{0x01467d6b, 0x3c254a04, 0x2a24b514, 0x1f5c4a54, 0x2cf1d835, 0x06184590, 0x1ccf5d10, 0x24f7e50d, 0x5d23}}, - {{0x31bc5458, 0x1f19cf1a, 0x10473a80, 0x29c1e9d4, 0x1af46d72, 0x2f616cb5, 0x10f7d7ac, 0x18fc98ff, 0xe66e}}}, + {{{0x01467d6b, 0x184a9408, 0x0892d453, 0x1ae252a5, 0x0f1d8357, 0x0308b216, 0x13d74406, 0x1bf286b9, 0x5d2393}}, + {{0x11bc5458, 0x1e339e35, 0x011cea01, 0x0e0f4ea2, 0x0f46d72a, 0x0c2d96ad, 0x1df5eb2f, 0x1e4c7fa1, 0xe66e63}}}, /* 5*16^30*G: */ - {{{0x1d159f7a, 0x02c7a4f2, 0x242e590f, 0x3e4ea73c, 0x3f873fec, 0x33ecaf4b, 0x3893f3ad, 0x15e94eaa, 0x4536}}, - {{0x0a02fb78, 0x2708adc2, 0x01dda5d9, 0x2526f53a, 0x01c7286f, 0x3bc244e8, 0x23dc5da2, 0x2bbfe200, 0xbfb5}}}, + {{{0x1d159f7a, 0x058f49e4, 0x10b9643c, 0x127539e4, 0x1873fecf, 0x1d95e97f, 0x04fceb73, 0x14a75571, 0x453657}}, + {{0x0a02fb78, 0x0e115b84, 0x07769766, 0x0937a9d0, 0x1c7286f9, 0x18489d00, 0x171768bb, 0x1ff10047, 0xbfb5ae}}}, /* 7*16^30*G: */ - {{{0x146cb42a, 0x07b7b7cf, 0x32390933, 0x014a14e9, 0x3d73e7bc, 0x12b7aa84, 0x04c464d1, 0x1532c1ec, 0x435b}}, - {{0x1af72dd0, 0x1f8937b7, 0x33949a6b, 0x37131e50, 0x20585d5e, 0x12953307, 0x18a1a49f, 0x300c791c, 0xd726}}}, + {{{0x146cb42a, 0x0f6f6f9e, 0x08e424cc, 0x0a50a74e, 0x173e7bc0, 0x16f5509e, 0x11193452, 0x1960f609, 0x435b54}}, + {{0x1af72dd0, 0x1f126f6e, 0x0e5269ad, 0x1898f286, 0x0585d5ed, 0x12a660f0, 0x086927d2, 0x063c8e31, 0xd726c0}}}, /* 9*16^30*G: */ - {{{0x1d2fc263, 0x25f6506c, 0x365d57ba, 0x33e04f96, 0x13da0e89, 0x2f11f138, 0x2dd7e19f, 0x2e067853, 0x1805}}, - {{0x30870ec7, 0x1991c2d3, 0x151ecaf2, 0x2306be39, 0x0b31489c, 0x236aa1af, 0x38171585, 0x190a0250, 0x101f}}}, + {{{0x1d2fc263, 0x0beca0d8, 0x19755eea, 0x1f027cb6, 0x1da0e89c, 0x023e2709, 0x15f867ef, 0x033c29db, 0x1805b8}}, + {{0x10870ec7, 0x132385a7, 0x147b2bc9, 0x1835f1ca, 0x131489c8, 0x0d5435e5, 0x05c56163, 0x05012870, 0x101f64}}}, /* 11*16^30*G: */ - {{{0x0076d1df, 0x28ac6dc3, 0x27fa1b39, 0x07882050, 0x375f45f4, 0x05ea28a9, 0x3194f406, 0x2bd0d9b4, 0xc73a}}, - {{0x25ad6605, 0x09e7545b, 0x1893720d, 0x16d5e947, 0x3cdcfef7, 0x3806f8ee, 0x3916ef9c, 0x3b1a7b33, 0x9201}}}, + {{{0x0076d1df, 0x1158db86, 0x1fe86ce6, 0x1c410284, 0x15f45f41, 0x1d45153b, 0x053d0185, 0x086cda63, 0xc73aaf}}, + {{0x05ad6605, 0x13cea8b7, 0x024dc834, 0x16af4a3b, 0x0dcfef75, 0x00df1dde, 0x05bbe738, 0x0d3d99f2, 0x9201ec}}}, /* 13*16^30*G: */ - {{{0x05a745c7, 0x0da0fde6, 0x17eac07d, 0x2289ce30, 0x1d52c1bc, 0x226dabd8, 0x036d2771, 0x3ba3df57, 0xe3dd}}, - {{0x378efcc2, 0x0e7c2501, 0x3d027b1a, 0x0a30bc5e, 0x3bd8f47c, 0x146e1aa9, 0x32b871be, 0x2674e464, 0x4871}}}, + {{{0x05a745c7, 0x1b41fbcc, 0x1fab01f4, 0x144e7182, 0x152c1bc8, 0x0db57b0e, 0x1b49dc62, 0x11efab86, 0xe3ddee}}, + {{0x178efcc2, 0x1cf84a03, 0x1409ec68, 0x1185e2f7, 0x1d8f47c2, 0x0dc3553d, 0x0e1c6f94, 0x1a723265, 0x487199}}}, /* 15*16^30*G: */ - {{{0x0d4170b3, 0x131ccfa1, 0x03a3587f, 0x051055bf, 0x00a1d540, 0x22a8461b, 0x1f1e5af6, 0x2377080d, 0x45c7}}, - {{0x111faa1d, 0x1bbe8fb5, 0x020cc731, 0x2c119819, 0x3b3a512c, 0x06a74513, 0x15c0cb0e, 0x265188e3, 0x11af}}} + {{{0x0d4170b3, 0x06399f42, 0x0e8d61fd, 0x0882adf8, 0x0a1d5401, 0x1508c360, 0x0796bda2, 0x1b8406be, 0x45c78d}}, + {{0x111faa1d, 0x177d1f6a, 0x08331cc5, 0x008cc0c8, 0x13a512cb, 0x14e8a27d, 0x1032c386, 0x08c471ab, 0x11af99}}} }, { /* 1*16^31*G: */ - {{{0x3ab5c2cf, 0x055e664b, 0x3b084de2, 0x04bc3087, 0x3a90a453, 0x1d1d0413, 0x21f5071e, 0x1f90c788, 0xe410}}, - {{0x2b955c2b, 0x00a100fc, 0x37b2410d, 0x1e24b73f, 0x1c2b323c, 0x2319a1d0, 0x01c9a394, 0x0479b3dc, 0x1e5f}}}, + {{{0x1ab5c2cf, 0x0abccc97, 0x0c213788, 0x05e1843f, 0x090a4531, 0x03a0827d, 0x1d41c79d, 0x0863c443, 0xe4107e}}, + {{0x0b955c2b, 0x014201f9, 0x1ec90434, 0x1125b9fe, 0x02b323c7, 0x03343a0e, 0x1268e523, 0x1cd9ee03, 0x1e5f11}}}, /* 3*16^31*G: */ - {{{0x09b67b7e, 0x2ed6d8f0, 0x11c3d485, 0x1adecae4, 0x3c114276, 0x3e5c077a, 0x39f7daac, 0x26997b85, 0x85df}}, - {{0x030a36e3, 0x22ce1a7a, 0x3bc6ea58, 0x3ea52747, 0x0e297386, 0x2df57bfc, 0x36308bb6, 0x2dea8e6b, 0xa6b4}}}, + {{{0x09b67b7e, 0x1dadb1e0, 0x070f5216, 0x16f65722, 0x01142766, 0x0b80ef5e, 0x1df6ab3e, 0x0cbdc2f3, 0x85df9a}}, + {{0x030a36e3, 0x059c34f4, 0x0f1ba962, 0x15293a3f, 0x0297386f, 0x1eaf7f87, 0x0c22edad, 0x154735ec, 0xa6b4b7}}}, /* 5*16^31*G: */ - {{{0x0b3510d3, 0x09f3f798, 0x0a1d6e41, 0x34c599c1, 0x2d292885, 0x22861970, 0x3cd08a8d, 0x24ff9fe7, 0x23c4}}, - {{0x3ae89a47, 0x0d18bb10, 0x2b9dbd71, 0x2678d789, 0x3fe6d8f7, 0x1d76793b, 0x014230c2, 0x15aa790d, 0xadf4}}}, + {{{0x0b3510d3, 0x13e7ef30, 0x0875b904, 0x062cce09, 0x1292885d, 0x10c32e16, 0x1422a362, 0x1fcff3f9, 0x23c493}}, + {{0x1ae89a47, 0x1a317621, 0x0e76f5c4, 0x13c6bc4d, 0x1e6d8f79, 0x0ecf277f, 0x108c309d, 0x153c8682, 0xadf456}}}, /* 7*16^31*G: */ - {{{0x0b49a71f, 0x331a4602, 0x0227c39a, 0x0dbadb19, 0x3235ddac, 0x264faeab, 0x1d0edde5, 0x1b42cc53, 0x9440}}, - {{0x10b249a9, 0x1c706513, 0x263cf944, 0x389c9872, 0x2fe897d0, 0x01f24241, 0x1f179cd2, 0x39dfa193, 0x61aa}}}, + {{{0x0b49a71f, 0x06348c04, 0x089f0e6b, 0x0dd6d8c8, 0x035ddac3, 0x09f5d579, 0x03b77966, 0x016629ba, 0x94406d}}, + {{0x10b249a9, 0x18e0ca26, 0x18f3e511, 0x04e4c394, 0x1e897d0e, 0x1e484837, 0x05e73481, 0x0fd0c9be, 0x61aae7}}}, /* 9*16^31*G: */ - {{{0x20e50c32, 0x17378cf1, 0x0c6873fe, 0x3c425cba, 0x2e8d3877, 0x04db7d6f, 0x06c14337, 0x2fd0f7a2, 0x3c2e}}, - {{0x0a93c124, 0x38be245f, 0x2e8c9989, 0x0b4230e6, 0x2e28e7be, 0x16e4f480, 0x0399c652, 0x3669b17a, 0xa703}}}, + {{{0x00e50c32, 0x0e6f19e3, 0x11a1cff9, 0x0212e5d1, 0x08d3877f, 0x1b6fadf7, 0x1050cdc4, 0x087bd10d, 0x3c2ebf}}, + {{0x0a93c124, 0x117c48be, 0x1a326627, 0x1a118735, 0x028e7be2, 0x1c9e9017, 0x06719496, 0x14d8bd07, 0xa703d9}}}, /* 11*16^31*G: */ - {{{0x03a2355a, 0x020f677b, 0x06049907, 0x1946fcd7, 0x055f1299, 0x0796e27b, 0x00eb9f39, 0x0db5c9e5, 0x9875}}, - {{0x1bd05276, 0x031d7130, 0x03adccdf, 0x17db1f1a, 0x257b48b8, 0x02c70527, 0x1117243e, 0x26b59d3c, 0x12f1}}}, + {{{0x03a2355a, 0x041ecef6, 0x1812641c, 0x0a37e6b8, 0x15f12996, 0x12dc4f62, 0x1ae7ce47, 0x1ae4f281, 0x987536}}, + {{0x1bd05276, 0x063ae260, 0x0eb7337c, 0x1ed8f8d0, 0x17b48b85, 0x18e0a4f2, 0x05c90f82, 0x1ace9e22, 0x12f19a}}}, /* 13*16^31*G: */ - {{{0x12f3ec22, 0x03c151f1, 0x1a8f8a6b, 0x3e1b73dc, 0x32ddddd1, 0x34e2c5fb, 0x04468f19, 0x2b102693, 0xd515}}, - {{0x25a2863b, 0x28518bac, 0x31b806ec, 0x355f7c00, 0x12bd464c, 0x17921001, 0x09b2e1ea, 0x12050891, 0x51c0}}}, + {{{0x12f3ec22, 0x0782a3e2, 0x0a3e29ac, 0x10db9ee3, 0x0ddddd1f, 0x1c58bf79, 0x11a3c674, 0x08134988, 0xd515ac}}, + {{0x05a2863b, 0x10a31759, 0x06e01bb2, 0x0afbe006, 0x0bd464cd, 0x12420029, 0x0cb87a97, 0x02844893, 0x51c048}}}, /* 15*16^31*G: */ - {{{0x1971c857, 0x16687a69, 0x3e6093fa, 0x32679b6a, 0x21cf3dde, 0x14f30e2d, 0x1b0bae24, 0x27526179, 0x070b}}, - {{0x0ac8dfc1, 0x3e72d8f7, 0x05461aaf, 0x2a0f687b, 0x373cfb33, 0x2042b918, 0x3625086b, 0x1186ffd2, 0xed80}}} + {{{0x1971c857, 0x0cd0f4d2, 0x19824fe9, 0x133cdb57, 0x1cf3ddec, 0x1e61c5b0, 0x02eb8914, 0x0930bcb6, 0x70b9d}}, + {{0x0ac8dfc1, 0x1ce5b1ee, 0x15186abf, 0x107b43d8, 0x13cfb33a, 0x0857231b, 0x09421ae0, 0x037fe96c, 0xed8046}}} }, { /* 1*16^32*G: */ - {{{0x1789bd85, 0x1f213f27, 0x297eac35, 0x0d7fdf70, 0x06766efc, 0x20bf5623, 0x35e67fb9, 0x1ce6fbb6, 0x447d}}, - {{0x32e25b32, 0x31f8cf25, 0x3fae5000, 0x0d26e569, 0x0aaff73d, 0x3a7654e9, 0x131eee12, 0x096ae0d0, 0x2d48}}}, + {{{0x1789bd85, 0x1e427e4e, 0x05fab0d5, 0x0bfefb85, 0x0766efc3, 0x17eac463, 0x199fee60, 0x137ddb6b, 0x447d73}}, + {{0x12e25b32, 0x03f19e4b, 0x1eb94003, 0x09372b4f, 0x0aff73d3, 0x0eca9d25, 0x07bb84ba, 0x15706826, 0x2d4825}}}, /* 3*16^32*G: */ - {{{0x1ea6db68, 0x0f86663b, 0x02632c27, 0x3eb61582, 0x1ef4f6dd, 0x0537e597, 0x2017f58b, 0x14cf80f2, 0xf8b6}}, - {{0x2e760da9, 0x26f496c2, 0x05ca0ed6, 0x2f5c3767, 0x2a3ec66b, 0x11b76942, 0x054862f0, 0x13bd7b11, 0xc30f}}}, + {{{0x1ea6db68, 0x1f0ccc76, 0x098cb09c, 0x15b0ac10, 0x0f4f6ddf, 0x06fcb2ef, 0x05fd62c5, 0x07c07940, 0xf8b653}}, + {{0x0e760da9, 0x0de92d85, 0x17283b5a, 0x1ae1bb38, 0x03ec66bb, 0x16ed2855, 0x1218bc11, 0x1ebd888a, 0xc30f4e}}}, /* 5*16^32*G: */ - {{{0x3924e753, 0x1b5753af, 0x0f8727c6, 0x005cc1cb, 0x2dfb755f, 0x3bc61ca7, 0x2847c548, 0x2274d560, 0xf352}}, - {{0x2b13a20c, 0x2916d70b, 0x12d0f04a, 0x18bf15ca, 0x0e1bd8c5, 0x3c2286d4, 0x013fb93d, 0x1e07b17b, 0x75c1}}}, + {{{0x1924e753, 0x16aea75f, 0x1e1c9f19, 0x02e60e59, 0x1fb755f0, 0x18c394f6, 0x11f1523b, 0x1a6ab050, 0xf35289}}, + {{0x0b13a20c, 0x122dae17, 0x0b43c12a, 0x05f8ae52, 0x01bd8c56, 0x0450da87, 0x0fee4f7c, 0x03d8bd82, 0x75c178}}}, /* 7*16^32*G: */ - {{{0x3018017e, 0x0e572d9c, 0x2df23d72, 0x0507fff5, 0x334e01af, 0x10617ed9, 0x01716483, 0x1add3691, 0xcfd0}}, - {{0x0e0dff50, 0x02b9ef93, 0x3779777a, 0x0c0c1e1a, 0x1a795000, 0x0ece561f, 0x3a913810, 0x2dea6dca, 0xb647}}}, + {{{0x1018017e, 0x1cae5b39, 0x17c8f5c8, 0x083fffad, 0x14e01af1, 0x0c2fdb39, 0x1c5920d0, 0x0e9b4882, 0xcfd06b}}, + {{0x0e0dff50, 0x0573df26, 0x1de5dde8, 0x0060f0d6, 0x07950003, 0x19cac3ed, 0x044e040e, 0x1536e575, 0xb647b7}}}, /* 9*16^32*G: */ - {{{0x392db860, 0x13206415, 0x29a247b0, 0x0224a20c, 0x15dbe981, 0x0b5b423c, 0x1dcd1151, 0x39d312b5, 0x0755}}, - {{0x20d09849, 0x3598036e, 0x3c2777a7, 0x24dd1933, 0x015bc2b2, 0x26cb608e, 0x19e4dd24, 0x2be9d4eb, 0xfe16}}}, + {{{0x192db860, 0x0640c82b, 0x06891ec1, 0x11251065, 0x1dbe9810, 0x0b68478a, 0x1344544b, 0x09895abb, 0x755e7}}, + {{0x00d09849, 0x0b3006dd, 0x109dde9f, 0x06e8c99f, 0x15bc2b29, 0x196c11c0, 0x19374926, 0x14ea75b3, 0xfe16af}}}, /* 11*16^32*G: */ - {{{0x2a26ba6b, 0x27bda557, 0x2da12c3a, 0x0b28a925, 0x30bbdedd, 0x043035fa, 0x2c96968a, 0x2a1330dc, 0x88fb}}, - {{0x244972f8, 0x01051e07, 0x00cfdce8, 0x12a78a38, 0x14788d48, 0x1b6916d4, 0x1be0fd26, 0x3bd9274e, 0x512a}}}, + {{{0x0a26ba6b, 0x0f7b4aaf, 0x1684b0ea, 0x1945492d, 0x0bbdedd2, 0x0606bf58, 0x05a5a284, 0x09986e59, 0x88fba8}}, + {{0x044972f8, 0x020a3c0f, 0x033f73a0, 0x153c51c0, 0x0788d484, 0x0d22da8a, 0x183f499b, 0x0c93a737, 0x512aef}}}, /* 13*16^32*G: */ - {{{0x14720cab, 0x2712290a, 0x339b17e3, 0x07a97505, 0x1c6f2c1a, 0x03db9d55, 0x15beb8e5, 0x2b32fb01, 0xe1a0}}, - {{0x34b185c9, 0x1b514fd5, 0x080254ea, 0x128a9c74, 0x2ebcbf08, 0x1be0c1df, 0x0c854183, 0x1a3edfa6, 0xe079}}}, + {{{0x14720cab, 0x0e245214, 0x0e6c5f8e, 0x1d4ba82e, 0x06f2c1a1, 0x1b73aaae, 0x0fae3943, 0x197d80ab, 0xe1a0ac}}, + {{0x14b185c9, 0x16a29fab, 0x000953a9, 0x1454e3a1, 0x0bcbf084, 0x1c183bf7, 0x015060db, 0x1f6fd319, 0xe07968}}}, /* 15*16^32*G: */ - {{{0x2c26c42a, 0x2a0a3f7f, 0x2b11bb62, 0x26fedf91, 0x27e6a024, 0x2cd624c7, 0x33c7e50d, 0x0ee1b9a9, 0x0ae9}}, - {{0x39f808ca, 0x0418cd0e, 0x1aadb649, 0x228e7bbd, 0x220b3727, 0x0b8fb707, 0x07e13a94, 0x3db7451e, 0x7028}}} + {{{0x0c26c42a, 0x14147eff, 0x0c46ed8a, 0x17f6fc8d, 0x1e6a0249, 0x1ac498f3, 0x11f9436c, 0x10dcd4e7, 0xae93b}}, + {{0x19f808ca, 0x08319a1d, 0x0ab6d924, 0x1473ddeb, 0x00b37278, 0x11f6e0f1, 0x184ea50b, 0x1ba28f0f, 0x7028f6}}} }, { /* 1*16^33*G: */ - {{{0x137de736, 0x3af62eb0, 0x288ce241, 0x3e355861, 0x1ec18ea2, 0x1d50ae33, 0x0cf3e893, 0x38c52527, 0x9022}}, - {{0x04c42ecc, 0x13bd7021, 0x0ea7657f, 0x124d9b11, 0x26ce087f, 0x02ec1148, 0x0a39466d, 0x1793ca41, 0x2fae}}}, + {{{0x137de736, 0x15ec5d60, 0x02338907, 0x11aac30d, 0x0c18ea2f, 0x0a15c66f, 0x1cfa24dd, 0x02929399, 0x9022e3}}, + {{0x04c42ecc, 0x077ae042, 0x1a9d95fd, 0x126cd889, 0x0ce087f4, 0x1d822913, 0x0e519b42, 0x09e52094, 0x2fae5e}}}, /* 3*16^33*G: */ - {{{0x109b01f5, 0x05c1b2e3, 0x273c0519, 0x0fcd460c, 0x37857af7, 0x3cb4fc6b, 0x3e945fb0, 0x1cb8c1db, 0x6e58}}, - {{0x2bcd5fde, 0x0c1d6366, 0x09a85a7c, 0x0c5e7538, 0x3ef0ebc1, 0x30752bce, 0x3717180c, 0x300bb235, 0x4213}}}, + {{{0x109b01f5, 0x0b8365c6, 0x1cf01464, 0x1e6a3064, 0x1857af73, 0x169f8d7b, 0x0517ec3c, 0x1c60edfd, 0x6e5872}}, + {{0x0bcd5fde, 0x183ac6cd, 0x06a169f0, 0x02f3a9c1, 0x0f0ebc13, 0x0ea579df, 0x05c60330, 0x05d91aee, 0x4213c0}}}, /* 5*16^33*G: */ - {{{0x2fe45b1f, 0x14e6dd1f, 0x26168c2b, 0x34557ecb, 0x17df827b, 0x3478d130, 0x23f504af, 0x082c6976, 0x2922}}, - {{0x134bb026, 0x3f902e2d, 0x0dd41045, 0x30d10c13, 0x298d7ff7, 0x31e57feb, 0x175aee37, 0x2814cafc, 0xe316}}}, + {{{0x0fe45b1f, 0x09cdba3f, 0x185a30ad, 0x02abf65c, 0x1df827bd, 0x0f1a260b, 0x1d412bf4, 0x1634bb47, 0x292220}}, + {{0x134bb026, 0x1f205c5a, 0x17504117, 0x06886099, 0x18d7ff7c, 0x1caffd74, 0x16bb8df1, 0x0a657e2e, 0xe316a0}}}, /* 7*16^33*G: */ - {{{0x23abd540, 0x3a14198a, 0x3166de43, 0x20101952, 0x093a340e, 0x093e1c84, 0x04f0ac32, 0x385201e9, 0x3644}}, - {{0x155da631, 0x071bf873, 0x26fa14de, 0x05df3b69, 0x21e29300, 0x0a14c27e, 0x2797611c, 0x245436f0, 0xec5a}}}, + {{{0x03abd540, 0x14283315, 0x059b790f, 0x0080ca96, 0x13a340e8, 0x07c39084, 0x1c2b0c89, 0x0900f489, 0x3644e1}}, + {{0x155da631, 0x0e37f0e6, 0x1be85378, 0x0ef9db4c, 0x1e293001, 0x02984fd0, 0x05d8470a, 0x0a1b784f, 0xec5a91}}}, /* 9*16^33*G: */ - {{{0x09142ccb, 0x28bf487a, 0x287ede31, 0x248296b1, 0x3bb4824c, 0x2ce3d264, 0x0d838e55, 0x1f6b85ff, 0xedfe}}, - {{0x2c593d75, 0x2e5474c6, 0x151142eb, 0x2910ada7, 0x15beb81d, 0x1574ad3d, 0x1af21618, 0x24848b83, 0xc886}}}, + {{{0x09142ccb, 0x117e90f4, 0x01fb78c6, 0x0414b58d, 0x1b4824c9, 0x1c7a4c9d, 0x00e3956c, 0x15c2ff9b, 0xedfe7d}}, + {{0x0c593d75, 0x1ca8e98d, 0x14450bae, 0x08856d3a, 0x1beb81da, 0x0e95a7aa, 0x1c858615, 0x0245c1b5, 0xc88692}}}, /* 11*16^33*G: */ - {{{0x0a41b208, 0x0f69c719, 0x2e27000f, 0x3dd1d737, 0x2a0de8e7, 0x05009af3, 0x1a695987, 0x25a2d016, 0x5311}}, - {{0x048e4b69, 0x24787e78, 0x036877f6, 0x0f077009, 0x33da113b, 0x196078ce, 0x22978a6c, 0x1ccacf70, 0xb78d}}}, + {{{0x0a41b208, 0x1ed38e32, 0x189c003c, 0x0e8eb9bd, 0x00de8e7f, 0x00135e75, 0x1a5661c5, 0x11680b34, 0x531196}}, + {{0x048e4b69, 0x08f0fcf0, 0x0da1dfda, 0x183b8048, 0x1da113b3, 0x0c0f19d9, 0x05e29b19, 0x0567b845, 0xb78d73}}}, /* 13*16^33*G: */ - {{{0x095daae7, 0x0f406d71, 0x07033bcb, 0x11b9bb1f, 0x20e1d5af, 0x08afdbd5, 0x3a594f7a, 0x347c8bfe, 0xf65d}}, - {{0x02556738, 0x35396a67, 0x2acd9b28, 0x018603e7, 0x3c4cd0eb, 0x1bf98df3, 0x366e820e, 0x2e083386, 0x9d71}}}, + {{{0x095daae7, 0x1e80dae2, 0x1c0cef2c, 0x0dcdd8f8, 0x0e1d5af4, 0x15fb7ab0, 0x1653de88, 0x1e45ff74, 0xf65dd1}}, + {{0x02556738, 0x0a72d4ce, 0x0b366ca3, 0x0c301f3d, 0x04cd0eb0, 0x1f31be7e, 0x1ba0839b, 0x0419c36c, 0x9d71b8}}}, /* 15*16^33*G: */ - {{{0x3afcf1ee, 0x2fbf0578, 0x2069a11a, 0x3eaa011c, 0x2807c60a, 0x2fd202aa, 0x2e248b41, 0x039fb732, 0xa667}}, - {{0x20c67fc8, 0x1e21c2af, 0x13cf38a3, 0x3ce62472, 0x17ac131e, 0x17dcbd25, 0x1c2f3a39, 0x05324e94, 0xa7fd}}} + {{{0x1afcf1ee, 0x1f7e0af1, 0x01a6846a, 0x155008e4, 0x007c60af, 0x1a405554, 0x0922d06f, 0x0fdb995c, 0xa6670e}}, + {{0x00c67fc8, 0x1c43855f, 0x0f3ce28d, 0x07312392, 0x1ac131ef, 0x1b97a4ab, 0x0bce8e57, 0x19274a38, 0xa7fd14}}} }, { /* 1*16^34*G: */ - {{{0x04cd3397, 0x10451705, 0x1515eb57, 0x0d304186, 0x156deddc, 0x21b3cad4, 0x1a723893, 0x3fc1067b, 0x73ba}}, - {{0x1adcb8e4, 0x07bca84e, 0x02613494, 0x27be4b3e, 0x0f825e77, 0x0347a306, 0x3ac5f6a0, 0x3798d25d, 0x1e97}}}, + {{{0x04cd3397, 0x008a2e0a, 0x1457ad5d, 0x09820c32, 0x16deddc3, 0x16795a8a, 0x1c8e24e1, 0x00833db4, 0x73baff}}, + {{0x1adcb8e4, 0x0f79509c, 0x0984d250, 0x1df259f0, 0x1825e779, 0x08f460c7, 0x117da803, 0x0c692ef5, 0x1e97de}}}, /* 3*16^34*G: */ - {{{0x161fb913, 0x3ac3e548, 0x2d312977, 0x04091855, 0x3ed04e3e, 0x0e237912, 0x20a18344, 0x0cc30cf9, 0x45f8}}, - {{0x0c15c3bc, 0x035205f0, 0x2fc33737, 0x1b421e7d, 0x3a7760f0, 0x3a01db62, 0x2906ef80, 0x33db6ff5, 0xc212}}}, + {{{0x161fb913, 0x1587ca90, 0x14c4a5df, 0x0048c2ad, 0x0d04e3e1, 0x046f225f, 0x0860d10e, 0x01867cc1, 0x45f833}}, + {{0x0c15c3bc, 0x06a40be0, 0x1f0cdcdc, 0x1a10f3ed, 0x07760f06, 0x003b6c5d, 0x01bbe03a, 0x0db7fad2, 0xc212cf}}}, /* 5*16^34*G: */ - {{{0x2e393654, 0x2bbe5a47, 0x3edd7c75, 0x1752f87c, 0x0d599196, 0x1680722f, 0x3bdab65f, 0x37126b35, 0x5544}}, - {{0x0f53206f, 0x0d842efe, 0x3d58e732, 0x07bfa5c0, 0x13519224, 0x3016d6e2, 0x3fd4ac04, 0x21625421, 0xed3e}}}, + {{{0x0e393654, 0x177cb48f, 0x1b75f1d6, 0x1a97c3e7, 0x15991965, 0x100e45e6, 0x16ad97d6, 0x09359af7, 0x5544dc}}, + {{0x0f53206f, 0x1b085dfc, 0x15639cc8, 0x1dfd2e07, 0x15192241, 0x02dadc49, 0x152b0130, 0x112a10ff, 0xed3e85}}}, /* 7*16^34*G: */ - {{{0x28a15dfd, 0x0fcd6650, 0x1fa9e551, 0x076eb009, 0x22f69574, 0x34bb556b, 0x2e7734b3, 0x2de41867, 0x2757}}, - {{0x3042c341, 0x323a1033, 0x0a7156df, 0x1a25e28f, 0x15500d17, 0x25d484f3, 0x2b12e5cc, 0x34b55530, 0xdf46}}}, + {{{0x08a15dfd, 0x1f9acca1, 0x1ea79544, 0x1b75804b, 0x0f695741, 0x176aad71, 0x1dcd2cf4, 0x120c33dc, 0x2757b7}}, + {{0x1042c341, 0x04742067, 0x09c55b7f, 0x112f1479, 0x1500d176, 0x1a909e6a, 0x04b97325, 0x1aaa9856, 0xdf46d2}}}, /* 9*16^34*G: */ - {{{0x3f840a5b, 0x3fb7d09a, 0x3ad4984e, 0x232b6974, 0x143ccd14, 0x10873304, 0x22bc8d98, 0x10df7943, 0xe872}}, - {{0x1377e86a, 0x21396154, 0x1396464b, 0x0e8d1b3e, 0x248bf5ac, 0x2f247d98, 0x29616593, 0x2f22449c, 0xf984}}}, + {{{0x1f840a5b, 0x1f6fa135, 0x0b52613b, 0x195b4ba7, 0x03ccd148, 0x10e6608a, 0x0f236610, 0x0fbca1c5, 0xe87243}}, + {{0x1377e86a, 0x0272c2a8, 0x0e59192e, 0x1468d9f2, 0x08bf5ac3, 0x048fb312, 0x185964ef, 0x11224e52, 0xf984bc}}}, /* 11*16^34*G: */ - {{{0x336afd6a, 0x255aa6e2, 0x1781e3d4, 0x187f1428, 0x33334a92, 0x3bdb579b, 0x375c0392, 0x372ae935, 0xc56c}}, - {{0x33f87c26, 0x1821afbb, 0x28cc723e, 0x3d20ec95, 0x194ef566, 0x3b7ac5fd, 0x2b070cd2, 0x15b8bce1, 0xd160}}}, + {{{0x136afd6a, 0x0ab54dc5, 0x1e078f52, 0x03f8a142, 0x1334a926, 0x1b6af379, 0x1700e4bb, 0x15749aee, 0xc56cdc}}, + {{0x13f87c26, 0x10435f77, 0x0331c8f9, 0x090764ad, 0x14ef566f, 0x0f58bfac, 0x01c334bb, 0x1c5e70d6, 0xd16056}}}, /* 13*16^34*G: */ - {{{0x2cfd2cd0, 0x36b66034, 0x19c0c131, 0x2504cd10, 0x08abb123, 0x34a160f9, 0x3f2869cf, 0x399ce3cf, 0xd3d6}}, - {{0x394ae2dc, 0x315e71dd, 0x2f6f8f14, 0x07e95a30, 0x3de59b00, 0x36a3fdcd, 0x19b68536, 0x23d7f345, 0xff44}}}, + {{{0x0cfd2cd0, 0x0d6cc069, 0x070304c7, 0x08266883, 0x0abb1239, 0x142c1f24, 0x0a1a73f4, 0x0e71e7fe, 0xd3d6e6}}, + {{0x194ae2dc, 0x02bce3bb, 0x1dbe3c53, 0x1f4ad185, 0x1e59b001, 0x147fb9be, 0x0da14db6, 0x0bf9a2b3, 0xff448f}}}, /* 15*16^34*G: */ - {{{0x1ab7a64c, 0x25622157, 0x209ab7a0, 0x14235a8e, 0x37d40656, 0x04cb5c88, 0x05c07b03, 0x1de215b9, 0x88f9}}, - {{0x1575f103, 0x017a6384, 0x16d2673a, 0x30c02488, 0x169e5836, 0x0c6bc95e, 0x15c74345, 0x173751ad, 0x4a74}}} + {{{0x1ab7a64c, 0x0ac442ae, 0x026ade82, 0x011ad474, 0x1d406565, 0x196b911b, 0x101ec0c4, 0x110adc8b, 0x88f977}}, + {{0x1575f103, 0x02f4c708, 0x1b499ce8, 0x06012442, 0x09e5836c, 0x0d792bcb, 0x11d0d14c, 0x1ba8d6ab, 0x4a745c}}} }, { /* 1*16^35*G: */ - {{{0x1fa4e33c, 0x38b97ecc, 0x3098cb30, 0x20efb1e2, 0x36fb9826, 0x1111b0a5, 0x025bbc97, 0x11ae4693, 0x9cf6}}, - {{0x0e0d4563, 0x27117818, 0x3c160321, 0x081609fa, 0x021f319e, 0x0238962e, 0x25a891e4, 0x1893707d, 0x37b0}}}, + {{{0x1fa4e33c, 0x1172fd98, 0x02632cc3, 0x077d8f16, 0x0fb98268, 0x023614bb, 0x16ef25d1, 0x17234984, 0x9cf646}}, + {{0x0e0d4563, 0x0e22f030, 0x10580c86, 0x00b04fd7, 0x01f319e2, 0x0712c5c1, 0x0a247902, 0x09b83ecb, 0x37b062}}}, /* 3*16^35*G: */ - {{{0x06bf1e67, 0x262d8633, 0x25caf63e, 0x1599d27f, 0x364e0f4c, 0x2994e09d, 0x364999d7, 0x10f78546, 0x83cb}}, - {{0x099acc97, 0x09fba2cc, 0x1d1169ea, 0x1d108b2f, 0x0418f828, 0x0601b989, 0x0f6f8efb, 0x232892e6, 0xbce2}}}, + {{{0x06bf1e67, 0x0c5b0c66, 0x172bd8fa, 0x0cce93fc, 0x04e0f4c5, 0x129c13bb, 0x126675e9, 0x1bc2a36c, 0x83cb43}}, + {{0x099acc97, 0x13f74598, 0x1445a7a8, 0x0884597b, 0x018f8287, 0x00373122, 0x1be3bec6, 0x1449731e, 0xbce28c}}}, /* 5*16^35*G: */ - {{{0x1c0f057e, 0x0c2b5d23, 0x1d53dd82, 0x3a18a1c0, 0x25022484, 0x103f0578, 0x2b08c033, 0x2cf95833, 0x3ff3}}, - {{0x2817965e, 0x3507df6a, 0x07017622, 0x0408dbb1, 0x067843a0, 0x3f45c15e, 0x2578f6f7, 0x2b5bceed, 0x7f17}}}, + {{{0x1c0f057e, 0x1856ba46, 0x154f7608, 0x10c50e03, 0x1022484e, 0x07e0af12, 0x02300cd0, 0x1cac19d6, 0x3ff3b3}}, + {{0x0817965e, 0x0a0fbed5, 0x1c05d88b, 0x0046dd88, 0x07843a01, 0x08b82bc3, 0x1e3dbdff, 0x0de776ca, 0x7f17ad}}}, /* 7*16^35*G: */ - {{{0x325e69f1, 0x14452d00, 0x022bcb51, 0x19ea3cb5, 0x16af9963, 0x067785cf, 0x3d83fdda, 0x36cb763f, 0x6e9e}}, - {{0x002b7e9b, 0x08385f8d, 0x19f281b7, 0x1c9d151e, 0x33bff61c, 0x155aad97, 0x3954eab3, 0x0885b3bf, 0xc082}}}, + {{{0x125e69f1, 0x088a5a01, 0x08af2d45, 0x0f51e5a8, 0x0af99636, 0x0ef0b9eb, 0x00ff7686, 0x05bb1ffb, 0x6e9edb}}, + {{0x002b7e9b, 0x1070bf1a, 0x07ca06dc, 0x04e8a8f3, 0x1bff61c7, 0x0b55b2f9, 0x153aacd5, 0x02d9dff2, 0xc08222}}}, /* 9*16^35*G: */ - {{{0x2288f038, 0x3c94bd9a, 0x35ff820b, 0x21da253a, 0x2c2d32f0, 0x2f06779b, 0x01c4befa, 0x203a0131, 0x5ee2}}, - {{0x36f1ee6e, 0x316aae1a, 0x0e6c6f41, 0x35e0cea6, 0x09eec011, 0x0161bfb3, 0x3e39284c, 0x1a7e519d, 0xbcd9}}}, + {{{0x0288f038, 0x19297b35, 0x17fe082f, 0x0ed129d6, 0x02d32f08, 0x00cef376, 0x112fbeaf, 0x1d009883, 0x5ee280}}, + {{0x16f1ee6e, 0x02d55c35, 0x19b1bd07, 0x0f067531, 0x1eec011d, 0x0c37f664, 0x0e4a1301, 0x1f28cefc, 0xbcd969}}}, /* 11*16^35*G: */ - {{{0x00c708c8, 0x02fcc95b, 0x370a86aa, 0x0d0c13cb, 0x3e288c2c, 0x38d97647, 0x205736df, 0x059b8170, 0xe1f0}}, - {{0x3896ed38, 0x1c635cec, 0x3b5a00ae, 0x1957c8bb, 0x233016fb, 0x118cafa2, 0x03b52044, 0x194fa45b, 0xe647}}}, + {{{0x00c708c8, 0x05f992b6, 0x1c2a1aa8, 0x08609e5e, 0x0288c2c3, 0x1b2ec8ff, 0x15cdb7f8, 0x0dc0b840, 0xe1f016}}, + {{0x1896ed38, 0x18c6b9d9, 0x0d6802b9, 0x0abe45df, 0x13016fb6, 0x1195f451, 0x0d481111, 0x07d22d87, 0xe64765}}}, /* 13*16^35*G: */ - {{{0x076edefb, 0x383c2729, 0x00e7d5d7, 0x162f6004, 0x39c7badd, 0x086ad0a5, 0x2345c7f1, 0x25a1eafd, 0x2808}}, - {{0x1d1b0ae0, 0x3bd15c8a, 0x20392122, 0x34c6c1ef, 0x0541c44d, 0x3867af64, 0x33191a67, 0x073ccf4e, 0x5d07}}}, + {{{0x076edefb, 0x10784e52, 0x039f575f, 0x117b0020, 0x1c7badd5, 0x0d5a14bc, 0x1171fc48, 0x10f57ec6, 0x280896}}, + {{0x1d1b0ae0, 0x17a2b914, 0x00e4848b, 0x06360f7c, 0x141c44dd, 0x0cf5ec82, 0x064699f8, 0x1e67a766, 0x5d071c}}}, /* 15*16^35*G: */ - {{{0x3344897a, 0x04b666f3, 0x24c269dd, 0x27b4c1d6, 0x25edab7b, 0x217a1490, 0x104cb705, 0x2c378a06, 0xeb15}}, - {{0x25bfe7ee, 0x3677a0f3, 0x17d0b82a, 0x11a62cbe, 0x332f8581, 0x22abe335, 0x26071089, 0x3745a709, 0x096c}}} + {{{0x1344897a, 0x096ccde7, 0x1309a774, 0x1da60eb4, 0x1edab7b9, 0x0f429212, 0x132dc161, 0x1bc50320, 0xeb15b0}}, + {{0x05bfe7ee, 0x0cef41e7, 0x1f42e0ab, 0x0d3165f2, 0x12f85814, 0x157c66b9, 0x01c42262, 0x02d384cc, 0x96cdd}}} }, { /* 1*16^36*G: */ - {{{0x123b716d, 0x09beb701, 0x34e1a6b8, 0x08e259bd, 0x18df9e0d, 0x171e4e34, 0x0a534e8a, 0x16f8e2e3, 0xf81f}}, - {{0x12632401, 0x19000bd4, 0x28783304, 0x01d6140e, 0x0e032866, 0x1b4a74e0, 0x306df1d5, 0x124ca707, 0xdc7f}}}, + {{{0x123b716d, 0x137d6e02, 0x13869ae0, 0x0712cdee, 0x0df9e0d2, 0x03c9c68c, 0x14d3a297, 0x1c717194, 0xf81f5b}}, + {{0x12632401, 0x120017a8, 0x01e0cc11, 0x0eb0a075, 0x00328660, 0x094e9c07, 0x1b7c755b, 0x065383e0, 0xdc7f49}}}, /* 3*16^36*G: */ - {{{0x39d19d8a, 0x1315a140, 0x1a552158, 0x1049e254, 0x2d490a3b, 0x1bb0d705, 0x286385af, 0x21143ec4, 0xa600}}, - {{0x190d2c4f, 0x36576ecd, 0x326573df, 0x3f8023e9, 0x29ca84f0, 0x1b5179ef, 0x37c72c8f, 0x1e7019e8, 0x7b4b}}}, + {{{0x19d19d8a, 0x062b4281, 0x09548561, 0x024f12a3, 0x1490a3b4, 0x161ae0b6, 0x18e16bdb, 0x0a1f6250, 0xa60084}}, + {{0x190d2c4f, 0x0caedd9a, 0x0995cf7f, 0x1c011f4e, 0x1ca84f0f, 0x0a2f3df4, 0x11cb23db, 0x180cf46f, 0x7b4b79}}}, /* 5*16^36*G: */ - {{{0x096cac9f, 0x1a61ece5, 0x044de722, 0x38e33a97, 0x2b0e1c59, 0x3025e63f, 0x1f354c64, 0x20ac659f, 0xde53}}, - {{0x2fa473d3, 0x33820bf6, 0x3d841157, 0x38f8a51c, 0x0f9f2bc2, 0x0ec02647, 0x0918562c, 0x2d9e2da7, 0x9c47}}}, + {{{0x096cac9f, 0x14c3d9ca, 0x11379c89, 0x0719d4b8, 0x10e1c59e, 0x04bcc7f5, 0x0d531930, 0x1632cfbe, 0xde5382}}, + {{0x0fa473d3, 0x070417ed, 0x1610455f, 0x07c528e7, 0x19f2bc2e, 0x1804c8e7, 0x06158b0e, 0x0f16d392, 0x9c47b6}}}, /* 7*16^36*G: */ - {{{0x06807a23, 0x32ca58de, 0x225ff3e7, 0x0008145a, 0x194ec840, 0x12e67544, 0x2a908534, 0x1ec201fc, 0xa722}}, - {{0x14115894, 0x311c660f, 0x328cdc91, 0x2fe055ed, 0x2075abe7, 0x2a11e482, 0x139e845d, 0x1d497517, 0xf550}}}, + {{{0x06807a23, 0x0594b1bc, 0x097fcf9f, 0x0040a2d4, 0x14ec8400, 0x1ccea88c, 0x04214d12, 0x0100fe55, 0xa7227b}}, + {{0x14115894, 0x0238cc1e, 0x0a337247, 0x1f02af6e, 0x075abe7b, 0x023c9050, 0x07a1176a, 0x04ba8ba7, 0xf55075}}}, /* 9*16^36*G: */ - {{{0x044d14c0, 0x29e5ff08, 0x1a8f35e5, 0x172ad7e8, 0x261d3900, 0x2af9ce8d, 0x04596465, 0x0ba3508d, 0xcd2b}}, - {{0x22496315, 0x1582b3c8, 0x1accecea, 0x36dbc32e, 0x00f671fd, 0x017bb76b, 0x070a24d5, 0x04b7e6c2, 0xf130}}}, + {{{0x044d14c0, 0x13cbfe10, 0x0a3cd796, 0x1956bf43, 0x01d39005, 0x1f39d1b3, 0x1659196a, 0x11a84688, 0xcd2b2e}}, + {{0x02496315, 0x0b056791, 0x0b33b3a9, 0x16de1973, 0x0f671fdd, 0x0f76ed60, 0x02893541, 0x1bf3610e, 0xf13012}}}, /* 11*16^36*G: */ - {{{0x399a1566, 0x1bd3ac48, 0x3228f696, 0x171956bf, 0x1f9dd8f2, 0x3ef26e0f, 0x1f7eb4ce, 0x3a1323c3, 0x11b2}}, - {{0x1c56bb73, 0x2692cf01, 0x0d809685, 0x12d56103, 0x3405cc82, 0x0b5a61e5, 0x23175d04, 0x1da76f28, 0x6103}}}, + {{{0x199a1566, 0x17a75891, 0x08a3da59, 0x18cab5fe, 0x19dd8f25, 0x1e4dc1ef, 0x1fad33be, 0x0991e1be, 0x11b2e8}}, + {{0x1c56bb73, 0x0d259e02, 0x16025a16, 0x16ab0819, 0x005cc824, 0x0b4c3cba, 0x05d7410b, 0x13b79446, 0x610376}}}, /* 13*16^36*G: */ - {{{0x1ba6f34a, 0x3427aca3, 0x245c6f87, 0x0a1a83f8, 0x19148531, 0x36828fbe, 0x3a070759, 0x064a57ca, 0xfb6d}}, - {{0x2bcf0452, 0x2d7cf208, 0x1685b1f9, 0x3f3e8b72, 0x2791b9ec, 0x223f5312, 0x346dd9e3, 0x0b4a75ef, 0xf29b}}}, + {{{0x1ba6f34a, 0x084f5946, 0x1171be1f, 0x10d41fc4, 0x11485312, 0x1051f7cc, 0x01c1d676, 0x052be574, 0xfb6d19}}, + {{0x0bcf0452, 0x1af9e411, 0x1a16c7e6, 0x19f45b92, 0x191b9ecf, 0x07ea6253, 0x1b7678e2, 0x053af7e8, 0xf29b2d}}}, /* 15*16^36*G: */ - {{{0x0a435427, 0x1328b4a8, 0x3e4db507, 0x24042609, 0x106651a6, 0x3d9d9436, 0x013c10aa, 0x27f3040f, 0xff42}}, - {{0x39853824, 0x39411434, 0x23a0da28, 0x16fb94d2, 0x18687620, 0x10272158, 0x2cdb094d, 0x3e59a293, 0x2add}}} + {{{0x0a435427, 0x06516950, 0x1936d41d, 0x0021304f, 0x06651a69, 0x13b286c8, 0x0f042abd, 0x19820782, 0xff429f}}, + {{0x19853824, 0x12822869, 0x0e8368a3, 0x17dca694, 0x06876205, 0x04e42b0c, 0x16c25350, 0x0cd149d9, 0x2addf9}}} }, { /* 1*16^37*G: */ - {{{0x07354b7a, 0x3b671f9e, 0x3915c978, 0x0bb295b0, 0x3cde1d02, 0x1fd18f94, 0x20848239, 0x151d35df, 0x8568}}, - {{0x116e04c6, 0x255100af, 0x3d6fdbd8, 0x2a247707, 0x2f728706, 0x3244eca9, 0x187b6eeb, 0x03ad42fd, 0x20b5}}}, + {{{0x07354b7a, 0x16ce3f3c, 0x045725e3, 0x1d94ad87, 0x0de1d022, 0x1a31f29e, 0x01208e5f, 0x0e9aefc1, 0x856854}}, + {{0x116e04c6, 0x0aa2015e, 0x15bf6f62, 0x1123b83f, 0x1728706a, 0x089d9537, 0x1edbbaf2, 0x16a17eb0, 0x20b50e}}}, /* 3*16^37*G: */ - {{{0x3b26165d, 0x3db31fe9, 0x277137ea, 0x04e8857d, 0x0c92dea7, 0x274824bf, 0x23e6549e, 0x1131d4ac, 0x6173}}, - {{0x06b2a286, 0x126ff72e, 0x37171a4c, 0x266b05b8, 0x0220b298, 0x1f442f46, 0x3835a49b, 0x0585e90d, 0xe990}}}, + {{{0x1b26165d, 0x1b663fd3, 0x1dc4dfab, 0x07442bec, 0x092dea71, 0x090497e6, 0x199527a7, 0x18ea5647, 0x617344}}, + {{0x06b2a286, 0x04dfee5c, 0x1c5c6931, 0x13582dc6, 0x020b2989, 0x0885e8c1, 0x0d6926df, 0x02f486f0, 0xe99016}}}, /* 5*16^37*G: */ - {{{0x10442770, 0x086fdd99, 0x101bad10, 0x063de9b8, 0x00fc2e90, 0x13076a79, 0x36a22da0, 0x00fb957e, 0xf8ac}}, - {{0x1b00c82d, 0x28a193c4, 0x1041d023, 0x1d80afe5, 0x0e6d17a9, 0x1b1d46cd, 0x11e8ea43, 0x23995667, 0x5a35}}}, + {{{0x10442770, 0x10dfbb32, 0x006eb440, 0x11ef4dc2, 0x0fc2e901, 0x00ed4f20, 0x088b6813, 0x1dcabf6d, 0xf8ac03}}, + {{0x1b00c82d, 0x11432788, 0x0107408e, 0x0c057f2a, 0x06d17a97, 0x03a8d9a7, 0x1a3a90db, 0x0cab33a3, 0x5a358e}}}, /* 7*16^37*G: */ - {{{0x365460de, 0x2f81b61b, 0x2bf77b8f, 0x1cfe342a, 0x0c8ea60c, 0x32f2f8c3, 0x095c66c6, 0x07ed496f, 0x8a73}}, - {{0x3f8dc207, 0x26166877, 0x2508ee3e, 0x219f8f14, 0x304dc435, 0x0a552ffe, 0x363198f5, 0x157178aa, 0x5858}}}, + {{{0x165460de, 0x1f036c37, 0x0fddee3e, 0x07f1a155, 0x08ea60c7, 0x1e5f1866, 0x1719b1b2, 0x16a4b792, 0x8a731f}}, + {{0x1f8dc207, 0x0c2cd0ef, 0x1423b8fa, 0x0cfc78a4, 0x04dc4358, 0x0aa5ffd8, 0x0c663d4a, 0x18bc556c, 0x585855}}}, /* 9*16^37*G: */ - {{{0x351634a5, 0x10aaeb7e, 0x1ed524e6, 0x3e429e0d, 0x17967f3c, 0x29ae80b3, 0x0f224bf0, 0x18184caa, 0xa20b}}, - {{0x3226afad, 0x1b04de57, 0x0d45edf2, 0x1d1d5f8f, 0x3b315bc6, 0x357fa0dc, 0x1b99dad3, 0x33a7da5f, 0x9c43}}}, + {{{0x151634a5, 0x0155d6fd, 0x1b549399, 0x1214f06b, 0x1967f3cf, 0x15d0166b, 0x0892fc29, 0x0c26551e, 0xa20b60}}, + {{0x1226afad, 0x1609bcaf, 0x1517b7c9, 0x08eafc79, 0x1315bc67, 0x0ff41b9d, 0x0676b4f5, 0x13ed2fb7, 0x9c43ce}}}, /* 11*16^37*G: */ - {{{0x33ba54a8, 0x010c8912, 0x03aa9707, 0x22c98d58, 0x05cc0ab5, 0x0e3b0d3f, 0x16709914, 0x07e4fc49, 0x016f}}, - {{0x264f2889, 0x35f187e9, 0x2a3b4e6e, 0x0ebc9d51, 0x1ce658d9, 0x26c46f92, 0x151576f2, 0x34d04562, 0x08bc}}}, + {{{0x13ba54a8, 0x02191225, 0x0eaa5c1c, 0x164c6ac0, 0x1cc0ab58, 0x0761a7e2, 0x1c26450e, 0x127e24ac, 0x16f1f}}, + {{0x064f2889, 0x0be30fd3, 0x08ed39bb, 0x15e4ea8d, 0x0e658d93, 0x188df24e, 0x055dbca6, 0x0822b12a, 0x8bcd3}}}, /* 13*16^37*G: */ - {{{0x27c16d94, 0x3bb924f3, 0x02845fdd, 0x160742a8, 0x0ec31fe2, 0x23f59f33, 0x034788c0, 0x2199c2f4, 0xe615}}, - {{0x314810ab, 0x2d3b466a, 0x3a443bbf, 0x19734791, 0x36f0ee4e, 0x2cae4fd2, 0x124be8c5, 0x00eba79c, 0x65ca}}}, + {{{0x07c16d94, 0x177249e7, 0x0a117f77, 0x103a1540, 0x0c31fe25, 0x1eb3e667, 0x11e23023, 0x0ce17a06, 0xe61586}}, + {{0x114810ab, 0x1a768cd5, 0x0910eefe, 0x0b9a3c8f, 0x0f0ee4e6, 0x15c9fa5b, 0x12fa316c, 0x15d3ce24, 0x65ca03}}}, /* 15*16^37*G: */ - {{{0x13ce728d, 0x35b72999, 0x071cd0bc, 0x33641f8a, 0x085347f4, 0x2822885b, 0x16a26555, 0x1fc2ce35, 0xdcd3}}, - {{0x17cacbcb, 0x35f44da6, 0x29dabeb8, 0x2b34d1b4, 0x06d6f3ca, 0x0ded8acf, 0x24c1872c, 0x36f5df36, 0x6574}}} + {{{0x13ce728d, 0x0b6e5332, 0x1c7342f3, 0x1b20fc50, 0x05347f4c, 0x04510b64, 0x08995568, 0x01671aad, 0xdcd37f}}, + {{0x17cacbcb, 0x0be89b4c, 0x076afae3, 0x19a68da5, 0x0d6f3caa, 0x1db159e3, 0x1061cb0d, 0x1aef9b49, 0x6574db}}} }, { /* 1*16^38*G: */ - {{{0x12378c16, 0x371b706c, 0x215622ad, 0x0d81d551, 0x39597d9e, 0x2794b5af, 0x33b11b31, 0x2dd6704a, 0x1136}}, - {{0x33488127, 0x27d66f42, 0x351cce37, 0x052a8a39, 0x29ecb296, 0x02af183f, 0x28fdd09f, 0x03f3d145, 0x7dec}}}, + {{{0x12378c16, 0x0e36e0d8, 0x05588ab7, 0x0c0eaa8c, 0x1597d9e3, 0x1296b5fc, 0x0c46cc67, 0x0b382567, 0x1136b7}}, + {{0x13488127, 0x0facde85, 0x147338de, 0x095451ce, 0x1ecb2961, 0x15e307f4, 0x1f7427c2, 0x19e8a2d1, 0x7dec0f}}}, /* 3*16^38*G: */ - {{{0x3b299740, 0x1c39b609, 0x13db1349, 0x03d19f5c, 0x3aad48f4, 0x2b44de4f, 0x14336cc4, 0x0fadc737, 0x5389}}, - {{0x3fff7509, 0x07a9bc6c, 0x1fde8cd5, 0x284cbbc8, 0x35dc8dd8, 0x0738a3a9, 0x1fbd8384, 0x229fa521, 0x2772}}}, + {{{0x1b299740, 0x18736c13, 0x0f6c4d25, 0x1e8cfae2, 0x0ad48f40, 0x089bc9fd, 0x0cdb312b, 0x16e39ba8, 0x53893e}}, + {{0x1fff7509, 0x0f5378d9, 0x1f7a3354, 0x0265de43, 0x1dc8dd8a, 0x0714753a, 0x0f60e107, 0x0fd290bf, 0x27728a}}}, /* 5*16^38*G: */ - {{{0x338000fc, 0x02cf2559, 0x3f03bc13, 0x0789dc1e, 0x3ae5604e, 0x0ddaebc7, 0x0da2757e, 0x3a775d53, 0xdd64}}, - {{0x1df4ac12, 0x3ea87143, 0x11e48f8b, 0x117408ae, 0x0a79ffbe, 0x2278f867, 0x132c96df, 0x24fac30a, 0x4321}}}, + {{{0x138000fc, 0x059e4ab3, 0x1c0ef04c, 0x1c4ee0f7, 0x0e5604e1, 0x1b5d78fd, 0x089d5f8d, 0x1baea99b, 0xdd64e9}}, + {{0x1df4ac12, 0x1d50e286, 0x07923e2f, 0x0ba04572, 0x079ffbe4, 0x0f1f0ce5, 0x0b25b7e2, 0x1d618526, 0x432193}}}, /* 7*16^38*G: */ - {{{0x33878c4a, 0x3e08545c, 0x151c055e, 0x20f40f21, 0x291b21d8, 0x1a718392, 0x3d516f2c, 0x116a1fbf, 0xff98}}, - {{0x3488df68, 0x2e9a11f5, 0x25cfebc6, 0x3ccdd1ad, 0x35e8ddf1, 0x22923b7f, 0x2428f8fd, 0x26bd2938, 0x835b}}}, + {{{0x13878c4a, 0x1c10a8b9, 0x1470157b, 0x07a0790a, 0x11b21d88, 0x0e307254, 0x145bcb1a, 0x150fdffa, 0xff9845}}, + {{0x1488df68, 0x1d3423eb, 0x173faf1a, 0x066e8d6c, 0x1e8ddf1f, 0x12476ffa, 0x0a3e3f62, 0x1e949c48, 0x835b9a}}}, /* 9*16^38*G: */ - {{{0x00f51524, 0x32a6e205, 0x3af86fc8, 0x2bada856, 0x1293de5f, 0x19e8c211, 0x1609ce87, 0x04fa2ee4, 0x954e}}, - {{0x05e30a69, 0x27f6cf65, 0x01e7cbde, 0x3ba90c45, 0x1ecbcfa9, 0x31890d1e, 0x24041d93, 0x0d8ffe4a, 0xecc8}}}, + {{{0x00f51524, 0x054dc40a, 0x0be1bf23, 0x1d6d42b7, 0x093de5fa, 0x1d184229, 0x0273a1d9, 0x1d17722c, 0x954e13}}, + {{0x05e30a69, 0x0fed9eca, 0x079f2f7a, 0x1d486228, 0x0cbcfa9e, 0x1121a3cf, 0x010764f1, 0x07ff2548, 0xecc836}}}, /* 11*16^38*G: */ - {{{0x04f77287, 0x3de6354f, 0x130d9e31, 0x0a54f0da, 0x18049741, 0x35431707, 0x1fb93dfc, 0x1fbdbe90, 0xb221}}, - {{0x24e7b5da, 0x1e8129dc, 0x05e93cb9, 0x02771ce7, 0x38c843d7, 0x3ef3e234, 0x0f3a2b5d, 0x14f8339f, 0xfb51}}}, + {{{0x04f77287, 0x1bcc6a9e, 0x0c3678c7, 0x12a786d2, 0x00497412, 0x0862e0ec, 0x0e4f7f35, 0x1edf483f, 0xb2217e}}, + {{0x04e7b5da, 0x1d0253b9, 0x17a4f2e5, 0x13b8e738, 0x0c843d70, 0x1e7c469c, 0x0e8ad77e, 0x1c19cf9e, 0xfb5153}}}, /* 13*16^38*G: */ - {{{0x05c723e9, 0x2bd4e5b2, 0x2a781718, 0x25ceeaa6, 0x1d5c351f, 0x31baba45, 0x1bdad122, 0x142c5ede, 0x3c39}}, - {{0x36834763, 0x38e1dd7d, 0x04906ae5, 0x076b2d5f, 0x06a8b0b0, 0x12edfa86, 0x110dbb49, 0x1cd88824, 0xb99b}}}, + {{{0x05c723e9, 0x17a9cb64, 0x09e05c62, 0x0e775535, 0x15c351f9, 0x175748ae, 0x16b448b1, 0x162f6f37, 0x3c3950}}, + {{0x16834763, 0x11c3bafb, 0x1241ab97, 0x1b596af8, 0x0a8b0b01, 0x1dbf50c3, 0x036ed252, 0x0c441222, 0xb99b73}}}, /* 15*16^38*G: */ - {{{0x3c18abeb, 0x1c5f5b88, 0x325d62a3, 0x27734641, 0x3aa944d5, 0x3b4be112, 0x21cdad1d, 0x1e8b33e5, 0x803c}}, - {{0x229bfa78, 0x290e6fc3, 0x26721cd6, 0x1f110f0a, 0x0b4409ed, 0x2b3c5a71, 0x2e9286b1, 0x141029e5, 0x83fb}}} + {{{0x1c18abeb, 0x18beb711, 0x09758a8d, 0x1b9a320e, 0x0a944d59, 0x097c225d, 0x136b477b, 0x0599f2c3, 0x803c7a}}, + {{0x029bfa78, 0x121cdf87, 0x19c8735a, 0x18887854, 0x14409ed7, 0x078b4e25, 0x04a1ac6b, 0x0814f2dd, 0x83fb50}}} }, { /* 1*16^39*G: */ - {{{0x143e832a, 0x31d8bbc6, 0x386df709, 0x3942ac05, 0x09f18e07, 0x15cea096, 0x2a51a90f, 0x3ca2e9f0, 0x0d2b}}, - {{0x1b20d37c, 0x2098ebc5, 0x05514464, 0x3b276e58, 0x34e7ed27, 0x1e842a52, 0x100ac708, 0x0fd0c4ef, 0x0cac}}}, + {{{0x143e832a, 0x03b1778c, 0x01b7dc27, 0x0a15602f, 0x1f18e07e, 0x19d412c4, 0x146a43d5, 0x1174f854, 0xd2bf2}}, + {{0x1b20d37c, 0x0131d78a, 0x15451192, 0x193b72c0, 0x0e7ed27e, 0x10854a5a, 0x02b1c21e, 0x086277a0, 0xcac3f}}}, /* 3*16^39*G: */ - {{{0x112c9666, 0x07ab12f0, 0x1ffcdf36, 0x3e31b0d9, 0x19531b1c, 0x2f30d6df, 0x3f82cfd9, 0x3a17ae59, 0x34e5}}, - {{0x192a3666, 0x168614f2, 0x1e3a526b, 0x11fb58f0, 0x3c46330f, 0x1195d732, 0x1a36b828, 0x1a0c4c88, 0xc0ce}}}, + {{{0x112c9666, 0x0f5625e0, 0x1ff37cd8, 0x118d86cb, 0x1531b1cf, 0x061adbec, 0x00b3f66f, 0x0bd72cff, 0x34e5e8}}, + {{0x192a3666, 0x0d0c29e4, 0x18e949ad, 0x0fdac783, 0x046330f4, 0x12bae65e, 0x0dae0a11, 0x06264434, 0xc0ce68}}}, /* 5*16^39*G: */ - {{{0x11209502, 0x0594af8d, 0x1d92665c, 0x105c8009, 0x19e15459, 0x124fbc24, 0x0d863a6c, 0x18b3167d, 0x7273}}, - {{0x17042b0d, 0x19df474f, 0x32760bbc, 0x234dfe6e, 0x291d20a1, 0x002e30b3, 0x3ab589f1, 0x3d08a6ea, 0x17b0}}}, + {{{0x11209502, 0x0b295f1a, 0x16499970, 0x02e4004b, 0x1e154594, 0x09f7848c, 0x018e9b12, 0x198b3e9b, 0x727362}}, + {{0x17042b0d, 0x13be8e9e, 0x09d82ef1, 0x1a6ff376, 0x11d20a18, 0x05c61674, 0x0d627c40, 0x04537575, 0x17b0f4}}}, /* 7*16^39*G: */ - {{{0x2447f959, 0x1579e4a2, 0x271d3684, 0x11f6aea0, 0x09eee9f9, 0x285312ed, 0x26cec973, 0x3c980152, 0xa0c3}}, - {{0x168b671f, 0x00e74922, 0x0d272c9b, 0x2d550096, 0x228208b1, 0x3e30432d, 0x32c4f382, 0x1cc24392, 0x508c}}}, + {{{0x0447f959, 0x0af3c945, 0x1c74da11, 0x0fb57504, 0x1eee9f94, 0x0a625da4, 0x13b25ce8, 0x0c00a94d, 0xa0c3f2}}, + {{0x168b671f, 0x01ce9244, 0x149cb26c, 0x0aa804b1, 0x08208b1b, 0x060865b1, 0x113ce0be, 0x0121c965, 0x508c73}}}, /* 9*16^39*G: */ - {{{0x1b37e1d3, 0x087e7c09, 0x0e4de230, 0x1d86f84f, 0x15fd0410, 0x2d0cef90, 0x1ca7a40c, 0x2c8c7de5, 0x7e81}}, - {{0x0155681a, 0x3d7f2899, 0x1c2e0e03, 0x3212fcac, 0x2c7c4e4e, 0x3a25b3b9, 0x3ed13125, 0x1686c3a6, 0xf385}}}, + {{{0x1b37e1d3, 0x10fcf812, 0x193788c0, 0x0c37c279, 0x1fd04107, 0x019df20a, 0x09e9032d, 0x063ef2b9, 0x7e81b2}}, + {{0x0155681a, 0x1afe5132, 0x10b8380f, 0x1097e563, 0x07c4e4ec, 0x04b67736, 0x144c497a, 0x0361d37d, 0xf3855a}}}, /* 11*16^39*G: */ - {{{0x16c051a0, 0x125dc57d, 0x35b3e6dc, 0x37ca491b, 0x0f2abddc, 0x1b639b6c, 0x026d84a3, 0x38871f60, 0x8035}}, - {{0x32d0dd12, 0x007aecbe, 0x18b62356, 0x39f718c2, 0x3dd318b3, 0x36f9a0de, 0x22bef375, 0x042912de, 0x0b88}}}, + {{{0x16c051a0, 0x04bb8afa, 0x16cf9b71, 0x1e5248de, 0x12abddcd, 0x0c736d87, 0x1b6128db, 0x038fb004, 0x8035e2}}, + {{0x12d0dd12, 0x00f5d97d, 0x02d88d58, 0x0fb8c613, 0x1d318b3e, 0x1f341bde, 0x0fbcdd76, 0x14896f45, 0xb8810}}}, /* 13*16^39*G: */ - {{{0x3f12c69e, 0x38030c27, 0x1651963c, 0x396bbd62, 0x04fcecaf, 0x2bc00408, 0x0a53306b, 0x0237f586, 0x1969}}, - {{0x1d114831, 0x34cc6410, 0x3fb886b8, 0x2cb8cdc7, 0x21054eb6, 0x3877ab74, 0x16e040be, 0x2fdacbe4, 0x3f65}}}, + {{{0x1f12c69e, 0x1006184f, 0x194658f3, 0x0b5deb12, 0x0fcecafe, 0x18008102, 0x14cc1aeb, 0x1bfac314, 0x196908}}, + {{0x1d114831, 0x0998c820, 0x1ee21ae3, 0x05c66e3f, 0x1054eb6b, 0x0ef56e90, 0x18102fb8, 0x0d65f22d, 0x3f65bf}}}, /* 15*16^39*G: */ - {{{0x0b89c5ed, 0x1263807f, 0x17a78c7e, 0x2d4c33de, 0x2d0f3577, 0x1b874842, 0x1a2af46e, 0x3f3ae258, 0xdb77}}, - {{0x2d25b46e, 0x27fc71fb, 0x0899afa5, 0x05b1eada, 0x19ad411f, 0x0ce6f932, 0x2e5ceecf, 0x370e1c73, 0x7fd1}}} + {{{0x0b89c5ed, 0x04c700fe, 0x1e9e31f9, 0x0a619ef2, 0x10f3577b, 0x10e90856, 0x0abd1b9b, 0x1d712c34, 0xdb77fc}}, + {{0x0d25b46e, 0x0ff8e3f7, 0x0266be96, 0x0d8f56d1, 0x1ad411f1, 0x1cdf264c, 0x173bb3cc, 0x070e39dc, 0x7fd1dc}}} }, { /* 1*16^40*G: */ - {{{0x37f82f2a, 0x3ba71d77, 0x2fdf43aa, 0x130d61d2, 0x3713269e, 0x08b7d0dc, 0x33617f56, 0x17d59bb1, 0x8a53}}, - {{0x223094b7, 0x17e682b0, 0x08c7669c, 0x394ce193, 0x1a92bfcd, 0x00a06421, 0x08bd737e, 0x30211a2c, 0x0455}}}, + {{{0x17f82f2a, 0x174e3aef, 0x1f7d0eab, 0x186b0e95, 0x113269e4, 0x16fa1b9b, 0x185fd588, 0x0acdd8e6, 0x8a535f}}, + {{0x023094b7, 0x0fcd0561, 0x031d9a71, 0x0a670c99, 0x092bfcde, 0x140c842d, 0x0f5cdf80, 0x108d1611, 0x455c0}}}, /* 3*16^40*G: */ - {{{0x2b348fa0, 0x2c53c85e, 0x11541ddf, 0x3f891641, 0x24b4bce0, 0x088c8db0, 0x3882dc2a, 0x324f777a, 0x86ea}}, - {{0x0da51cee, 0x3b8e0255, 0x1cfee8a4, 0x09b658d4, 0x2f46716c, 0x0dbe7a35, 0x04d8d5a4, 0x0e14f2ef, 0x948f}}}, + {{{0x0b348fa0, 0x18a790bd, 0x0550777e, 0x1c48b20a, 0x0b4bce0f, 0x1191b612, 0x00b70a88, 0x07bbbd71, 0x86eac9}}, + {{0x0da51cee, 0x171c04aa, 0x13fba293, 0x0db2c6a3, 0x146716c2, 0x17cf46b7, 0x1635690d, 0x0a797789, 0x948f38}}}, /* 5*16^40*G: */ - {{{0x19222c03, 0x2bd07ff2, 0x3e5e1037, 0x2339dfa1, 0x19f40794, 0x39f5e121, 0x33aae3f5, 0x27aebe7e, 0x8bf0}}, - {{0x2a72bb54, 0x0517dd0b, 0x220e1d4a, 0x27b03877, 0x25ba309c, 0x22c76f9f, 0x27a733b4, 0x2eabf8b8, 0x509c}}}, + {{{0x19222c03, 0x17a0ffe4, 0x197840de, 0x19cefd0f, 0x1f407948, 0x1ebc242c, 0x0ab8fd79, 0x175f3f67, 0x8bf09e}}, + {{0x0a72bb54, 0x0a2fba17, 0x08387528, 0x1d81c3bc, 0x1ba309c9, 0x18edf3f2, 0x09cced22, 0x15fc5c4f, 0x509cba}}}, /* 7*16^40*G: */ - {{{0x11ae9300, 0x114e8b07, 0x1c48280b, 0x0711c11d, 0x33735b5e, 0x0c2eb68b, 0x30fc6191, 0x0b72edf9, 0xe85e}}, - {{0x1546e25e, 0x0a837f74, 0x38c31bb7, 0x2df86177, 0x3c2707de, 0x29ed6e08, 0x0e0bfc7b, 0x2be9b547, 0x451a}}}, + {{{0x11ae9300, 0x029d160e, 0x1120a02d, 0x188e08eb, 0x1735b5e1, 0x05d6d179, 0x1f18644c, 0x1976fce1, 0xe85e2d}}, + {{0x1546e25e, 0x1506fee8, 0x030c6edc, 0x0fc30bbf, 0x02707deb, 0x1dadc11e, 0x02ff1ee9, 0x14daa39c, 0x451aaf}}}, /* 9*16^40*G: */ - {{{0x05260cb8, 0x14975558, 0x2b2152f2, 0x1bd2a033, 0x27dbf683, 0x009f686e, 0x12f82a3f, 0x2c3c8a32, 0x3f5f}}, - {{0x1852c964, 0x0bed2d10, 0x05ec3327, 0x0fa1d47f, 0x2783f2fa, 0x237854d9, 0x199870e3, 0x0d36b692, 0xc558}}}, + {{{0x05260cb8, 0x092eaab0, 0x0c854bc9, 0x1e95019d, 0x1dbf6836, 0x13ed0dd3, 0x1e0a8fc0, 0x1e451925, 0x3f5fb0}}, + {{0x1852c964, 0x17da5a20, 0x17b0cc9c, 0x1d0ea3f8, 0x183f2fa3, 0x0f0a9b33, 0x061c38e3, 0x1b5b4933, 0xc55834}}}, /* 11*16^40*G: */ - {{{0x1a1cd60f, 0x2a91110b, 0x03092ea4, 0x25a62a73, 0x1a002b9f, 0x3b41d2d3, 0x1999657a, 0x1588ac63, 0x3368}}, - {{0x0fd57d67, 0x2fdcdd94, 0x050b8b24, 0x3bd6932f, 0x27af175f, 0x1630037a, 0x07cd9ba8, 0x1427bc49, 0xd42f}}}, + {{{0x1a1cd60f, 0x15222216, 0x0c24ba92, 0x0d315398, 0x0002b9f9, 0x083a5a6d, 0x06595ebb, 0x045631b3, 0x336856}}, + {{0x0fd57d67, 0x1fb9bb28, 0x142e2c92, 0x1eb49978, 0x1af175fe, 0x06006f53, 0x1366ea16, 0x13de248f, 0xd42f50}}}, /* 13*16^40*G: */ - {{{0x37576342, 0x014edbae, 0x199222af, 0x0b2220ce, 0x0979d95b, 0x03e76258, 0x00080f7d, 0x3ad7023c, 0x4813}}, - {{0x17376316, 0x130557ae, 0x06a904f6, 0x0b719f54, 0x33524aca, 0x005a1238, 0x24240f66, 0x0ff508ce, 0x0004}}}, + {{{0x17576342, 0x029db75d, 0x06488abc, 0x19110673, 0x179d95b2, 0x1cec4b04, 0x0203df43, 0x0b811e00, 0x4813eb}}, + {{0x17376316, 0x060aaf5c, 0x1aa413d9, 0x1b8cfaa0, 0x1524aca2, 0x0b424719, 0x0903d980, 0x1a846748, 0x043f}}}, /* 15*16^40*G: */ - {{{0x3f69b2be, 0x3d9c5c77, 0x01111c09, 0x107dd3b7, 0x386e56ba, 0x08b6eeb8, 0x2997af13, 0x3c7e696b, 0x80c3}}, - {{0x0102d2f5, 0x2412e5f1, 0x0b7a8bf8, 0x12dd2cd7, 0x1d5a9bf1, 0x0389d96c, 0x1de85298, 0x08502802, 0x0a93}}} + {{{0x1f69b2be, 0x1b38b8ef, 0x04447027, 0x03ee9db8, 0x06e56ba4, 0x16ddd71c, 0x05ebc4c8, 0x1f34b5d3, 0x80c3f1}}, + {{0x0102d2f5, 0x0825cbe2, 0x0dea2fe2, 0x16e966b9, 0x15a9bf14, 0x113b2d8e, 0x1a14a603, 0x0814013b, 0xa9321}}} }, { /* 1*16^41*G: */ - {{{0x2476c81d, 0x320dfd3f, 0x1e53d5e9, 0x28c0c3a6, 0x28a366b7, 0x1f349cf6, 0x01a019af, 0x2437f72d, 0xad60}}, - {{0x2e6705dd, 0x062af213, 0x33048df8, 0x0ff70d93, 0x1bd8a839, 0x35d70b31, 0x0c91eacc, 0x3477523d, 0x77b5}}}, + {{{0x0476c81d, 0x041bfa7f, 0x194f57a7, 0x06061d33, 0x0a366b7a, 0x06939ed4, 0x08066bdf, 0x1bfb9683, 0xad6090}}, + {{0x0e6705dd, 0x0c55e427, 0x0c1237e0, 0x1fb86c9e, 0x1d8a8393, 0x1ae1662d, 0x047ab335, 0x1ba91e99, 0x77b5d1}}}, /* 3*16^41*G: */ - {{{0x22725490, 0x2891cdf3, 0x3cb59900, 0x30c90188, 0x09863c4a, 0x36a94cec, 0x1697ca2a, 0x116edc6b, 0xd90b}}, - {{0x2feb1299, 0x03e13e12, 0x3c466ccb, 0x3701effc, 0x38cbd80c, 0x22d5a1cd, 0x3350f09d, 0x24a3b06e, 0x3326}}}, + {{{0x02725490, 0x11239be7, 0x12d66402, 0x06480c47, 0x1863c4ac, 0x15299d84, 0x05f28ab6, 0x176e35ad, 0xd90b45}}, + {{0x0feb1299, 0x07c27c25, 0x1119b32c, 0x180f7fe7, 0x0cbd80cd, 0x1ab439bc, 0x143c2762, 0x11d83766, 0x332692}}}, /* 5*16^41*G: */ - {{{0x3e933668, 0x1dace995, 0x06babf0a, 0x00b6133e, 0x1f06befb, 0x14e4ebe8, 0x13fc7ac0, 0x2485cc48, 0xac25}}, - {{0x32776fb5, 0x1b9dfd9c, 0x29e1e7a1, 0x21906271, 0x18ed7c6f, 0x3b04fbaf, 0x3a8ba850, 0x280e1c36, 0x6c79}}}, + {{{0x1e933668, 0x1b59d32b, 0x1aeafc29, 0x05b099f0, 0x106befb0, 0x1c9d7d0f, 0x1f1eb014, 0x02e62427, 0xac2592}}, + {{0x12776fb5, 0x173bfb39, 0x07879e85, 0x0c83138d, 0x0ed7c6f8, 0x009f75ec, 0x02ea143b, 0x070e1b75, 0x6c79a0}}}, /* 7*16^41*G: */ - {{{0x128de7e3, 0x2985f048, 0x3ea996d9, 0x210ab0ea, 0x3431bf86, 0x083ef69e, 0x1f3a8873, 0x0dd2ba5e, 0x7bc3}}, - {{0x2e6e5e29, 0x1e82ccba, 0x0c0ccf06, 0x3cb6ce6d, 0x0bacbd55, 0x31deb9b9, 0x14e5de00, 0x3c091821, 0xb431}}}, + {{{0x128de7e3, 0x130be090, 0x1aa65b66, 0x08558757, 0x031bf868, 0x07ded3da, 0x0ea21cc8, 0x095d2f3e, 0x7bc337}}, + {{0x0e6e5e29, 0x1d059975, 0x10333c19, 0x05b67369, 0x1acbd55f, 0x1bd73725, 0x19778031, 0x048c10a9, 0xb431f0}}}, /* 9*16^41*G: */ - {{{0x035e057d, 0x2b2c8c8e, 0x2d89a5b4, 0x33c436bd, 0x01119329, 0x321cbf0d, 0x202b268b, 0x052514eb, 0xbf9c}}, - {{0x2da20fea, 0x3d592ca0, 0x05c479b6, 0x02e78607, 0x07a54244, 0x14c4fc17, 0x23be0f38, 0x2e27c97c, 0x92ac}}}, + {{{0x035e057d, 0x1659191c, 0x162696d2, 0x1e21b5ed, 0x1119329c, 0x0397e1a0, 0x0ac9a2f2, 0x128a75c0, 0xbf9c14}}, + {{0x0da20fea, 0x1ab25941, 0x1711e6db, 0x173c3038, 0x1a542440, 0x189f82e3, 0x0f83ce14, 0x13e4be47, 0x92acb8}}}, /* 11*16^41*G: */ - {{{0x021d6584, 0x0ab35f08, 0x3b3d9e5d, 0x1c175910, 0x1f014ef2, 0x25f68d6b, 0x04f8a96e, 0x020e6d5e, 0x55bf}}, - {{0x0ed744ea, 0x35593d0a, 0x2e5a5a80, 0x2785080a, 0x3c7dcf08, 0x32fdaea2, 0x21ccf27a, 0x01ccf92d, 0x3d98}}}, + {{{0x021d6584, 0x1566be10, 0x0cf67974, 0x00bac887, 0x1014ef27, 0x1ed1ad6f, 0x1e2a5ba5, 0x0736af09, 0x55bf08}}, + {{0x0ed744ea, 0x0ab27a14, 0x19696a03, 0x1c284055, 0x07dcf089, 0x1fb5d45e, 0x133c9eb2, 0x067c96c3, 0x3d9807}}}, /* 13*16^41*G: */ - {{{0x01068c5e, 0x35a77db9, 0x3e573d0d, 0x117b9b92, 0x15d4872a, 0x2b8539e0, 0x38d519f2, 0x138594cd, 0xfcf2}}, - {{0x27c19d75, 0x187d14fc, 0x014855b7, 0x05da92ca, 0x12e7aee9, 0x1d7886d6, 0x3ffe35c6, 0x2c394cdb, 0x186b}}}, + {{{0x01068c5e, 0x0b4efb72, 0x195cf437, 0x0bdcdc97, 0x1d4872a4, 0x10a73c0a, 0x15467cab, 0x02ca66f1, 0xfcf24e}}, + {{0x07c19d75, 0x10fa29f9, 0x052156dd, 0x0ed49650, 0x0e7aee91, 0x0f10dac9, 0x1f8d719d, 0x1ca66dff, 0x186bb0}}}, /* 15*16^41*G: */ - {{{0x220da860, 0x2df657c1, 0x049d1008, 0x0d146a92, 0x191f2f84, 0x36d94d0f, 0x167eca1f, 0x20340bd4, 0x7bc2}}, - {{0x07aac76d, 0x38a44104, 0x0c1632eb, 0x38668bf7, 0x1ee6e0f2, 0x09afe9c1, 0x131e5e26, 0x1b5deeef, 0xb33f}}} + {{{0x020da860, 0x1becaf83, 0x12744022, 0x08a35490, 0x11f2f843, 0x1b29a1ec, 0x1fb287f6, 0x1a05ea2c, 0x7bc280}}, + {{0x07aac76d, 0x11488208, 0x1058cbaf, 0x03345fb9, 0x0e6e0f2e, 0x15fd382f, 0x07978989, 0x0ef777a6, 0xb33f6d}}} }, { /* 1*16^42*G: */ - {{{0x13c4a205, 0x14bcb0da, 0x110a848a, 0x06b7e27d, 0x3929fcde, 0x1955c1d6, 0x1bbc4e46, 0x1b1458c1, 0xb6e0}}, - {{0x1db36d05, 0x0dfd3619, 0x02a9f875, 0x3e65066a, 0x1ed73b63, 0x07c49b9e, 0x323f5c5e, 0x09df086c, 0xbdb4}}}, + {{{0x13c4a205, 0x097961b4, 0x042a1229, 0x15bf13ea, 0x129fcde1, 0x0ab83adc, 0x0f139199, 0x0a2c60b7, 0xb6e06c}}, + {{0x1db36d05, 0x1bfa6c32, 0x0aa7e1d4, 0x13283350, 0x0d73b63f, 0x189373cf, 0x0fd71787, 0x0f843664, 0xbdb427}}}, /* 3*16^42*G: */ - {{{0x39e27907, 0x0be087db, 0x0d9e4d69, 0x06b52ce2, 0x1fbd6877, 0x257575bf, 0x01c4e6b3, 0x390fe109, 0x0ed9}}, - {{0x2e78c4fb, 0x04fd3d41, 0x0ba1905f, 0x05473fae, 0x120e0ce9, 0x303f63ac, 0x32347f5b, 0x21d2bfda, 0xb5af}}}, + {{{0x19e27907, 0x17c10fb7, 0x167935a4, 0x15a96711, 0x1bd68771, 0x0eaeb7ef, 0x1139ace5, 0x07f08483, 0xed9e4}}, + {{0x0e78c4fb, 0x09fa7a83, 0x0e86417c, 0x0a39fd71, 0x00e0ce91, 0x07ec7589, 0x0d1fd6f0, 0x095fed64, 0xb5af87}}}, /* 5*16^42*G: */ - {{{0x35b38f54, 0x1b415c94, 0x0af07ce3, 0x0aa18397, 0x3ee1f92e, 0x09a36d23, 0x18f7dc55, 0x390401db, 0x57a7}}, - {{0x245f2809, 0x3e9e0798, 0x107eba75, 0x35db8e6a, 0x02dd21df, 0x32288ef2, 0x0ad24194, 0x03c0f23b, 0xfd7f}}}, + {{{0x15b38f54, 0x1682b929, 0x0bc1f38d, 0x150c1cb9, 0x0e1f92e2, 0x146da47f, 0x1df71549, 0x0200edb1, 0x57a7e4}}, + {{0x045f2809, 0x1d3c0f31, 0x01fae9d7, 0x0edc7352, 0x0dd21dfd, 0x0511de41, 0x14906532, 0x00791d95, 0xfd7f0f}}}, /* 7*16^42*G: */ - {{{0x27a79593, 0x1bfaefe6, 0x25c49794, 0x1e9c9274, 0x0a5cf334, 0x366c9633, 0x35dbef52, 0x26b8bcfb, 0x2479}}, - {{0x10920d55, 0x18e235d7, 0x3eb1398d, 0x250d87e6, 0x23e30099, 0x0f46a74d, 0x07b7b32c, 0x2d498bb2, 0x9436}}}, + {{{0x07a79593, 0x17f5dfcd, 0x17125e51, 0x14e493a4, 0x05cf3347, 0x0d92c665, 0x16fbd4b6, 0x1c5e7deb, 0x24799a}}, + {{0x10920d55, 0x11c46bae, 0x1ac4e635, 0x086c3f37, 0x1e300999, 0x08d4e9b1, 0x0deccb0f, 0x04c5d90f, 0x9436b5}}}, /* 9*16^42*G: */ - {{{0x0bf5abdc, 0x0085bad4, 0x10b65066, 0x1b34ebef, 0x0d5d6045, 0x04472c20, 0x07026ed3, 0x05f1a213, 0xf150}}, - {{0x2def85b7, 0x1d778ae2, 0x3b85584b, 0x3719d709, 0x05e232cb, 0x20d078ff, 0x302a8ecd, 0x3bc70b17, 0xdea7}}}, + {{{0x0bf5abdc, 0x010b75a8, 0x02d94198, 0x19a75f7a, 0x15d60456, 0x08e58406, 0x009bb4c4, 0x18d1098e, 0xf15017}}, + {{0x0def85b7, 0x1aef15c5, 0x0e15612d, 0x18ceb84f, 0x1e232cbd, 0x1a0f1fe2, 0x0aa3b360, 0x03858be0, 0xdea7ef}}}, /* 11*16^42*G: */ - {{{0x3e78e9b1, 0x27c94ac7, 0x2c141e86, 0x1e39b713, 0x12dfcc89, 0x3e0c7dd4, 0x0beaa6e0, 0x3883e26d, 0xe196}}, - {{0x0a77eed7, 0x105d587f, 0x2ed35f44, 0x234044af, 0x32ed9a90, 0x1022f9da, 0x285a62a6, 0x1b617e06, 0xa5d6}}}, + {{{0x1e78e9b1, 0x0f92958f, 0x10507a1a, 0x11cdb89d, 0x0dfcc897, 0x018fba89, 0x1aa9b83e, 0x01f13697, 0xe196e2}}, + {{0x0a77eed7, 0x00bab0fe, 0x1b4d7d11, 0x1a02257d, 0x0ed9a908, 0x045f3b59, 0x1698a990, 0x10bf0350, 0xa5d66d}}}, /* 13*16^42*G: */ - {{{0x3b1cb64b, 0x1bb8cf95, 0x18ac3d57, 0x02794958, 0x39ed14d6, 0x1ff35c54, 0x30302f39, 0x3d779b06, 0x7779}}, - {{0x3aba3aab, 0x23863472, 0x0aa9533d, 0x2a0a508f, 0x22e3fae2, 0x2ac4d29e, 0x03ebeadf, 0x108fd1d3, 0x09a8}}}, + {{{0x1b1cb64b, 0x17719f2b, 0x02b0f55d, 0x13ca4ac3, 0x1ed14d60, 0x1e6b8a9c, 0x0c0bce5f, 0x1bcd8360, 0x7779f5}}, + {{0x1aba3aab, 0x070c68e5, 0x0aa54cf6, 0x10528479, 0x0e3fae2a, 0x189a53d1, 0x1afab7ea, 0x07e8e987, 0x9a842}}}, /* 15*16^42*G: */ - {{{0x11d1b492, 0x3b6161da, 0x019a6f53, 0x28186308, 0x328ce8df, 0x3db66aba, 0x3a2f11e5, 0x2e52f908, 0x8605}}, - {{0x38ac6598, 0x1c75defd, 0x01e925c5, 0x08d49b52, 0x03d1a8ee, 0x3db83085, 0x35758f3e, 0x184a1f79, 0xa8e5}}} + {{{0x11d1b492, 0x16c2c3b4, 0x0669bd4f, 0x00c31840, 0x08ce8dfa, 0x16cd5759, 0x0bc4797d, 0x097c8474, 0x8605b9}}, + {{0x18ac6598, 0x18ebbdfb, 0x07a49715, 0x06a4da90, 0x1d1a8ee2, 0x170610a1, 0x1d63cfbd, 0x050fbcea, 0xa8e561}}} }, { /* 1*16^43*G: */ - {{{0x29aa52df, 0x3357d392, 0x02a627f3, 0x3114ac6d, 0x11ece618, 0x31062766, 0x08bf76db, 0x04725fd8, 0x45a5}}, - {{0x125ec16c, 0x2d4af448, 0x22955ce7, 0x2466c9f4, 0x225ad25a, 0x0ccdff2d, 0x29b6d3fe, 0x03b1dcfa, 0x73be}}}, + {{{0x09aa52df, 0x06afa725, 0x0a989fcf, 0x08a56368, 0x1ece618c, 0x00c4ecc8, 0x0fddb6f1, 0x192fec11, 0x45a511}}, + {{0x125ec16c, 0x1a95e890, 0x0a55739e, 0x03364fa4, 0x05ad25a9, 0x19bfe5b1, 0x0db4ff8c, 0x18ee7d53, 0x73be0e}}}, /* 3*16^43*G: */ - {{{0x2e75bc7f, 0x159d4fbe, 0x2f7fb1f6, 0x31c5c36d, 0x0d4c7b95, 0x103c485f, 0x393438ef, 0x2b13f9ca, 0x0b57}}, - {{0x0972e9a9, 0x13c5cb74, 0x049fc620, 0x3e5b0390, 0x3e94fab1, 0x30d33e95, 0x1f3b5f28, 0x2fe09dea, 0xceed}}}, + {{{0x0e75bc7f, 0x0b3a9f7d, 0x1dfec7d9, 0x0e2e1b6d, 0x14c7b95c, 0x07890be6, 0x0d0e3bd0, 0x09fce572, 0xb57ac}}, + {{0x0972e9a9, 0x078b96e8, 0x127f1881, 0x12d81c80, 0x094fab1f, 0x1a67d2bf, 0x0ed7ca30, 0x104ef53e, 0xceedbf}}}, /* 5*16^43*G: */ - {{{0x033125ff, 0x0dd0cf3e, 0x25a81421, 0x1155ec16, 0x1cae9935, 0x1a0b6728, 0x3d148cf4, 0x2cfedb92, 0x1178}}, - {{0x18486abd, 0x203e5c27, 0x0e54d1be, 0x322b7342, 0x310ed10d, 0x3798dfa8, 0x3d95b382, 0x25faa6ea, 0xdfd6}}}, + {{{0x033125ff, 0x1ba19e7c, 0x16a05084, 0x0aaf60b4, 0x0ae99354, 0x016ce50e, 0x05233d1a, 0x1f6dc97a, 0x1178b3}}, + {{0x18486abd, 0x007cb84e, 0x195346fa, 0x115b9a11, 0x10ed10dc, 0x131bf518, 0x056ce0b7, 0x1d53757b, 0xdfd697}}}, /* 7*16^43*G: */ - {{{0x3662d955, 0x2cda5733, 0x08ce44f3, 0x1135a16d, 0x27569384, 0x20edfa34, 0x0e907f8a, 0x28209be5, 0x8ac7}}, - {{0x246b3dae, 0x31a8b6f9, 0x16c138db, 0x3d20716f, 0x359ad9e3, 0x1f948d32, 0x3231cc9d, 0x102483cc, 0xc80f}}}, + {{{0x1662d955, 0x19b4ae67, 0x033913ce, 0x09ad0b69, 0x15693844, 0x1dbf4693, 0x041fe2a0, 0x104df29d, 0x8ac7a0}}, + {{0x046b3dae, 0x03516df3, 0x1b04e36f, 0x09038b7a, 0x19ad9e3f, 0x1291a65a, 0x0c73275f, 0x1241e664, 0xc80f40}}}, /* 9*16^43*G: */ - {{{0x288803e5, 0x3361e6b7, 0x13465cb7, 0x06adf383, 0x169e02cc, 0x1fea1c01, 0x1f2111ab, 0x22ca1677, 0xc0f4}}, - {{0x076619ee, 0x1a4c880a, 0x3828edba, 0x0b9381c2, 0x20d7d393, 0x2991c9f9, 0x3ca369c9, 0x09adbe20, 0x3d43}}}, + {{{0x088803e5, 0x06c3cd6f, 0x0d1972df, 0x156f9c1a, 0x09e02cc1, 0x1d43802b, 0x08446adf, 0x050b3bbe, 0xc0f48b}}, + {{0x076619ee, 0x14991014, 0x00a3b6e9, 0x1c9c0e17, 0x0d7d3932, 0x12393f30, 0x08da7269, 0x16df1079, 0x3d4326}}}, /* 11*16^43*G: */ - {{{0x1e1f515c, 0x25b59c26, 0x16539afa, 0x2d228c88, 0x37b8c0e2, 0x2723843f, 0x1766da01, 0x1c03c0d4, 0x2ce8}}, - {{0x052eed6e, 0x1464d926, 0x2c3d52c9, 0x2a7734f8, 0x2f5d2ca7, 0x2cbd0bdf, 0x2c4a7bac, 0x27d3ced7, 0x7387}}}, + {{{0x1e1f515c, 0x0b6b384c, 0x194e6bea, 0x09146442, 0x1b8c0e2b, 0x047087fb, 0x19b68067, 0x01e06a2e, 0x2ce870}}, + {{0x052eed6e, 0x08c9b24c, 0x10f54b25, 0x13b9a7c5, 0x15d2ca7a, 0x17a17bf7, 0x129eeb2c, 0x09e76bd8, 0x73879f}}}, /* 13*16^43*G: */ - {{{0x24dcf274, 0x16a8ddd7, 0x0acea244, 0x1c801a0b, 0x3cca1d80, 0x386ec3f5, 0x3c109145, 0x1098772d, 0xfac4}}, - {{0x312f0472, 0x0da61803, 0x34594b16, 0x0809f189, 0x2e97bd73, 0x1c8f5753, 0x2a8a87cc, 0x3f718559, 0x9713}}}, + {{{0x04dcf274, 0x0d51bbaf, 0x0b3a8911, 0x0400d059, 0x0ca1d807, 0x0dd87ebe, 0x04245178, 0x0c3b96f8, 0xfac442}}, + {{0x112f0472, 0x1b4c3007, 0x11652c58, 0x004f8c4e, 0x097bd732, 0x11eaea77, 0x02a1f31c, 0x18c2acd5, 0x9713fd}}}, /* 15*16^43*G: */ - {{{0x3dc39d21, 0x2d792daa, 0x09adc682, 0x0dcfaf50, 0x19281368, 0x24790e86, 0x03e00465, 0x398596d0, 0xf891}}, - {{0x05ca579f, 0x1642385f, 0x1460254d, 0x2a5fb13d, 0x1bc43b73, 0x3ae2a38b, 0x1fced18a, 0x14ec4aef, 0x129f}}} + {{{0x1dc39d21, 0x1af25b55, 0x06b71a0a, 0x0e7d7a81, 0x12813683, 0x0f21d0cc, 0x18011964, 0x02cb6807, 0xf891e6}}, + {{0x05ca579f, 0x0c8470be, 0x11809535, 0x12fd89ea, 0x1c43b73a, 0x1c54716d, 0x13b462ba, 0x162577bf, 0x129f53}}} }, { /* 1*16^44*G: */ - {{{0x1076f57b, 0x233c6ae6, 0x2cac6072, 0x02e1b8f3, 0x32a53f03, 0x1f8d4073, 0x0c79cb92, 0x06159220, 0x20e1}}, - {{0x2da7afe6, 0x160efb6e, 0x0e1b71e8, 0x383726d0, 0x2de9979f, 0x370f8fed, 0x37ef731b, 0x2cd4ab10, 0xff67}}}, + {{{0x1076f57b, 0x0678d5cc, 0x12b181ca, 0x170dc79d, 0x0a53f030, 0x11a80e79, 0x1e72e49f, 0x0ac91018, 0x20e118}}, + {{0x0da7afe6, 0x0c1df6dd, 0x186dc7a1, 0x01b93681, 0x1e9979fe, 0x01f1fdb6, 0x1bdcc6f7, 0x0a55886f, 0xff67b3}}}, /* 3*16^44*G: */ - {{{0x0b661da4, 0x1278ebb5, 0x0a84a5c8, 0x02946b19, 0x061a2194, 0x31ff640c, 0x206ce8f7, 0x0a96ee19, 0xffca}}, - {{0x2f9b8a5a, 0x26120d7a, 0x1687f6f8, 0x23e1eb79, 0x346c8c47, 0x33268523, 0x1cdc8a53, 0x2c38cadc, 0xce1c}}}, + {{{0x0b661da4, 0x04f1d76a, 0x0a129721, 0x14a358c9, 0x01a21940, 0x1fec8183, 0x1b3a3df1, 0x0b770cc0, 0xffca2a}}, + {{0x0f9b8a5a, 0x0c241af5, 0x1a1fdbe2, 0x1f0f5bca, 0x06c8c478, 0x04d0a47a, 0x172294f3, 0x1c656e39, 0xce1cb0}}}, /* 5*16^44*G: */ - {{{0x1c8cfd22, 0x32b0784e, 0x236be583, 0x0ac19c6d, 0x2d354a4e, 0x14d45436, 0x116ab636, 0x273b7ff0, 0xff20}}, - {{0x13bc5535, 0x0e26c53a, 0x1684b942, 0x13d2e4b2, 0x0ff1c80d, 0x35074933, 0x10f7e207, 0x3ce5d1a7, 0xad79}}}, + {{{0x1c8cfd22, 0x0560f09c, 0x0daf960f, 0x160ce36c, 0x1354a4e2, 0x1a8a86d6, 0x1aad8d94, 0x1dbff822, 0xff209c}}, + {{0x13bc5535, 0x1c4d8a74, 0x1a12e508, 0x1e972592, 0x1f1c80d4, 0x00e92667, 0x1df881f5, 0x12e8d3a1, 0xad79f3}}}, /* 7*16^44*G: */ - {{{0x0f4e983e, 0x201f9616, 0x017f77ce, 0x279bb21c, 0x3b4b156d, 0x0102034c, 0x39ba9586, 0x3c0b42c1, 0x33d5}}, - {{0x11ea37a9, 0x35c36e1e, 0x1630c956, 0x1c6aa496, 0x3ba1eb7a, 0x0f585956, 0x0478473c, 0x169db4e7, 0x01eb}}}, + {{{0x0f4e983e, 0x003f2c2c, 0x05fddf3a, 0x1cdd90e0, 0x14b156d9, 0x0040699d, 0x0ea56181, 0x05a160f3, 0x33d5f0}}, + {{0x11ea37a9, 0x0b86dc3c, 0x18c3255b, 0x035524b2, 0x1a1eb7a7, 0x0b0b2add, 0x1e11cf0f, 0x0eda7388, 0x1eb5a}}}, /* 9*16^44*G: */ - {{{0x21e52a73, 0x1a569e7d, 0x305a1bcb, 0x38c45b25, 0x3b5e65d0, 0x25d366b6, 0x21690a9e, 0x348f6989, 0x8f1b}}, - {{0x2bea8f2e, 0x1f685147, 0x31850a85, 0x0140b992, 0x03eade59, 0x1a790c1d, 0x1a8b8b87, 0x23d8e4eb, 0x4c7a}}}, + {{{0x01e52a73, 0x14ad3cfb, 0x01686f2d, 0x0622d92e, 0x15e65d0e, 0x1a6cd6dd, 0x1a42a7a5, 0x07b4c4c2, 0x8f1bd2}}, + {{0x0bea8f2e, 0x1ed0a28f, 0x06142a15, 0x0a05cc96, 0x1eade590, 0x0f2183a1, 0x02e2e1da, 0x0c7275b5, 0x4c7a8f}}}, /* 11*16^44*G: */ - {{{0x3d2bc078, 0x210bfb0b, 0x1f3ef5a5, 0x281d814a, 0x1880aec4, 0x0a62df6b, 0x237f3ee6, 0x327fbded, 0x963b}}, - {{0x1afb8657, 0x376c8c7d, 0x043a3c27, 0x3b010a3d, 0x00a4f1c5, 0x0f9424a6, 0x2762280a, 0x0e0ff347, 0x7ed3}}}, + {{{0x1d2bc078, 0x0217f617, 0x1cfbd696, 0x00ec0a53, 0x080aec4a, 0x0c5bed6c, 0x1fcfb98a, 0x1fdef6c6, 0x963bc9}}, + {{0x1afb8657, 0x0ed918fa, 0x10e8f09f, 0x180851e8, 0x0a4f1c5e, 0x128494c0, 0x188a028f, 0x07f9a3ce, 0x7ed338}}}, /* 13*16^44*G: */ - {{{0x2fb608ad, 0x21c79dba, 0x08fd93a6, 0x20159536, 0x08bc4974, 0x06b772df, 0x1a844e63, 0x1b6b6187, 0x89fe}}, - {{0x064d4dad, 0x00501b9e, 0x0f0a87b6, 0x2a7544f8, 0x25df39ae, 0x15f7fedc, 0x0e8fc87b, 0x09e08c7d, 0x2898}}}, + {{{0x0fb608ad, 0x038f3b75, 0x03f64e9a, 0x00aca9b1, 0x0bc49748, 0x16ee5be4, 0x011398c6, 0x15b0c3b5, 0x89fe6d}}, + {{0x064d4dad, 0x00a0373c, 0x1c2a1ed8, 0x13aa27c1, 0x1df39aea, 0x1effdb92, 0x03f21ed5, 0x10463e9d, 0x289827}}}, /* 15*16^44*G: */ - {{{0x19ae4a29, 0x1c62606c, 0x2232a0b0, 0x0bf69ba8, 0x166984df, 0x35eb1384, 0x39759510, 0x011fcef5, 0xc348}}, - {{0x0eb09235, 0x12566b13, 0x149aebf3, 0x08ba67c1, 0x0dae9a84, 0x2a374838, 0x21c5613d, 0x207c815a, 0x5847}}} + {{{0x19ae4a29, 0x18c4c0d8, 0x08ca82c1, 0x1fb4dd44, 0x06984df2, 0x1d62708b, 0x1d654435, 0x0fe77af2, 0xc34804}}, + {{0x0eb09235, 0x04acd626, 0x126bafcd, 0x05d33e0a, 0x1ae9a842, 0x06e90706, 0x11584f6a, 0x1e40ad43, 0x584781}}} }, { /* 1*16^45*G: */ - {{{0x19273a8f, 0x34514ba2, 0x14fd54ad, 0x3751e39a, 0x17dac93f, 0x23b1ff7f, 0x2027b031, 0x313e1c8e, 0x5c9c}}, - {{0x1ce80d6e, 0x376b29a5, 0x11acab5a, 0x000d9d68, 0x08af964f, 0x1d6274dc, 0x2d259a82, 0x381e877f, 0x84ef}}}, + {{{0x19273a8f, 0x08a29744, 0x13f552b7, 0x1a8f1cd2, 0x1dac93fd, 0x163fefeb, 0x09ec0c63, 0x1f0e4740, 0x5c9cc4}}, + {{0x1ce80d6e, 0x0ed6534a, 0x06b2ad6b, 0x006ceb42, 0x0af964f0, 0x0c4e9b84, 0x0966a09d, 0x0f43bfda, 0x84efe0}}}, /* 3*16^45*G: */ - {{{0x0883e382, 0x32326151, 0x15536f38, 0x1813f3bd, 0x007431d0, 0x0900e548, 0x3d85c5be, 0x3864aef7, 0x5ac8}}, - {{0x1dfeaadc, 0x04dcf66f, 0x14d9d2e5, 0x1dbb284f, 0x163976de, 0x23ffcbc2, 0x28c8039c, 0x3940131e, 0xfcb7}}}, + {{{0x0883e382, 0x0464c2a2, 0x154dbce3, 0x009f9dea, 0x07431d06, 0x001ca900, 0x01716f89, 0x12577bfb, 0x5ac8e1}}, + {{0x1dfeaadc, 0x09b9ecde, 0x13674b94, 0x0dd9427a, 0x03976de7, 0x1ff9784b, 0x1200e723, 0x00098f51, 0xfcb7e5}}}, /* 5*16^45*G: */ - {{{0x2f01a3e8, 0x3290c1df, 0x248094eb, 0x3ad950cb, 0x167362c6, 0x05751383, 0x121182d5, 0x01a62de4, 0x99dc}}, - {{0x00f61114, 0x0a1917f9, 0x3f8f2945, 0x299c0d35, 0x180044b7, 0x2b1c45c7, 0x182bc697, 0x273748ee, 0x67c6}}}, + {{{0x0f01a3e8, 0x052183bf, 0x120253af, 0x16ca865c, 0x07362c6e, 0x0ea2706b, 0x0460b545, 0x1316f224, 0x99dc06}}, + {{0x00f61114, 0x14322ff2, 0x1e3ca514, 0x0ce069af, 0x00044b7a, 0x0388b8ec, 0x0af1a5eb, 0x1ba47730, 0x67c69c}}}, /* 7*16^45*G: */ - {{{0x0cd535ab, 0x20fdec01, 0x0764dc33, 0x093620fa, 0x0fb9f377, 0x090d5f3f, 0x00616440, 0x3cd86381, 0xabe2}}, - {{0x117b9c1a, 0x01c46cd1, 0x3ac8dd99, 0x379e8630, 0x2df7957f, 0x36fcac80, 0x1b293de0, 0x35932dd5, 0x4f02}}}, + {{{0x0cd535ab, 0x01fbd802, 0x1d9370ce, 0x09b107d0, 0x1b9f3772, 0x01abe7e7, 0x18591009, 0x0c31c080, 0xabe2f3}}, + {{0x117b9c1a, 0x0388d9a2, 0x0b237664, 0x1cf43187, 0x1f7957fd, 0x1f959016, 0x0a4f7836, 0x0996eab6, 0x4f02d6}}}, /* 9*16^45*G: */ - {{{0x2909970c, 0x2d2d9acd, 0x1e6e4e0d, 0x0636e966, 0x26099e45, 0x1bec7ddf, 0x1e72137c, 0x3435e30e, 0x227c}}, - {{0x1f809727, 0x21692b8c, 0x2b99ec42, 0x043b0fdf, 0x3f5defa2, 0x1b21d073, 0x1391d87d, 0x39dc7206, 0x2225}}}, + {{{0x0909970c, 0x1a5b359b, 0x19b93836, 0x11b74b33, 0x0099e451, 0x1d8fbbf3, 0x1c84df1b, 0x1af1873c, 0x227cd0}}, + {{0x1f809727, 0x02d25718, 0x0e67b10a, 0x01d87efd, 0x15defa21, 0x043a0e7f, 0x04761f5b, 0x0e390327, 0x2225e7}}}, /* 11*16^45*G: */ - {{{0x09e65b59, 0x366b7f26, 0x144ff77c, 0x10408bdf, 0x0d053b7a, 0x3ba4c2a3, 0x1c5b6827, 0x11a082bb, 0x3631}}, - {{0x29b4c2cf, 0x20285909, 0x1c5b6e9c, 0x10f240ed, 0x227fc1c1, 0x09e3e480, 0x172928e8, 0x36d885e2, 0x1d87}}}, + {{{0x09e65b59, 0x0cd6fe4c, 0x113fddf3, 0x02045efa, 0x1053b7a4, 0x14985466, 0x16da09fb, 0x10415db8, 0x363146}}, + {{0x09b4c2cf, 0x0050b213, 0x116dba72, 0x0792076b, 0x07fc1c14, 0x1c7c9011, 0x0a4a3a09, 0x0c42f12e, 0x1d87db}}}, /* 13*16^45*G: */ - {{{0x0d4c2506, 0x05ec562f, 0x19e9faf0, 0x1b1771fc, 0x1d1fec5b, 0x29a33862, 0x318a3e74, 0x35ad9a1a, 0xf65e}}, - {{0x3913dfac, 0x314b7094, 0x0d6542bc, 0x0a3bf0d3, 0x36e7bd41, 0x1770bf4d, 0x3aae8525, 0x2f1a0ca2, 0xd6d0}}}, + {{{0x0d4c2506, 0x0bd8ac5e, 0x07a7ebc0, 0x18bb8fe3, 0x11fec5b6, 0x14670c4e, 0x028f9d29, 0x16cd0d63, 0xf65ed6}}, + {{0x1913dfac, 0x0296e129, 0x15950af3, 0x11df8699, 0x0e7bd412, 0x0e17e9bb, 0x0ba14957, 0x0d065175, 0xd6d0bc}}}, /* 15*16^45*G: */ - {{{0x3b47a80b, 0x0793e5d4, 0x02497578, 0x25f16999, 0x2bdba8ff, 0x36709dbe, 0x2135729d, 0x37be847d, 0x66a0}}, - {{0x3f795e8b, 0x3dc657e3, 0x26edd200, 0x0c290a14, 0x2ef474c2, 0x237c9586, 0x2ca41cad, 0x2a9b78de, 0x3e24}}} + {{{0x1b47a80b, 0x0f27cba9, 0x0925d5e0, 0x0f8b4cc8, 0x1dba8ff9, 0x0e13b7d5, 0x0d5ca776, 0x1f423ec2, 0x66a0de}}, + {{0x1f795e8b, 0x1b8cafc7, 0x1bb74803, 0x014850a4, 0x0f474c23, 0x0f92b0d7, 0x09072b63, 0x0dbc6f59, 0x3e24aa}}} }, { /* 1*16^46*G: */ - {{{0x28523eb3, 0x1f766acc, 0x16c6c4ae, 0x068e9d55, 0x3dcde335, 0x3061113c, 0x0b5ab46a, 0x353afe2a, 0xbaff}}, - {{0x15acf387, 0x25e0c033, 0x348b6ee1, 0x144733ef, 0x1ac09c24, 0x2a3acde5, 0x15e83003, 0x0f7176f2, 0x0fa9}}}, + {{{0x08523eb3, 0x1eecd599, 0x1b1b12b9, 0x1474eaaa, 0x1cde3351, 0x0c22279e, 0x16ad1ab0, 0x1d7f1516, 0xbaffd4}}, + {{0x15acf387, 0x0bc18066, 0x122dbb86, 0x02399f7e, 0x0c09c245, 0x0759bcad, 0x1a0c00ea, 0x18bb792b, 0xfa93d}}}, /* 3*16^46*G: */ - {{{0x34737641, 0x00266d3b, 0x2c2e13ad, 0x3eb03059, 0x163fb71a, 0x22d448d9, 0x089ed777, 0x11489107, 0x91b4}}, - {{0x2101bbe0, 0x0944aca7, 0x2077d03f, 0x35f7199b, 0x2fb428c9, 0x0c8d6ac0, 0x1a9762c1, 0x18ef4dff, 0x3f44}}}, + {{{0x14737641, 0x004cda77, 0x10b84eb4, 0x158182cd, 0x03fb71af, 0x1a891b2b, 0x07b5dde2, 0x04488391, 0x91b445}}, + {{0x0101bbe0, 0x1289594f, 0x01df40fc, 0x0fb8ccdc, 0x1b428c9d, 0x11ad5817, 0x05d8b04c, 0x17a6ffb5, 0x3f4463}}}, /* 5*16^46*G: */ - {{{0x26dd01df, 0x1a8aeae0, 0x38fefb9c, 0x0fbfdd94, 0x28916574, 0x3a9b1f21, 0x1b07aa37, 0x04d77a0b, 0x296d}}, - {{0x2a3a0dc8, 0x25434c82, 0x1e66f604, 0x3ebd8639, 0x0777cadf, 0x1c4a5ddb, 0x145e42b8, 0x13b764b8, 0x1405}}}, + {{{0x06dd01df, 0x1515d5c1, 0x03fbee71, 0x1dfeeca7, 0x09165743, 0x1363e434, 0x01ea8dfa, 0x0bbd05b6, 0x296d13}}, + {{0x0a3a0dc8, 0x0a869905, 0x199bd812, 0x15ec31cb, 0x177cadff, 0x094bbb63, 0x1790ae1c, 0x1bb25c28, 0x14054e}}}, /* 7*16^46*G: */ - {{{0x1650f5dd, 0x19f9bc1b, 0x191b2c8c, 0x3ff84908, 0x1e4a9654, 0x0f0bc7c6, 0x27a318f1, 0x10bce44d, 0x4b09}}, - {{0x3aeddc6d, 0x0ba96f31, 0x0e73a62c, 0x0f19e0b9, 0x13c25f02, 0x17040558, 0x0abc0e05, 0x2aa98d9b, 0x7432}}}, + {{{0x1650f5dd, 0x13f37836, 0x046cb231, 0x1fc24843, 0x04a9654f, 0x0178f8cf, 0x08c63c4f, 0x1e7226cf, 0x4b0942}}, + {{0x1aeddc6d, 0x1752de63, 0x19ce98b0, 0x18cf05c9, 0x1c25f023, 0x0080ab09, 0x0f038157, 0x14c6cd95, 0x7432aa}}}, /* 9*16^46*G: */ - {{{0x04e4a96f, 0x28dd7a3c, 0x1655b147, 0x2218ad0d, 0x12e4af18, 0x3b6e3f13, 0x0c11a833, 0x1de98bfb, 0x0363}}, - {{0x11e08cdb, 0x2ebedf81, 0x30913268, 0x02630850, 0x14626384, 0x0c3155e1, 0x3df838d9, 0x06474d53, 0xa1de}}}, + {{{0x04e4a96f, 0x11baf478, 0x1956c51e, 0x10c5686a, 0x0e4af188, 0x0dc7e269, 0x046a0cfb, 0x14c5fd98, 0x36377}}, + {{0x11e08cdb, 0x1d7dbf02, 0x0244c9a2, 0x13184286, 0x06263840, 0x062abc2a, 0x1e0e364c, 0x03a6a9fb, 0xa1de19}}}, /* 11*16^46*G: */ - {{{0x279b5a59, 0x107f4f85, 0x269e62a1, 0x087a27ac, 0x183251c6, 0x2fb55c27, 0x1e162bcb, 0x06bdcc3d, 0xa104}}, - {{0x2c5514a3, 0x234ad008, 0x2ac66d9d, 0x0c1a4387, 0x3c2afbfb, 0x194361ce, 0x18b19422, 0x05daaa3d, 0xad42}}}, + {{{0x079b5a59, 0x00fe9f0b, 0x1a798a85, 0x03d13d64, 0x03251c62, 0x16ab84ec, 0x058af2ef, 0x1ee61ebc, 0xa1041a}}, + {{0x0c5514a3, 0x0695a011, 0x0b19b676, 0x00d21c3d, 0x02afbfb3, 0x086c39de, 0x0c650899, 0x0d551eb1, 0xad4217}}}, /* 13*16^46*G: */ - {{{0x0ddd597b, 0x2ba36c1b, 0x085758de, 0x224c5c33, 0x292007d8, 0x1c6b43e7, 0x25647033, 0x19eb42c7, 0xda21}}, - {{0x3de7fa04, 0x1a05c9f8, 0x04f9f462, 0x378a9485, 0x18ebf6cd, 0x19c03a9e, 0x2ed361ff, 0x24ad8951, 0xa219}}}, + {{{0x0ddd597b, 0x1746d836, 0x015d637a, 0x1262e199, 0x12007d88, 0x0d687cf4, 0x191c0cdc, 0x15a163ca, 0xda2167}}, + {{0x1de7fa04, 0x140b93f1, 0x13e7d189, 0x1c54a428, 0x0ebf6cdd, 0x180753cc, 0x14d87fd9, 0x16c4a8dd, 0xa21992}}}, /* 15*16^46*G: */ - {{{0x33f7dbb0, 0x24d2888a, 0x2bf29c09, 0x3b88f709, 0x24f29df4, 0x18ee1c85, 0x2c678bc8, 0x36f08dfd, 0x1c3f}}, - {{0x32e16d32, 0x1932f725, 0x020f8add, 0x01918e00, 0x0b18d41f, 0x3a94e529, 0x29813f0a, 0x03c40de4, 0x3926}}} + {{{0x13f7dbb0, 0x09a51115, 0x0fca7026, 0x1c47b84d, 0x0f29df4e, 0x1dc390b2, 0x19e2f218, 0x1846fed8, 0x1c3fdb}}, + {{0x12e16d32, 0x1265ee4b, 0x083e2b75, 0x0c8c7000, 0x118d41f0, 0x129ca525, 0x004fc2ba, 0x0206f253, 0x39260f}}} }, { /* 1*16^47*G: */ - {{{0x3a111101, 0x0d482362, 0x2db3c5f8, 0x27c2c69d, 0x3e4c9647, 0x0a8d3495, 0x2d766ed2, 0x0a8263f3, 0x06ad}}, - {{0x1fb37ef4, 0x069eea75, 0x30e89aec, 0x10a760ad, 0x2b62a0de, 0x13006ee7, 0x05e3559a, 0x22c7163e, 0x2d5b}}}, + {{{0x1a111101, 0x1a9046c5, 0x16cf17e0, 0x1e1634ed, 0x04c96479, 0x11a692bf, 0x1d9bb48a, 0x0131f9da, 0x6ad2a}}, + {{0x1fb37ef4, 0x0d3dd4ea, 0x03a26bb0, 0x053b056e, 0x162a0de4, 0x000ddcf5, 0x18d56693, 0x038b1f0b, 0x2d5b8b}}}, /* 3*16^47*G: */ - {{{0x302bef6f, 0x1bf0e11d, 0x131ee437, 0x2b93c611, 0x18d475bb, 0x1e2f59af, 0x3cd7204f, 0x32955b0e, 0xf1a2}}, - {{0x0f6c1ca3, 0x06cb47f6, 0x3d52b401, 0x2d1faa07, 0x020168b0, 0x15505f70, 0x0313edf4, 0x166bc122, 0xb39b}}}, + {{{0x102bef6f, 0x17e1c23b, 0x0c7b90dd, 0x1c9e308a, 0x0d475bba, 0x05eb35ec, 0x15c813de, 0x0aad8779, 0xf1a2ca}}, + {{0x0f6c1ca3, 0x0d968fec, 0x154ad004, 0x08fd503f, 0x00168b0b, 0x0a0bee01, 0x04fb7d15, 0x15e09106, 0xb39b59}}}, /* 5*16^47*G: */ - {{{0x20455367, 0x0180a3f2, 0x0d613e08, 0x313cb209, 0x3f1851e6, 0x2405963a, 0x38030ee1, 0x2b527f8e, 0xe924}}, - {{0x28257e92, 0x3f4633e0, 0x3a6752b5, 0x368c6a93, 0x2fbb6f52, 0x0214e4f5, 0x03ed5752, 0x1f65e685, 0xfcc9}}}, + {{{0x00455367, 0x030147e5, 0x1584f820, 0x09e59049, 0x11851e6c, 0x00b2c75f, 0x00c3b864, 0x093fc770, 0xe924ad}}, + {{0x08257e92, 0x1e8c67c1, 0x099d4ad7, 0x1463549f, 0x1bb6f52d, 0x029c9eb7, 0x1b55d482, 0x12f34287, 0xfcc97d}}}, /* 7*16^47*G: */ - {{{0x02f8f1e7, 0x247c24e5, 0x1d1f9e2e, 0x352a9753, 0x3b22f68d, 0x2e4d4417, 0x3026fa00, 0x271f717d, 0xf49d}}, - {{0x114d9972, 0x088a2ac6, 0x24d7a839, 0x2c004f13, 0x14f67901, 0x174ecee6, 0x3acae6ae, 0x175080f8, 0xf558}}}, + {{{0x02f8f1e7, 0x08f849ca, 0x147e78ba, 0x0954ba9b, 0x122f68dd, 0x09a882fd, 0x09be802e, 0x0fb8bee0, 0xf49d9c}}, + {{0x114d9972, 0x1114558c, 0x135ea0e4, 0x0002789c, 0x0f67901b, 0x09d9dcca, 0x12b9ab97, 0x08407c75, 0xf5585d}}}, /* 9*16^47*G: */ - {{{0x3b219a79, 0x2cea59df, 0x29827a77, 0x1335105f, 0x1189e65c, 0x0f0d55d5, 0x29d48b0e, 0x1340f91a, 0x28b0}}, - {{0x102dbe24, 0x22fdf364, 0x2004be5f, 0x059b33e1, 0x3e206b86, 0x3f95c860, 0x0cf1459c, 0x36a79685, 0xf658}}}, + {{{0x1b219a79, 0x19d4b3bf, 0x0609e9de, 0x19a882fd, 0x189e65c4, 0x01aabaa8, 0x1522c38f, 0x007c8d53, 0x28b04d}}, + {{0x102dbe24, 0x05fbe6c8, 0x0012f97e, 0x0cd99f0c, 0x0206b861, 0x12b90c1f, 0x1c51673f, 0x13cb4299, 0xf658da}}}, /* 11*16^47*G: */ - {{{0x17774af9, 0x0a08b671, 0x1460ad8b, 0x05ae9944, 0x2aefb54c, 0x140e4a21, 0x1fe93d68, 0x19af9f30, 0x3f47}}, - {{0x1d4de990, 0x1f35fd93, 0x1b7326ff, 0x2a533f7e, 0x2e5f511c, 0x05e241b9, 0x31cba3ab, 0x0375a9cc, 0xcc81}}}, + {{{0x17774af9, 0x14116ce2, 0x1182b62c, 0x0d74ca22, 0x0efb54c1, 0x01c94435, 0x1a4f5a14, 0x17cf983f, 0x3f4766}}, + {{0x1d4de990, 0x1e6bfb26, 0x0dcc9bfd, 0x1299fbf3, 0x05f511ca, 0x1c483737, 0x12e8eac5, 0x1ad4e663, 0xcc810d}}}, /* 13*16^47*G: */ - {{{0x08e57705, 0x21067c79, 0x04d598e7, 0x33adfeb2, 0x2f361721, 0x2b6ad075, 0x0ee791f2, 0x2780b03e, 0xe324}}, - {{0x38caec0c, 0x252c67a0, 0x27384220, 0x065175c5, 0x086b5a50, 0x1de307c9, 0x29507dcb, 0x1961c04d, 0xa666}}}, + {{{0x08e57705, 0x020cf8f2, 0x1356639e, 0x1d6ff590, 0x1361721c, 0x0d5a0eb7, 0x19e47cab, 0x00581f1d, 0xe3249e}}, + {{0x18caec0c, 0x0a58cf41, 0x1ce10882, 0x128bae2c, 0x06b5a501, 0x1c60f924, 0x141f72dd, 0x10e026d2, 0xa66665}}}, /* 15*16^47*G: */ - {{{0x325b93ac, 0x1e2f3abe, 0x187f8d2c, 0x38809441, 0x3bb4e917, 0x279da4f7, 0x3961cbdf, 0x1602f7ed, 0xa689}}, - {{0x2f589aab, 0x28f47135, 0x1c4fd3ae, 0x3c7e05f6, 0x059ff2fc, 0x3cbc057c, 0x0783eaa7, 0x32a52d3c, 0x4657}}} + {{{0x125b93ac, 0x1c5e757d, 0x01fe34b1, 0x0404a20b, 0x1b4e917e, 0x13b49efd, 0x1872f7e7, 0x017bf6f2, 0xa68958}}, + {{0x0f589aab, 0x11e8e26b, 0x113f4eba, 0x03f02fb3, 0x19ff2fcf, 0x1780af82, 0x00faa9fc, 0x12969e0f, 0x4657ca}}} }, { /* 1*16^48*G: */ - {{{0x313728be, 0x33c83fec, 0x3c6b94a6, 0x10e56468, 0x315fc596, 0x1bfe0d10, 0x09276273, 0x259de9e1, 0xa6d3}}, - {{0x0357f5f4, 0x0aeae0cf, 0x284059bf, 0x12a48308, 0x27ecdf82, 0x22eaf4b4, 0x3881666b, 0x211d26c2, 0x674f}}}, + {{{0x113728be, 0x07907fd9, 0x11ae529b, 0x072b2347, 0x15fc5964, 0x1fc1a218, 0x09d89cdb, 0x0ef4f092, 0xa6d396}}, + {{0x0357f5f4, 0x15d5c19e, 0x010166fc, 0x15241845, 0x1ecdf824, 0x1d5e9693, 0x00599ae2, 0x0e936171, 0x674f84}}}, /* 3*16^48*G: */ - {{{0x0f15d864, 0x0152d5a7, 0x1cc8d3cc, 0x01bf71a8, 0x26cf3524, 0x23b39ef8, 0x2db0dafc, 0x19b5f177, 0x07ef}}, - {{0x340907fe, 0x1189509d, 0x0ce4a8b5, 0x11c38ec7, 0x3d505e9f, 0x10314887, 0x1e6a506d, 0x0c976e27, 0x2db3}}}, + {{{0x0f15d864, 0x02a5ab4e, 0x13234f30, 0x0dfb8d43, 0x0cf35240, 0x1673df13, 0x0c36bf23, 0x1af8bbdb, 0x7ef66}}, + {{0x140907fe, 0x0312a13b, 0x1392a2d5, 0x0e1c7639, 0x1505e9f4, 0x062910fe, 0x1a941b50, 0x0bb713bc, 0x2db332}}}, /* 5*16^48*G: */ - {{{0x17c7c05e, 0x1a5450f0, 0x0e5416ac, 0x20f2e54b, 0x328c0bb2, 0x0e9cbdd7, 0x1c46014f, 0x1397f01b, 0x82df}}, - {{0x18fff26b, 0x2584f40b, 0x02db300b, 0x057651a1, 0x17cbd1cf, 0x08588448, 0x2420a275, 0x22326325, 0xe4e1}}}, + {{{0x17c7c05e, 0x14a8a1e0, 0x19505ab1, 0x07972a59, 0x08c0bb28, 0x1397baf9, 0x118053ce, 0x0bf80db8, 0x82df4e}}, + {{0x18fff26b, 0x0b09e816, 0x0b6cc02e, 0x0bb28d08, 0x1cbd1cf1, 0x0b10890b, 0x08289d48, 0x193192c8, 0xe4e188}}}, /* 7*16^48*G: */ - {{{0x140368b0, 0x02b87505, 0x3ee949d8, 0x09308be3, 0x247a6213, 0x396e34e3, 0x30c6a7d9, 0x3f26f04a, 0x261e}}, - {{0x3deb011f, 0x0eb49566, 0x39b5d301, 0x0d02f878, 0x0fff797e, 0x2214b359, 0x2fce9fdc, 0x0ab6f8e1, 0x8a9d}}}, + {{{0x140368b0, 0x0570ea0a, 0x1ba52760, 0x09845f1f, 0x07a62132, 0x0dc69c72, 0x11a9f679, 0x13782561, 0x261efc}}, + {{0x1deb011f, 0x1d692acd, 0x06d74c04, 0x0817c3c7, 0x1ff797e3, 0x02966b27, 0x13a7f722, 0x1b7c70df, 0x8a9d2a}}}, /* 9*16^48*G: */ - {{{0x15eb8034, 0x040cfa54, 0x2e8ca4af, 0x02ccd7d5, 0x27692df3, 0x29f96767, 0x0279149a, 0x37f5de8b, 0x6d48}}, - {{0x1ab0ce30, 0x21cc21e9, 0x23e8961e, 0x00843a8a, 0x05476308, 0x39e59278, 0x1d12f3d5, 0x1c914597, 0x3cb4}}}, + {{{0x15eb8034, 0x0819f4a8, 0x1a3292bc, 0x1666bead, 0x1692df30, 0x1f2cecf3, 0x1e4526a9, 0x1aef4584, 0x6d48df}}, + {{0x1ab0ce30, 0x039843d2, 0x0fa2587a, 0x0421d454, 0x14763080, 0x1cb24f02, 0x04bcf579, 0x08a2cbba, 0x3cb472}}}, /* 11*16^48*G: */ - {{{0x140535c8, 0x1450f7f1, 0x08db13eb, 0x3c2958c3, 0x054e6f65, 0x048fed3f, 0x18923a49, 0x30079eee, 0x93a5}}, - {{0x3d59b844, 0x1255d020, 0x35bedffc, 0x28588124, 0x15a5c166, 0x2a10d638, 0x0c2f4c16, 0x03a41260, 0x2d44}}}, + {{{0x140535c8, 0x08a1efe2, 0x036c4fad, 0x014ac619, 0x14e6f65f, 0x11fda7e2, 0x048e9244, 0x03cf7731, 0x93a5c0}}, + {{0x1d59b844, 0x04aba041, 0x16fb7ff1, 0x02c40926, 0x1a5c166a, 0x021ac70a, 0x0bd305aa, 0x12093018, 0x2d440e}}}, /* 13*16^48*G: */ - {{{0x1e2047ba, 0x0986959a, 0x3b0f652a, 0x11c1265a, 0x167031e5, 0x3683805f, 0x272bbb35, 0x2e4a4584, 0x3fb0}}, - {{0x1db24158, 0x1ffb353b, 0x17009d35, 0x1082b9dc, 0x266dc86c, 0x09887265, 0x3df94ca7, 0x1eb9a085, 0x9d46}}}, + {{{0x1e2047ba, 0x130d2b34, 0x0c3d94a8, 0x0e0932d7, 0x07031e54, 0x10700beb, 0x0aeecd76, 0x0522c24e, 0x3fb0b9}}, + {{0x1db24158, 0x1ff66a76, 0x1c0274d5, 0x0415cee2, 0x06dc86c4, 0x110e4cb3, 0x1e5329c9, 0x1cd042fb, 0x9d467a}}}, /* 15*16^48*G: */ - {{{0x22df71c1, 0x02f6f6eb, 0x3bb723a0, 0x0c61afab, 0x33e4381c, 0x18eea778, 0x283d5d07, 0x250e7823, 0xdab0}}, - {{0x24c3a1e3, 0x21cd2104, 0x0b44e3bb, 0x258cc329, 0x120b3d6e, 0x2ba1bc83, 0x21cef385, 0x2f079513, 0x763c}}} + {{{0x02df71c1, 0x05ededd7, 0x0edc8e80, 0x030d7d5f, 0x1e4381c3, 0x1dd4ef19, 0x0f5741d8, 0x073c11d0, 0xdab094}}, + {{0x04c3a1e3, 0x039a4209, 0x0d138eee, 0x0c661949, 0x00b3d6e9, 0x14379069, 0x13bce16b, 0x03ca89c3, 0x763cbc}}} }, { /* 1*16^49*G: */ - {{{0x0514c6fd, 0x3bbd8bfd, 0x1ab013e6, 0x1a0ed343, 0x3f5936fd, 0x136d5c43, 0x0f4e033d, 0x36a00227, 0xac25}}, - {{0x05830541, 0x02d4e5dc, 0x03bf37a6, 0x0260fa09, 0x1b338c81, 0x36a4c4a8, 0x04c7b883, 0x2766172d, 0xebc6}}}, + {{{0x0514c6fd, 0x177b17fa, 0x0ac04f9b, 0x10769a1b, 0x15936fd6, 0x0dab887f, 0x1380cf53, 0x1001139e, 0xac25da}}, + {{0x05830541, 0x05a9cbb8, 0x0efcde98, 0x1307d048, 0x1338c810, 0x1498950d, 0x11ee20f6, 0x130b9689, 0xebc69d}}}, /* 3*16^49*G: */ - {{{0x32fd0e3d, 0x065071f8, 0x027ad608, 0x0c793715, 0x165547e6, 0x1d219c78, 0x23c8bb4d, 0x399b126e, 0xeea7}}, - {{0x191d5868, 0x01047da3, 0x019e3cc1, 0x32eb688c, 0x1b7d985a, 0x10fc9efa, 0x09261288, 0x3516e7e2, 0x83fe}}}, + {{{0x12fd0e3d, 0x0ca0e3f1, 0x09eb5820, 0x03c9b8a8, 0x05547e63, 0x04338f0b, 0x122ed35d, 0x0d893747, 0xeea7e6}}, + {{0x191d5868, 0x0208fb46, 0x0678f304, 0x175b4460, 0x17d985ac, 0x1f93df4d, 0x0984a210, 0x0b73f112, 0x83fed4}}}, /* 5*16^49*G: */ - {{{0x2ccb63b3, 0x067c53c9, 0x0408e5d1, 0x37ff9b11, 0x03c67b7d, 0x0652cd50, 0x221bdbad, 0x38b4fa4f, 0x9a3d}}, - {{0x3df93fcf, 0x0714ca5d, 0x35822600, 0x300767fb, 0x013c4c49, 0x3c9cdbba, 0x112c8809, 0x26e41844, 0x2f80}}}, + {{{0x0ccb63b3, 0x0cf8a793, 0x10239744, 0x1ffcd888, 0x1c67b7dd, 0x0a59aa01, 0x06f6eb46, 0x1a7d27c4, 0x9a3de2}}, + {{0x1df93fcf, 0x0e2994bb, 0x16089800, 0x003b3fde, 0x13c4c49c, 0x139b7740, 0x0b22027c, 0x120c2222, 0x2f809b}}}, /* 7*16^49*G: */ - {{{0x163f1117, 0x13b28d37, 0x27f6d8be, 0x225bdc2e, 0x3fadaf34, 0x0034c048, 0x392db051, 0x20bd2d4e, 0xa7c3}}, - {{0x1934cb9a, 0x04883178, 0x3c4a68cc, 0x13addbb4, 0x1dcfb5ae, 0x27ddddc1, 0x1bf88045, 0x394459d8, 0x1b91}}}, + {{{0x163f1117, 0x07651a6e, 0x1fdb62f9, 0x12dee174, 0x1adaf348, 0x0698091f, 0x0b6c1440, 0x1e96a772, 0xa7c382}}, + {{0x1934cb9a, 0x091062f0, 0x1129a330, 0x1d6edda7, 0x1cfb5ae4, 0x1bbbb82e, 0x1e201167, 0x022cec37, 0x1b91e5}}}, /* 9*16^49*G: */ - {{{0x26774a96, 0x02f20716, 0x038e3e85, 0x08c7f646, 0x26f497e8, 0x10eff20e, 0x21213871, 0x2a663361, 0x555a}}, - {{0x06db0e34, 0x35025cb6, 0x0e26fa69, 0x035752f2, 0x10bbb89a, 0x11079c4d, 0x3bc6999d, 0x0a1a3481, 0xb053}}}, + {{{0x06774a96, 0x05e40e2d, 0x0e38fa14, 0x063fb230, 0x0f497e82, 0x1dfe41d3, 0x084e1c50, 0x1319b0c2, 0x555aa9}}, + {{0x06db0e34, 0x0a04b96c, 0x189be9a7, 0x1aba9791, 0x0bbb89a0, 0x00f389a8, 0x11a66751, 0x0d1a40f7, 0xb05328}}}, /* 11*16^49*G: */ - {{{0x2f7dac7d, 0x0bdfbbce, 0x12412123, 0x15cae484, 0x37c36916, 0x335e3e35, 0x27ad7b58, 0x0bd6cd22, 0x01a4}}, - {{0x0195e46e, 0x1e2528c6, 0x0cea96b2, 0x0abca4ca, 0x3f921617, 0x1fe552e2, 0x07781349, 0x270e1548, 0x957a}}}, + {{{0x0f7dac7d, 0x17bf779d, 0x0904848c, 0x0e572422, 0x1c369165, 0x0bc7c6bb, 0x0b5ed633, 0x0b66914f, 0x1a42f}}, + {{0x0195e46e, 0x1c4a518c, 0x13aa5ac9, 0x15e52651, 0x19216172, 0x1caa5c5f, 0x1e04d25f, 0x070aa40e, 0x957a9c}}}, /* 13*16^49*G: */ - {{{0x202afc36, 0x00ae8750, 0x03071d3e, 0x137bb545, 0x05d3a313, 0x2c27bc6d, 0x1ce3d3a5, 0x3d4dfac1, 0x4b47}}, - {{0x2f8133ff, 0x3a27dda9, 0x25fbda34, 0x16b2fa6c, 0x0df57334, 0x2c1be83a, 0x05f0c2dc, 0x1140e672, 0xf2fc}}}, + {{{0x002afc36, 0x015d0ea1, 0x0c1c74f8, 0x1bddaa28, 0x1d3a3134, 0x04f78da2, 0x18f4e96c, 0x06fd60b9, 0x4b47f5}}, + {{0x0f8133ff, 0x144fbb53, 0x17ef68d3, 0x1597d364, 0x1f573345, 0x037d0746, 0x1c30b72c, 0x0073390b, 0xf2fc45}}}, /* 15*16^49*G: */ - {{{0x37d17f68, 0x2afcb8f1, 0x38bad86a, 0x056877f2, 0x2e418f79, 0x145bd4da, 0x0e8ced56, 0x3b273149, 0x6b3d}}, - {{0x09232402, 0x3eb9e883, 0x2dccb68c, 0x3caa5aa9, 0x0d5d4747, 0x2606d05b, 0x3d9ef050, 0x0e4dff7b, 0xb865}}} + {{{0x17d17f68, 0x15f971e3, 0x02eb61aa, 0x0b43bf97, 0x0418f791, 0x0b7a9b57, 0x033b5594, 0x1398a49d, 0x6b3dec}}, + {{0x09232402, 0x1d73d106, 0x1732da33, 0x0552d54d, 0x15d4747f, 0x00da0b66, 0x07bc1426, 0x06ffbdfb, 0xb86539}}} }, { /* 1*16^50*G: */ - {{{0x2fd20bae, 0x17538de8, 0x1b4a8115, 0x00d59cb5, 0x2d343a26, 0x2ee8485d, 0x0fcd9027, 0x143b70ef, 0x2852}}, - {{0x14e0ab97, 0x27791569, 0x1eff323f, 0x26c68b3c, 0x06c1716e, 0x0a12b441, 0x17ea83f7, 0x3021bd2b, 0x7866}}}, + {{{0x0fd20bae, 0x0ea71bd1, 0x0d2a0455, 0x06ace5ab, 0x1343a260, 0x1d090bb6, 0x136409ee, 0x1db8779f, 0x285250}}, + {{0x14e0ab97, 0x0ef22ad2, 0x1bfcc8fe, 0x163459e3, 0x0c1716e9, 0x02568823, 0x1aa0fdca, 0x10de95af, 0x7866c0}}}, /* 3*16^50*G: */ - {{{0x2636a50b, 0x3221daae, 0x3b75196c, 0x0bbd85aa, 0x38baf65d, 0x1be84bf1, 0x1a75c583, 0x31595175, 0xf1e3}}, - {{0x2b3128b6, 0x3dde453a, 0x22d7a6ed, 0x1fe95db4, 0x25f3136b, 0x0da99fda, 0x2fce76c7, 0x211e9b87, 0x12b8}}}, + {{{0x0636a50b, 0x0443b55d, 0x0dd465b3, 0x1dec2d57, 0x0baf65d2, 0x1d097e3c, 0x1d7160db, 0x0ca8bab4, 0xf1e3c5}}, + {{0x0b3128b6, 0x1bbc8a75, 0x0b5e9bb7, 0x1f4aeda4, 0x1f3136b7, 0x1533fb52, 0x139db1cd, 0x0f4dc3df, 0x12b884}}}, /* 5*16^50*G: */ - {{{0x0e583340, 0x05fc4c85, 0x134f3b25, 0x1706dad7, 0x1b228cf4, 0x1f36afea, 0x134a76d8, 0x1ca72078, 0x584d}}, - {{0x34fb24b9, 0x0bdb97a5, 0x094c0707, 0x05dc2999, 0x30affa8f, 0x01f164c0, 0x180abcd3, 0x20291583, 0x2fdd}}}, + {{{0x0e583340, 0x0bf8990a, 0x0d3cec94, 0x1836d6ba, 0x1228cf45, 0x06d5fd4d, 0x129db61f, 0x13903c26, 0x584d72}}, + {{0x14fb24b9, 0x17b72f4b, 0x05301c1c, 0x0ee14cc9, 0x0affa8f1, 0x1e2c9818, 0x02af34c1, 0x148ac1b0, 0x2fdd80}}}, /* 7*16^50*G: */ - {{{0x0235809b, 0x0b20fb78, 0x1eb81739, 0x15cb7c2d, 0x383c453c, 0x380a3708, 0x3df7d1e2, 0x2b80320d, 0xbaae}}, - {{0x0154fd62, 0x35876297, 0x1d2e7e5c, 0x170f10a8, 0x09f29983, 0x08c1ef2d, 0x24b80b4a, 0x2220cfcc, 0x3257}}}, + {{{0x0235809b, 0x1641f6f0, 0x1ae05ce4, 0x0e5be16b, 0x03c453c5, 0x0146e11c, 0x1df478b8, 0x001906fb, 0xbaaeae}}, + {{0x0154fd62, 0x0b0ec52e, 0x14b9f973, 0x18788543, 0x1f299835, 0x183de5a4, 0x0e02d288, 0x1067e649, 0x325788}}}, /* 9*16^50*G: */ - {{{0x0d612268, 0x18010b10, 0x25ed016f, 0x33d677c2, 0x14b8b906, 0x0e7be90e, 0x2131a651, 0x3918d830, 0x06c7}}, - {{0x260166a0, 0x32d2d804, 0x02e7098b, 0x2362969e, 0x3453ca23, 0x3f1d738b, 0x1d8cd747, 0x35577dcb, 0xcb6a}}}, + {{{0x0d612268, 0x10021620, 0x17b405bd, 0x1eb3be14, 0x0b8b906c, 0x0f7d21ca, 0x0c69944e, 0x0c6c1842, 0x6c7e4}}, + {{0x060166a0, 0x05a5b009, 0x0b9c262f, 0x1b14b4f0, 0x053ca238, 0x03ae717a, 0x0335d1ff, 0x0bbee5bb, 0xcb6ad5}}}, /* 11*16^50*G: */ - {{{0x012fbdc8, 0x350e8d6e, 0x2c0e2a3b, 0x278832a8, 0x11a36db8, 0x0bb31edc, 0x2643e5bc, 0x0c77aaf5, 0x0641}}, - {{0x29f99380, 0x34ffcc26, 0x1fb020a5, 0x0eb89a2c, 0x15759860, 0x0e0364d2, 0x27028f2b, 0x1feb0cb5, 0x882c}}}, + {{{0x012fbdc8, 0x0a1d1adc, 0x1038a8ef, 0x1c419545, 0x1a36db89, 0x1663db88, 0x10f96f0b, 0x1bd57acc, 0x64131}}, + {{0x09f99380, 0x09ff984d, 0x1ec08297, 0x15c4d163, 0x17598603, 0x006c9a4a, 0x00a3cace, 0x15865ace, 0x882c7f}}}, /* 13*16^50*G: */ - {{{0x0bac9f32, 0x17ac0019, 0x1689b067, 0x0e087316, 0x1b640044, 0x1905bf86, 0x1c2378a1, 0x2deb309d, 0x366b}}, - {{0x3c85d47d, 0x0bc3973e, 0x3f0268a4, 0x37394301, 0x21cfc01f, 0x1e0eae35, 0x1af064f0, 0x1edc21e1, 0x7d10}}}, + {{{0x0bac9f32, 0x0f580032, 0x1a26c19d, 0x104398b2, 0x16400443, 0x00b7f0cd, 0x08de2859, 0x15984eb8, 0x366bb7}}, + {{0x1c85d47d, 0x17872e7d, 0x1c09a290, 0x19ca180f, 0x1cfc01fd, 0x01d5c6b0, 0x1c193c1e, 0x0e10f0b5, 0x7d107b}}}, /* 15*16^50*G: */ - {{{0x06dd27eb, 0x0f2d494a, 0x33b56230, 0x231570de, 0x3e32ecb9, 0x1f438e6e, 0x33c006b2, 0x36c95f31, 0xb767}}, - {{0x0f65dac4, 0x1548691f, 0x0600ed41, 0x2dc02d12, 0x19d85b64, 0x2b2e05ae, 0x229cb5ce, 0x0230c984, 0xdc13}}} + {{{0x06dd27eb, 0x1e5a9294, 0x0ed588c0, 0x18ab86f6, 0x032ecb98, 0x0871cddf, 0x1001ac9f, 0x04af98e7, 0xb767db}}, + {{0x0f65dac4, 0x0a90d23e, 0x1803b505, 0x0e016890, 0x1d85b64b, 0x05c0b5cc, 0x072d73ab, 0x1864c245, 0xdc1308}}} }, { /* 1*16^51*G: */ - {{{0x3e07e4f1, 0x1c7ce8a8, 0x0dc267c1, 0x31451f74, 0x38890e1f, 0x37af01fb, 0x0366f818, 0x30418bb4, 0xc472}}, - {{0x06b0daa9, 0x1c71a0f6, 0x22b5d8a5, 0x3cedec78, 0x1667d885, 0x0aad6a13, 0x370e9643, 0x03806517, 0x4182}}}, + {{{0x1e07e4f1, 0x18f9d151, 0x17099f05, 0x0a28fba1, 0x0890e1fc, 0x15e03f7c, 0x19be0637, 0x00c5da06, 0xc472c1}}, + {{0x06b0daa9, 0x18e341ec, 0x0ad76295, 0x076f63c4, 0x067d885f, 0x15ad426b, 0x03a590ca, 0x00328bee, 0x41820e}}}, /* 3*16^51*G: */ - {{{0x22f8acb1, 0x0da54d2a, 0x13f053f4, 0x27595518, 0x2cc31eb3, 0x06de92e3, 0x1e3d685e, 0x23ce6551, 0x86f8}}, - {{0x05098a19, 0x12c10b44, 0x11652711, 0x3a98afba, 0x11b1214e, 0x325e3ed6, 0x238d6b37, 0x375a69a0, 0x2ccf}}}, + {{{0x02f8acb1, 0x1b4a9a55, 0x0fc14fd0, 0x1acaa8c2, 0x0c31eb39, 0x1bd25c76, 0x0f5a1786, 0x0732a8bc, 0x86f88f}}, + {{0x05098a19, 0x05821688, 0x05949c45, 0x14c57dd2, 0x1b1214ee, 0x0bc7dac8, 0x035acdf2, 0x0d34d047, 0x2ccfdd}}}, /* 5*16^51*G: */ - {{{0x3cadab66, 0x220ddedb, 0x1d35602d, 0x31a8cf0f, 0x19f9a0e1, 0x1d9a5983, 0x08e747df, 0x2f87f265, 0xa2a3}}, - {{0x0c1aeb12, 0x3d284921, 0x080ad25e, 0x0b7a294d, 0x235ee1fb, 0x01fb5d34, 0x0be67065, 0x3639ad49, 0xa93b}}}, + {{{0x1cadab66, 0x041bbdb7, 0x14d580b6, 0x0d46787b, 0x1f9a0e1c, 0x134b306c, 0x19d1f7dd, 0x03f93291, 0xa2a3be}}, + {{0x0c1aeb12, 0x1a509242, 0x002b497b, 0x1bd14a69, 0x15ee1fb2, 0x1f6ba691, 0x199c1941, 0x1cd6a497, 0xa93bd8}}}, /* 7*16^51*G: */ - {{{0x207c25bf, 0x2274884c, 0x22d8097b, 0x3ef1ddef, 0x0080be82, 0x384919df, 0x38db9367, 0x1f3b55b9, 0x354e}}, - {{0x1a864211, 0x048e8e65, 0x1a0aa215, 0x35d5b2c1, 0x0fe5585f, 0x2f609297, 0x14070e6e, 0x18ba6ee6, 0x629d}}}, + {{{0x007c25bf, 0x04e91099, 0x0b6025ee, 0x178eef7c, 0x080be82f, 0x09233be0, 0x16e4d9f8, 0x1daadcf1, 0x354e7c}}, + {{0x1a864211, 0x091d1cca, 0x082a8854, 0x0ead960b, 0x1e5585fd, 0x0c1252e7, 0x01c39baf, 0x1d377328, 0x629d62}}}, /* 9*16^51*G: */ - {{{0x35e1dad8, 0x29f60b81, 0x2c4bd2e4, 0x2029e161, 0x099f498b, 0x173dc830, 0x2805b79b, 0x326abd77, 0xc751}}, - {{0x2e4afc8b, 0x04dacd84, 0x20a8c02d, 0x3e25c28e, 0x09a4ffe6, 0x1307f5b7, 0x19de2beb, 0x190dff1e, 0xcb98}}}, + {{{0x15e1dad8, 0x13ec1703, 0x112f4b92, 0x014f0b0d, 0x19f498b8, 0x07b90604, 0x016de6d7, 0x155ebbd0, 0xc751c9}}, + {{0x0e4afc8b, 0x09b59b09, 0x02a300b4, 0x112e1474, 0x1a4ffe6f, 0x00feb6e4, 0x178afad3, 0x06ff8f33, 0xcb9864}}}, /* 11*16^51*G: */ - {{{0x099d9ba2, 0x0c486c84, 0x3aaa757d, 0x3d95f5a5, 0x0f9ca80c, 0x2d4a1ad4, 0x1d02178a, 0x33106e74, 0xaee9}}, - {{0x3ed2ad58, 0x2358120e, 0x217490e7, 0x0b9a389a, 0x06b1f531, 0x25efec03, 0x2a36f7be, 0x3cc0b6d4, 0xb72c}}}, + {{{0x099d9ba2, 0x1890d908, 0x0aa9d5f4, 0x0cafad2f, 0x19ca80cf, 0x09435a87, 0x0085e2ad, 0x08373a3a, 0xaee9cc}}, + {{0x1ed2ad58, 0x06b0241d, 0x05d2439e, 0x1cd1c4d4, 0x0b1f5312, 0x1dfd8063, 0x0dbdefa5, 0x005b6a54, 0xb72cf3}}}, /* 13*16^51*G: */ - {{{0x094d208d, 0x0ffc2092, 0x3f391a46, 0x036a3fc3, 0x1ff0cefb, 0x3d82bcac, 0x12ec56bf, 0x0fd1a9e4, 0x0d0d}}, - {{0x1d45d1b1, 0x18bd4fde, 0x31ddabfd, 0x04f03469, 0x109ff0b2, 0x1d36997e, 0x37169b04, 0x06e02b87, 0xdc37}}}, + {{{0x094d208d, 0x1ff84124, 0x1ce46918, 0x1b51fe1f, 0x1f0cefb0, 0x1057958f, 0x1b15affd, 0x08d4f225, 0xd0d3f}}, + {{0x1d45d1b1, 0x117a9fbc, 0x0776aff5, 0x0781a34e, 0x09ff0b21, 0x06d32fc8, 0x05a6c11d, 0x1015c3ee, 0xdc371b}}}, /* 15*16^51*G: */ - {{{0x19cfd890, 0x1ba08b20, 0x0071145c, 0x0db0dcdf, 0x1441e1cb, 0x3360e1f9, 0x37535f47, 0x051ad104, 0x778d}}, - {{0x16f057f2, 0x26a1fe9f, 0x2d20acac, 0x32915223, 0x06cd3796, 0x09c6365e, 0x11af72a5, 0x2e84cec0, 0x3c85}}} + {{{0x19cfd890, 0x17411640, 0x01c45171, 0x0d86e6f8, 0x041e1cb3, 0x0c1c3f2a, 0x14d7d1f3, 0x0d68826e, 0x778d14}}, + {{0x16f057f2, 0x0d43fd3e, 0x1482b2b2, 0x148a911d, 0x0cd3796c, 0x18c6cbc3, 0x0bdca949, 0x02676023, 0x3c85ba}}} }, { /* 1*16^52*G: */ - {{{0x039bb85f, 0x083c270e, 0x050e62c3, 0x007ec1a8, 0x15345801, 0x160b266b, 0x2432b557, 0x0e634599, 0x55d5}}, - {{0x0fed936f, 0x1fd8c461, 0x033d9e1f, 0x035a9fc6, 0x3aa72ad9, 0x31aa7a3a, 0x38e2d059, 0x08a4127f, 0x576e}}}, + {{{0x039bb85f, 0x10784e1c, 0x14398b0c, 0x03f60d40, 0x13458010, 0x0164cd6a, 0x0cad55d6, 0x11a2ccc8, 0x55d539}}, + {{0x0fed936f, 0x1fb188c2, 0x0cf6787d, 0x1ad4fe30, 0x0a72ad90, 0x154f475d, 0x18b41671, 0x12093ff1, 0x576e22}}}, /* 3*16^52*G: */ - {{{0x12ea285a, 0x01f8ae48, 0x3b910d1c, 0x007079bd, 0x00a7a39f, 0x20163777, 0x3888b785, 0x19022053, 0x1bb4}}, - {{0x107dc702, 0x303229e6, 0x12fa94ed, 0x14a8d2e6, 0x34a4fc1e, 0x3f66e24a, 0x21125a40, 0x05afebeb, 0x8a30}}}, + {{{0x12ea285a, 0x03f15c90, 0x0e443470, 0x0383cdef, 0x0a7a39f0, 0x02c6eee0, 0x022de160, 0x011029f1, 0x1bb464}}, + {{0x107dc702, 0x006453cc, 0x0bea53b7, 0x05469732, 0x0a4fc1e5, 0x0cdc495a, 0x0496903f, 0x17f5f5c2, 0x8a3016}}}, /* 5*16^52*G: */ - {{{0x1539785a, 0x1404a403, 0x0297f014, 0x22341dae, 0x227a548c, 0x1cf899e1, 0x3a14ee09, 0x139c380b, 0x04bc}}, - {{0x0a62e3bb, 0x0e6411d7, 0x23275c35, 0x1c05dc9e, 0x3dfb4f87, 0x16873cfc, 0x34cc3a5f, 0x3c892e32, 0x5729}}}, + {{{0x1539785a, 0x08094806, 0x0a5fc051, 0x11a0ed70, 0x07a548c8, 0x1f133c31, 0x053b825c, 0x0e1c05f4, 0x4bc4e}}, + {{0x0a62e3bb, 0x1cc823ae, 0x0c9d70d4, 0x002ee4f4, 0x1fb4f877, 0x10e79f9e, 0x130e97d6, 0x04971969, 0x5729f2}}}, /* 7*16^52*G: */ - {{{0x2114cfb5, 0x04b52ec7, 0x3d5a6a31, 0x0d8626a8, 0x1f0876d1, 0x1ce786df, 0x08173587, 0x24bf707e, 0xd3e4}}, - {{0x297f7045, 0x33ae6a95, 0x2754eefb, 0x223c1b91, 0x15fea39c, 0x3899dafc, 0x0c48b1fe, 0x29c29cfe, 0x3604}}}, + {{{0x0114cfb5, 0x096a5d8f, 0x1569a8c4, 0x0c313547, 0x10876d13, 0x1cf0dbef, 0x05cd61dc, 0x1fb83f10, 0xd3e492}}, + {{0x097f7045, 0x075cd52b, 0x1d53bbef, 0x11e0dc8c, 0x1fea39c8, 0x133b5f8a, 0x122c7fb8, 0x014e7f18, 0x3604a7}}}, /* 9*16^52*G: */ - {{{0x2c55ddff, 0x2899d2ee, 0x0d4b7871, 0x2b46cfd9, 0x0dc1791d, 0x3948c43f, 0x042538a4, 0x3095618a, 0xbebf}}, - {{0x3ea2f303, 0x3536c328, 0x10baa706, 0x32a08b59, 0x36576c3c, 0x284712dd, 0x204ce8a3, 0x38997025, 0x850d}}}, + {{{0x0c55ddff, 0x1133a5dd, 0x152de1c6, 0x1a367ec9, 0x1c1791da, 0x091887e6, 0x094e2939, 0x0ab0c508, 0xbebfc2}}, + {{0x1ea2f303, 0x0a6d8651, 0x02ea9c1b, 0x15045aca, 0x0576c3cc, 0x08e25bbb, 0x133a28e8, 0x0cb812c0, 0x850de2}}}, /* 11*16^52*G: */ - {{{0x099ead51, 0x06bd0793, 0x1d9224e9, 0x28d50e88, 0x0784715d, 0x0a4c7458, 0x20d602fb, 0x21371cf4, 0x36e9}}, - {{0x2e0e5e3e, 0x1bee7509, 0x04280afc, 0x2aefb05c, 0x232b203b, 0x2f7f26b3, 0x3485f4bf, 0x1c51c86f, 0x1437}}}, + {{{0x099ead51, 0x0d7a0f26, 0x164893a4, 0x06a87443, 0x184715da, 0x098e8b03, 0x1580beca, 0x1b8e7a41, 0x36e984}}, + {{0x0e0e5e3e, 0x17dcea13, 0x10a02bf1, 0x177d82e0, 0x12b203ba, 0x0fe4d671, 0x017d2fef, 0x08e437e9, 0x143771}}}, /* 13*16^52*G: */ - {{{0x23093df0, 0x2a2ddeec, 0x376464d7, 0x17892059, 0x1793af78, 0x1451e553, 0x204aef31, 0x1d4010fd, 0x91b6}}, - {{0x12cc9f14, 0x337a30df, 0x1caf67f5, 0x0da17e3e, 0x221c5d93, 0x31eb6a5b, 0x0a00d477, 0x36c79609, 0x07fe}}}, + {{{0x03093df0, 0x145bbdd9, 0x1d91935e, 0x1c4902ce, 0x193af785, 0x0a3caa6b, 0x12bbcc54, 0x00087ec0, 0x91b675}}, + {{0x12cc9f14, 0x06f461be, 0x12bd9fd7, 0x0d0bf1f3, 0x01c5d933, 0x1d6d4b71, 0x00351df1, 0x03cb0494, 0x7fedb}}}, /* 15*16^52*G: */ - {{{0x3b7b8dc4, 0x08d9ee1b, 0x29b3848a, 0x0d24c0a2, 0x202fac5b, 0x25f8680d, 0x0883e7c4, 0x30f1e871, 0xc5d9}}, - {{0x1b2df0ea, 0x35925e34, 0x1fd4936e, 0x363dcbf4, 0x050af3d0, 0x230e1817, 0x1b79e580, 0x2e78973f, 0x3e59}}} + {{{0x1b7b8dc4, 0x11b3dc37, 0x06ce1228, 0x09260515, 0x02fac5b3, 0x1f0d01b0, 0x00f9f125, 0x18f43891, 0xc5d9c3}}, + {{0x1b2df0ea, 0x0b24bc68, 0x1f524dbb, 0x11ee5fa3, 0x10af3d0d, 0x01c302e2, 0x1e796023, 0x1c4b9fb6, 0x3e59b9}}} }, { /* 1*16^53*G: */ - {{{0x32513926, 0x18b6f270, 0x3ec85ecc, 0x09a2503b, 0x3c3383cc, 0x3aeac92f, 0x0872694f, 0x21918f28, 0x8842}}, - {{0x2fb8a54d, 0x3b90a0aa, 0x3dbc15a0, 0x03ac48ba, 0x181207ce, 0x1836cd97, 0x2dd5a696, 0x10a70070, 0xf778}}}, + {{{0x12513926, 0x116de4e1, 0x1b217b31, 0x0d1281df, 0x03383cc2, 0x1d5925fe, 0x1c9a53fa, 0x08c79410, 0x884286}}, + {{0x0fb8a54d, 0x17214155, 0x16f05683, 0x1d6245d7, 0x01207ce0, 0x06d9b2ec, 0x1569a598, 0x1380385b, 0xf77842}}}, /* 3*16^53*G: */ - {{{0x2520f1f1, 0x34aeb065, 0x07f7da4e, 0x3c6d2799, 0x0f6f4ad7, 0x17f45a33, 0x30819d5a, 0x274dbddb, 0x3bad}}, - {{0x1698df4d, 0x2865c1c9, 0x2b672586, 0x26606893, 0x2c0e8049, 0x27e9f677, 0x0e659bcd, 0x2778cf89, 0x49f9}}}, + {{{0x0520f1f1, 0x095d60cb, 0x1fdf693b, 0x03693cc8, 0x16f4ad7f, 0x1e8b4667, 0x00675697, 0x06deede1, 0x3bad9d}}, + {{0x1698df4d, 0x10cb8392, 0x0d9c961a, 0x1303449d, 0x00e80499, 0x1d3ecef6, 0x1966f367, 0x1c67c49c, 0x49f99d}}}, /* 5*16^53*G: */ - {{{0x3185ae66, 0x2c7912a2, 0x3a783df0, 0x3b05b6fb, 0x24118ba6, 0x1f7d4f44, 0x0c46d67a, 0x292c6b6c, 0xa6b3}}, - {{0x0bfbf21b, 0x2fad54fe, 0x1b248dd7, 0x2fc2977d, 0x29e8d8bc, 0x06a47365, 0x09623136, 0x3a35d8e2, 0x0cb6}}}, + {{{0x1185ae66, 0x18f22545, 0x09e0f7c2, 0x182db7df, 0x0118ba6e, 0x0fa9e892, 0x11b59e9f, 0x1635b618, 0xa6b3a4}}, + {{0x0bfbf21b, 0x1f5aa9fc, 0x0c92375e, 0x1e14bbeb, 0x1e8d8bcb, 0x148e6cb4, 0x188c4d86, 0x1aec7112, 0xcb6e8}}}, /* 7*16^53*G: */ - {{{0x2c630e3a, 0x25a13393, 0x3f3f1c2a, 0x0418305f, 0x3f10c1f6, 0x1f8e9f61, 0x114a4e22, 0x23d69b24, 0x1f84}}, - {{0x06ca610a, 0x3bb67fda, 0x2359724a, 0x28e49aff, 0x1da4264b, 0x2720f46a, 0x2f963862, 0x154b3341, 0xa028}}}, + {{{0x0c630e3a, 0x0b426727, 0x1cfc70aa, 0x00c182ff, 0x110c1f61, 0x11d3ec3f, 0x1293889f, 0x0b4d9222, 0x1f848f}}, + {{0x06ca610a, 0x176cffb4, 0x0d65c92b, 0x0724d7fc, 0x1a4264ba, 0x041e8d4e, 0x058e18a7, 0x0599a0df, 0xa02855}}}, /* 9*16^53*G: */ - {{{0x041bcd10, 0x37fbcf37, 0x1b44e154, 0x2e555d91, 0x0a2eb211, 0x2899df1b, 0x1c3588b1, 0x3952fa52, 0xcfd1}}, - {{0x2a62e732, 0x30057ae6, 0x0553965a, 0x36645742, 0x052fafac, 0x1d46f56c, 0x158bb9c5, 0x07d7d802, 0xf4e3}}}, + {{{0x041bcd10, 0x0ff79e6e, 0x0d138553, 0x12aaec8b, 0x02eb211b, 0x133be365, 0x0d622c68, 0x097d2938, 0xcfd1e5}}, + {{0x0a62e732, 0x000af5cd, 0x154e596b, 0x1322ba10, 0x12fafacd, 0x08dead82, 0x02ee715d, 0x0bec012b, 0xf4e31f}}}, /* 11*16^53*G: */ - {{{0x228da5fb, 0x3e987648, 0x2870e724, 0x392fd78a, 0x31291b90, 0x1e578f9d, 0x09e5512c, 0x1cc3011b, 0x4b3e}}, - {{0x3c169e48, 0x3fc298e2, 0x023472bb, 0x28e84727, 0x20b48c65, 0x32e81ee3, 0x260e9e80, 0x2593688d, 0x8c40}}}, + {{{0x028da5fb, 0x1d30ec91, 0x01c39c93, 0x097ebc55, 0x1291b90e, 0x0af1f3b8, 0x19544b1e, 0x01808d93, 0x4b3e73}}, + {{0x1c169e48, 0x1f8531c5, 0x08d1caef, 0x07423938, 0x0b48c65a, 0x1d03dc70, 0x03a7a032, 0x09b446cc, 0x8c4096}}}, /* 13*16^53*G: */ - {{{0x1f894780, 0x23a46962, 0x09aec5db, 0x3a7328d6, 0x02d8f737, 0x12e2952d, 0x38fe71d5, 0x0577dd10, 0xafe9}}, - {{0x1511d444, 0x3e5a554f, 0x2c0af452, 0x27a2f9ce, 0x3f2e3690, 0x2d0d08cc, 0x04686a94, 0x30d02348, 0x3cae}}}, + {{{0x1f894780, 0x0748d2c4, 0x06bb176e, 0x139946b1, 0x0d8f737e, 0x1c52a5a1, 0x1f9c7552, 0x1bee8871, 0xafe915}}, + {{0x1511d444, 0x1cb4aa9e, 0x102bd14b, 0x1d17ce75, 0x12e36909, 0x01a1199f, 0x1a1aa52d, 0x0811a408, 0x3caec3}}}, /* 15*16^53*G: */ - {{{0x1182fa6e, 0x168c7f2f, 0x181c8aff, 0x298cb75a, 0x35c9e7c0, 0x1a8e8db4, 0x3ac85586, 0x120a043f, 0x0c05}}, - {{0x261cd145, 0x3af3faad, 0x376d01f6, 0x39991612, 0x1d602bf5, 0x2a2e2519, 0x1f533d1a, 0x34b2b43c, 0x2f9c}}} + {{{0x1182fa6e, 0x0d18fe5e, 0x00722bfd, 0x0c65bad3, 0x1c9e7c0a, 0x11d1b69a, 0x1215619a, 0x05021ff5, 0xc0548}}, + {{0x061cd145, 0x15e7f55b, 0x1db407db, 0x0cc8b096, 0x1602bf5e, 0x05c4a32e, 0x14cf46aa, 0x195a1e3e, 0x2f9cd2}}} }, { /* 1*16^54*G: */ - {{{0x14441fbb, 0x382d756b, 0x1ed115e3, 0x2aa14829, 0x3925559e, 0x183157b6, 0x221d47fb, 0x23138877, 0xb495}}, - {{0x0add7118, 0x31f8f27d, 0x14638414, 0x2e7d84cb, 0x0cb7e12d, 0x0107ef0e, 0x240efe5c, 0x39efe659, 0xfcd6}}}, + {{{0x14441fbb, 0x105aead6, 0x1b44578f, 0x150a414b, 0x125559ea, 0x062af6dc, 0x0751fed8, 0x09c43bc4, 0xb4958c}}, + {{0x0add7118, 0x03f1e4fa, 0x118e1053, 0x13ec265a, 0x0b7e12db, 0x00fde1c6, 0x03bf9701, 0x17f32cc8, 0xfcd6e7}}}, /* 3*16^54*G: */ - {{{0x371f07f1, 0x2bb5a130, 0x0d70c4a5, 0x233b6dcc, 0x06684b87, 0x3a82d918, 0x0444d232, 0x0fd79ec8, 0xb3a4}}, - {{0x201dfda5, 0x0f348bd3, 0x1cb0ecc5, 0x1e1de833, 0x175ee7ec, 0x0c89cda6, 0x3d6b8418, 0x13d6c923, 0x34c6}}}, + {{{0x171f07f1, 0x176b4261, 0x15c31296, 0x19db6e61, 0x0684b878, 0x105b2303, 0x11348cba, 0x0bcf6408, 0xb3a43f}}, + {{0x001dfda5, 0x1e6917a7, 0x12c3b314, 0x10ef419b, 0x15ee7ec7, 0x1139b4cb, 0x1ae1060c, 0x0b6491fa, 0x34c64f}}}, /* 5*16^54*G: */ - {{{0x2b559d49, 0x3df25e91, 0x1dc9b44f, 0x386d1a43, 0x0008b148, 0x18bff613, 0x3e14ac26, 0x261a691a, 0x452e}}, - {{0x1a0d6ba7, 0x11f1811b, 0x31ee4257, 0x20a15b0e, 0x21ee5259, 0x0015ed9d, 0x380d0f5c, 0x22a3c657, 0x8c5e}}}, + {{{0x0b559d49, 0x1be4bd23, 0x1726d13f, 0x0368d21b, 0x008b148e, 0x17fec260, 0x052b0998, 0x0d348d7c, 0x452e98}}, + {{0x1a0d6ba7, 0x03e30236, 0x07b9095d, 0x050ad876, 0x1ee52598, 0x02bdb3b0, 0x0343d700, 0x11e32bf0, 0x8c5e8a}}}, /* 7*16^54*G: */ - {{{0x13ce94da, 0x0de99fad, 0x2829e605, 0x2c93d095, 0x0474ee8b, 0x378370eb, 0x162bb51c, 0x3d75231b, 0x19a7}}, - {{0x3025e7bb, 0x0c111c58, 0x225eb037, 0x1894c1ab, 0x00a2e8fb, 0x29475108, 0x075c32f6, 0x12e9ea4c, 0xa250}}}, + {{{0x13ce94da, 0x1bd33f5a, 0x00a79814, 0x049e84ad, 0x074ee8bb, 0x106e1d62, 0x0aed4737, 0x1a918dac, 0x19a7f5}}, + {{0x1025e7bb, 0x182238b1, 0x097ac0dc, 0x04a60d5c, 0x0a2e8fb6, 0x08ea2100, 0x170cbda9, 0x14f5260e, 0xa2504b}}}, /* 9*16^54*G: */ - {{{0x147dc697, 0x25a5b31b, 0x1e15b9bb, 0x3b862bed, 0x3c6fa417, 0x3ac2cad7, 0x334dc011, 0x16c08293, 0xbdaf}}, - {{0x06a479e2, 0x24472f9e, 0x1b7a477b, 0x048b9e21, 0x17aa0855, 0x15d791ed, 0x2836c8cf, 0x031b2f7e, 0x3cec}}}, + {{{0x147dc697, 0x0b4b6636, 0x1856e6ee, 0x1c315f6b, 0x06fa417e, 0x18595afe, 0x1370047a, 0x004149e6, 0xbdaf5b}}, + {{0x06a479e2, 0x088e5f3c, 0x0de91dee, 0x045cf10b, 0x1aa08551, 0x1af23dab, 0x0db233d5, 0x0d97bf50, 0x3cec0c}}}, /* 11*16^54*G: */ - {{{0x2ce05e10, 0x2802e46d, 0x3e106202, 0x3bdf27d0, 0x0e70db8a, 0x12dffa13, 0x1d15dab8, 0x2eba57ce, 0x265d}}, - {{0x171324f4, 0x3dfc062c, 0x164c67ff, 0x18fce4cf, 0x0b5dcb06, 0x0f3a2d5b, 0x037adf3b, 0x18f4268c, 0x58df}}}, + {{{0x0ce05e10, 0x1005c8db, 0x1841880a, 0x1ef93e87, 0x070db8ae, 0x1bff4267, 0x0576ae12, 0x1d2be73a, 0x265dba}}, + {{0x171324f4, 0x1bf80c58, 0x19319fff, 0x07e7267a, 0x15dcb066, 0x0745ab65, 0x1eb7cecf, 0x1a134606, 0x58df63}}}, /* 13*16^54*G: */ - {{{0x33fe5938, 0x3456f156, 0x236d7cde, 0x320c0f6d, 0x1668669e, 0x1d2754e9, 0x2639689f, 0x020fc5f9, 0xc43e}}, - {{0x183732f3, 0x19e5d5bb, 0x24407477, 0x188c1c58, 0x04402eab, 0x240c0eaf, 0x3cc58350, 0x00a48e7e, 0x54c6}}}, + {{{0x13fe5938, 0x08ade2ad, 0x0db5f37b, 0x10607b6c, 0x068669ec, 0x04ea9d2b, 0x0e5a27dd, 0x07e2fccc, 0xc43e08}}, + {{0x183732f3, 0x13cbab76, 0x1101d1dd, 0x0460e2c4, 0x0402eab6, 0x0181d5e2, 0x1160d424, 0x12473f79, 0x54c602}}}, /* 15*16^54*G: */ - {{{0x1dd52975, 0x0c71c3de, 0x2b44180c, 0x33c3f4c1, 0x3266ba2b, 0x314369de, 0x3848665a, 0x3c5c028f, 0x7868}}, - {{0x3c626fac, 0x005bb540, 0x29690443, 0x3dbe7b29, 0x11276c68, 0x3e871b6c, 0x17ee1113, 0x25f3cc48, 0xe890}}} + {{{0x1dd52975, 0x18e387bc, 0x0d106030, 0x1e1fa60d, 0x066ba2bc, 0x086d3bd9, 0x121996b1, 0x0e0147f0, 0x7868f1}}, + {{0x1c626fac, 0x00b76a81, 0x05a4110c, 0x0df3d94d, 0x1276c68f, 0x10e36d88, 0x1b8444fe, 0x19e6242f, 0xe89097}}} }, { /* 1*16^55*G: */ - {{{0x2e12e1df, 0x3093990d, 0x1761d04a, 0x29ff42df, 0x06027cd8, 0x12fc4ecd, 0x132b6413, 0x2465a23a, 0xd0e0}}, - {{0x1fd28fbe, 0x2995136e, 0x046b8df6, 0x13312f66, 0x1bf86754, 0x2d82da47, 0x11452b4e, 0x26967f9f, 0x069c}}}, + {{{0x0e12e1df, 0x0127321b, 0x1d87412b, 0x0ffa16fa, 0x0027cd8a, 0x1f89d9a3, 0x0ad904d2, 0x12d11d26, 0xd0e091}}, + {{0x1fd28fbe, 0x132a26dc, 0x11ae37da, 0x19897b30, 0x1f867544, 0x105b48ed, 0x114ad3ad, 0x0b3fcfa2, 0x69c9a}}}, /* 3*16^55*G: */ - {{{0x084aa098, 0x2c361440, 0x16e3e02b, 0x3040502a, 0x01fa8509, 0x29f6b2ff, 0x308eb398, 0x2915284c, 0xb517}}, - {{0x0540efbf, 0x0012d67d, 0x12447fd6, 0x3522d51a, 0x326fa3a4, 0x28f8bec3, 0x3879a60e, 0x21df4307, 0x0a3d}}}, + {{{0x084aa098, 0x186c2880, 0x1b8f80ae, 0x02028152, 0x1fa8509c, 0x1ed65fe0, 0x03ace629, 0x0a942661, 0xb517a4}}, + {{0x0540efbf, 0x0025acfa, 0x0911ff58, 0x0916a8d2, 0x06fa3a4d, 0x1f17d879, 0x1e6983a8, 0x0fa183f0, 0xa3d87}}}, /* 5*16^55*G: */ - {{{0x0744bfa1, 0x3656b2a9, 0x093643d6, 0x09b49f38, 0x33e387cc, 0x089c4b63, 0x166f67bc, 0x050e12d4, 0xf8ec}}, - {{0x32b65f6d, 0x1a49398c, 0x3900060c, 0x18deb170, 0x160f610a, 0x1a3ec9a7, 0x3b9a6323, 0x0d2c844f, 0x7611}}}, + {{{0x0744bfa1, 0x0cad6552, 0x04d90f5b, 0x0da4f9c1, 0x1e387cc2, 0x13896c79, 0x1bd9ef08, 0x07096a2c, 0xf8ec14}}, + {{0x12b65f6d, 0x14927319, 0x04001831, 0x06f58b87, 0x00f610a6, 0x07d934eb, 0x0698c8da, 0x164227f7, 0x761134}}}, /* 7*16^55*G: */ - {{{0x3227a4bb, 0x18b0efa4, 0x38d99f2f, 0x39ac7c03, 0x14f2e64b, 0x1d3ab487, 0x3fae794e, 0x3fde36de, 0x320c}}, - {{0x30f3d2d4, 0x2073241a, 0x1e2f9705, 0x11c8dd02, 0x3f629960, 0x1e5a8953, 0x28692ab7, 0x3a3501ca, 0xaf9f}}}, + {{{0x1227a4bb, 0x1161df49, 0x03667cbd, 0x0d63e01f, 0x0f2e64be, 0x075690ea, 0x0b9e539d, 0x0f1b6f7f, 0x320cff}}, + {{0x10f3d2d4, 0x00e64835, 0x18be5c16, 0x0e46e813, 0x16299604, 0x0b512a7f, 0x1a4aadde, 0x1a80e550, 0xaf9fe8}}}, /* 9*16^55*G: */ - {{{0x1c2ca683, 0x2d6d6979, 0x295a7373, 0x1b3cd782, 0x03426a20, 0x377732d5, 0x2ed8517e, 0x379f1a9e, 0x0c08}}, - {{0x3db5f259, 0x0901b6d5, 0x0ea68c69, 0x3235edf8, 0x0e0e79c3, 0x20a6737f, 0x16e19b7c, 0x1b6157a8, 0xddb7}}}, + {{{0x1c2ca683, 0x1adad2f2, 0x0569cdce, 0x19e6bc15, 0x1426a206, 0x0ee65aa1, 0x16145fb7, 0x0f8d4f5d, 0xc08de}}, + {{0x1db5f259, 0x12036dab, 0x1a9a31a4, 0x11af6fc1, 0x00e79c3c, 0x14ce6fe7, 0x1866df20, 0x10abd42d, 0xddb76d}}}, /* 11*16^55*G: */ - {{{0x252ae5cd, 0x319eb3e0, 0x0fdd7861, 0x2d94bebd, 0x24390995, 0x1bde9133, 0x07c3d18e, 0x31dab431, 0xd1f8}}, - {{0x3e6d2dda, 0x3ae5ef0f, 0x189f4fc7, 0x2eba055a, 0x21203239, 0x265ec07d, 0x0e802ac7, 0x17719848, 0x74d4}}}, + {{{0x052ae5cd, 0x033d67c1, 0x1f75e187, 0x0ca5f5e9, 0x0390995b, 0x1bd22672, 0x10f4639b, 0x0d5a188f, 0xd1f8c7}}, + {{0x1e6d2dda, 0x15cbde1f, 0x027d3f1f, 0x15d02ad3, 0x1203239b, 0x0bd80fb0, 0x000ab1e6, 0x18cc241d, 0x74d45d}}}, /* 13*16^55*G: */ - {{{0x2bdc603f, 0x1e4019aa, 0x3dffe5ab, 0x1b597359, 0x3620d8c9, 0x0cfb1899, 0x090c093e, 0x20da4fce, 0xa6cb}}, - {{0x096befcc, 0x2b380f83, 0x0661735c, 0x07b05a93, 0x110b72fb, 0x366f6931, 0x3cafc8f2, 0x3239187c, 0xd823}}}, + {{{0x0bdc603f, 0x1c803355, 0x17ff96ad, 0x1acb9acf, 0x020d8c96, 0x1f63133b, 0x03024f8c, 0x0d27e712, 0xa6cb83}}, + {{0x096befcc, 0x16701f06, 0x1985cd72, 0x1d82d498, 0x10b72fb1, 0x0ded2628, 0x0bf23cb6, 0x1c8c3e79, 0xd823c8}}}, /* 15*16^55*G: */ - {{{0x22c374b0, 0x278e984b, 0x170db4a2, 0x16cd662d, 0x024ef0bf, 0x3b25c549, 0x0332136b, 0x27247a9b, 0x8a6c}}, - {{0x378c08bd, 0x2fdf3e36, 0x00f4d583, 0x054d3d0d, 0x0132a046, 0x1e217724, 0x1ffaf79a, 0x1fd3d973, 0xe4bc}}} + {{{0x02c374b0, 0x0f1d3097, 0x1c36d28a, 0x166b316a, 0x04ef0bf5, 0x04b8a921, 0x0c84dafb, 0x123d4d86, 0x8a6c9c}}, + {{0x178c08bd, 0x1fbe7c6d, 0x03d3560e, 0x0a69e868, 0x132a0461, 0x042ee480, 0x1ebde69e, 0x09ecb9bf, 0xe4bc7f}}} }, { /* 1*16^56*G: */ - {{{0x2895df07, 0x29c0fc43, 0x1876bd86, 0x1d7cfe80, 0x208ffefd, 0x2c1b9c33, 0x3dfeeeb5, 0x2e1509e0, 0x68f6}}, - {{0x38712655, 0x031dbe29, 0x310bf7f9, 0x14a4f4bc, 0x245028cf, 0x201137f6, 0x00ce6fbc, 0x3faea4b9, 0xcbe1}}}, + {{{0x0895df07, 0x1381f887, 0x01daf61a, 0x0be7f403, 0x08ffefd7, 0x03738670, 0x1fbbad6c, 0x0a84f07b, 0x68f6b8}}, + {{0x18712655, 0x063b7c53, 0x042fdfe4, 0x0527a5e6, 0x05028cf5, 0x0226fed2, 0x139bef20, 0x17525c81, 0xcbe1fe}}}, /* 3*16^56*G: */ - {{{0x3aa89692, 0x1063e88c, 0x14c2308e, 0x0ec235be, 0x18a77671, 0x1b990490, 0x28f4de99, 0x329c6059, 0x3bdf}}, - {{0x1a510308, 0x0f6f6d0c, 0x1e2ef139, 0x370318d1, 0x1a5333c7, 0x098546bb, 0x167b8494, 0x07da1594, 0x0a72}}}, + {{{0x1aa89692, 0x00c7d119, 0x1308c239, 0x1611adf2, 0x0a776713, 0x1320920c, 0x1d37a65b, 0x0e302cd1, 0x3bdfca}}, + {{0x1a510308, 0x1ededa18, 0x18bbc4e4, 0x1818c68b, 0x05333c7d, 0x10a8d76d, 0x1ee12509, 0x0d0aca2c, 0xa721f}}}, /* 5*16^56*G: */ - {{{0x037ea1d7, 0x1e6c8d0b, 0x09aae4d0, 0x0e4d963e, 0x0d9e4fb2, 0x0a154946, 0x21056353, 0x2b256dd4, 0xaca8}}, - {{0x1ba973a2, 0x37bec412, 0x13935e9d, 0x3b6ff710, 0x072189e1, 0x01312e4a, 0x1cc20943, 0x3159f75d, 0x7f12}}}, + {{{0x037ea1d7, 0x1cd91a16, 0x06ab9341, 0x126cb1f1, 0x19e4fb23, 0x02a928c6, 0x0158d4ca, 0x12b6ea42, 0xaca8ac}}, + {{0x1ba973a2, 0x0f7d8824, 0x0e4d7a77, 0x1b7fb882, 0x12189e1e, 0x0625c943, 0x108250c1, 0x0cfbaeb9, 0x7f12c5}}}, /* 7*16^56*G: */ - {{{0x13245b7f, 0x36c9e073, 0x0597fbf5, 0x1f59a5a4, 0x185311a3, 0x3086be63, 0x27c0e206, 0x11c136d9, 0xfa90}}, - {{0x0ddf6bef, 0x3e0cf7c5, 0x24f1d47e, 0x27bb3498, 0x31c189cb, 0x3e8fb503, 0x036a42d6, 0x230d9d2a, 0x1a1c}}}, + {{{0x13245b7f, 0x0d93c0e6, 0x165fefd7, 0x1acd2d20, 0x05311a37, 0x10d7cc6c, 0x103881b0, 0x009b6ccf, 0xfa9047}}, + {{0x0ddf6bef, 0x1c19ef8a, 0x13c751fb, 0x1dd9a4c4, 0x1c189cb9, 0x11f6a078, 0x1a90b5be, 0x06ce9506, 0x1a1c8c}}}, /* 9*16^56*G: */ - {{{0x37f0953a, 0x187de3f5, 0x315439ab, 0x124520ff, 0x3a92a818, 0x0ae3874b, 0x17d8cd67, 0x06aae47d, 0x1d43}}, - {{0x1d68f260, 0x1f1675da, 0x0707e7c1, 0x238a6a42, 0x15fae0f4, 0x0c320f38, 0x1121ebc5, 0x19f0efc6, 0x08d6}}}, + {{{0x17f0953a, 0x10fbc7eb, 0x0550e6ad, 0x122907fe, 0x092a8184, 0x1c70e97d, 0x163359ca, 0x15723eaf, 0x1d431a}}, + {{0x1d68f260, 0x1e2cebb4, 0x1c1f9f05, 0x1c535210, 0x1fae0f48, 0x0641e70a, 0x087af14c, 0x1877e322, 0x8d667}}}, /* 11*16^56*G: */ - {{{0x25227c70, 0x28c45c4d, 0x3a3ea705, 0x0afaaccc, 0x31c60ff3, 0x12cd6cb8, 0x21137dda, 0x3a83568f, 0x6dee}}, - {{0x0369b9b7, 0x35b68e04, 0x29083dba, 0x1ebb0795, 0x2acc8428, 0x132ebfbd, 0x03e40001, 0x0fc3f1d1, 0xcbb9}}}, + {{{0x05227c70, 0x1188b89b, 0x08fa9c16, 0x17d56667, 0x1c60ff32, 0x19ad9718, 0x04df7692, 0x01ab47c2, 0x6deeea}}, + {{0x0369b9b7, 0x0b6d1c08, 0x0420f6eb, 0x15d83cad, 0x0cc84287, 0x05d7f7b5, 0x19000053, 0x01f8e887, 0xcbb93f}}}, /* 13*16^56*G: */ - {{{0x0421b54d, 0x2d7f57a2, 0x1564a4ff, 0x26cae0e9, 0x3a9dca57, 0x3274aec7, 0x178d8d4a, 0x170418d5, 0x2813}}, - {{0x0ee5d868, 0x3733c26e, 0x1e310d8a, 0x01253324, 0x3f8c15ef, 0x2a75d041, 0x1be1506f, 0x12af8e14, 0x9ed8}}}, + {{{0x0421b54d, 0x1afeaf44, 0x159293fe, 0x1657074a, 0x09dca579, 0x0e95d8fd, 0x036352b2, 0x020c6aaf, 0x28135c}}, + {{0x0ee5d868, 0x0e6784dc, 0x18c4362b, 0x09299923, 0x18c15ef0, 0x0eba083f, 0x18541bea, 0x17c70a37, 0x9ed84a}}}, /* 15*16^56*G: */ - {{{0x28e4ac10, 0x05f95647, 0x0e24a9a9, 0x25aa04ab, 0x3fb56879, 0x0f316827, 0x1077bd6c, 0x015d882c, 0x339a}}, - {{0x0d1312a0, 0x1db6a191, 0x01cc66ef, 0x0e79e23d, 0x0f553e50, 0x1537de2b, 0x2947f438, 0x17efb75a, 0xca98}}} + {{{0x08e4ac10, 0x0bf2ac8f, 0x1892a6a4, 0x0d502559, 0x1b568799, 0x062d04ff, 0x1def5b0f, 0x0ec41620, 0x339a05}}, + {{0x0d1312a0, 0x1b6d4322, 0x07319bbd, 0x13cf11e8, 0x1553e503, 0x06fbc567, 0x11fd0e15, 0x17dbad52, 0xca985f}}} }, { /* 1*16^57*G: */ - {{{0x27ea1f34, 0x0d36ac5d, 0x0739e0dd, 0x1af4d501, 0x3353d664, 0x10745e4e, 0x34b66c3b, 0x18288f51, 0x7f94}}, - {{0x0d9063ec, 0x22fb0b2b, 0x0e34ffc5, 0x3fe05449, 0x076661c6, 0x07cafe3c, 0x0618769f, 0x059de3ec, 0xd0d5}}}, + {{{0x07ea1f34, 0x1a6d58bb, 0x1ce78374, 0x17a6a808, 0x153d6646, 0x0e8bc9d9, 0x0d9b0ed0, 0x1447a8e9, 0x7f9460}}, + {{0x0d9063ec, 0x05f61656, 0x18d3ff16, 0x1f02a249, 0x16661c6f, 0x195fc783, 0x061da7c7, 0x0ef1f60c, 0xd0d516}}}, /* 3*16^57*G: */ - {{{0x3dfc0a9d, 0x316dd326, 0x0f77aa0d, 0x1108d6c5, 0x20a2a2de, 0x038d91ab, 0x29e022a6, 0x39fe130c, 0xdb43}}, - {{0x1e9ad713, 0x02c424ea, 0x2d2f054f, 0x0e411cd5, 0x2f9fa488, 0x15b20533, 0x2b591b8a, 0x2368af8d, 0xb016}}}, + {{{0x1dfc0a9d, 0x02dba64d, 0x1ddea837, 0x0846b629, 0x0a2a2de4, 0x11b23570, 0x1808a983, 0x1f098653, 0xdb43e7}}, + {{0x1e9ad713, 0x058849d4, 0x14bc153c, 0x1208e6ad, 0x19fa4883, 0x1640a677, 0x1646e295, 0x1457c6d6, 0xb0168d}}}, /* 5*16^57*G: */ - {{{0x0283808d, 0x02f2c5dd, 0x1643a893, 0x23c1f38d, 0x3a78980f, 0x057a4487, 0x121aeb85, 0x0c207b83, 0xe9af}}, - {{0x39b39d33, 0x19b0be38, 0x1136d199, 0x1ae49445, 0x2f497197, 0x3c99543f, 0x3126085a, 0x32122711, 0xa976}}}, + {{{0x0283808d, 0x05e58bba, 0x190ea24c, 0x1e0f9c6a, 0x078980f8, 0x0f4890fd, 0x06bae145, 0x103dc1a4, 0xe9af30}}, + {{0x19b39d33, 0x13617c71, 0x04db4665, 0x1724a22a, 0x14971976, 0x132a87f7, 0x098216bc, 0x091388e2, 0xa976c8}}}, /* 7*16^57*G: */ - {{{0x2d8426df, 0x1a4bd0b2, 0x26f8a0a2, 0x104e5693, 0x3883590f, 0x2b24e0ef, 0x06980703, 0x0cd8cb20, 0x6eb7}}, - {{0x200b4267, 0x3fdd67b8, 0x3fe1b833, 0x14ba5f20, 0x008e8d92, 0x392cb3b3, 0x07a9a030, 0x1bb045cc, 0x96c5}}}, + {{{0x0d8426df, 0x1497a165, 0x1be28289, 0x0272b49c, 0x083590f4, 0x049c1dfc, 0x0601c0eb, 0x0c65900d, 0x6eb733}}, + {{0x000b4267, 0x1fbacf71, 0x1f86e0cf, 0x05d2f907, 0x08e8d925, 0x05967660, 0x0a680c39, 0x1822e60f, 0x96c56e}}}, /* 9*16^57*G: */ - {{{0x1a16453d, 0x1f45b5f0, 0x21033dbf, 0x1fa1ef9d, 0x34d0e68b, 0x106e47e2, 0x15f45e17, 0x275781e7, 0xd397}}, - {{0x27b6d737, 0x0f2ee0c5, 0x26961a4f, 0x377d98a2, 0x32456917, 0x02495d4d, 0x1adb9a4d, 0x24cd75e6, 0xc55f}}}, + {{{0x1a16453d, 0x1e8b6be0, 0x040cf6fd, 0x1d0f7cec, 0x0d0e68b7, 0x0dc8fc5a, 0x1d1785d0, 0x0bc0f3ab, 0xd3979d}}, + {{0x07b6d737, 0x1e5dc18b, 0x1a58693c, 0x1becc514, 0x0456917d, 0x092ba9b9, 0x16e69342, 0x06baf335, 0xc55f93}}}, /* 11*16^57*G: */ - {{{0x2d326504, 0x3a866697, 0x3b5202cc, 0x16a6d189, 0x2efc12f6, 0x20ee2306, 0x0c2342c3, 0x24a7396e, 0x54c3}}, - {{0x3ec9e107, 0x2fc047e9, 0x08a67268, 0x294f6798, 0x14ab4447, 0x26a8a124, 0x216d0c48, 0x0c09583a, 0x4696}}}, + {{{0x0d326504, 0x150ccd2f, 0x0d480b33, 0x15368c4f, 0x0fc12f65, 0x1dc460d7, 0x08d0b0e0, 0x139cb718, 0x54c392}}, + {{0x1ec9e107, 0x1f808fd3, 0x0299c9a2, 0x0a7b3cc1, 0x0ab4447a, 0x1514248a, 0x1b431226, 0x04ac1d42, 0x469630}}}, /* 13*16^57*G: */ - {{{0x3b5ecce7, 0x0113d5da, 0x00d21353, 0x0a0562c3, 0x1659c873, 0x3a3a0f06, 0x2d6c5b84, 0x3a6ca199, 0x3744}}, - {{0x2a247721, 0x004c8505, 0x2a6f8392, 0x3a2d7c14, 0x29ec3c28, 0x39a55bac, 0x047aa0e0, 0x383e3664, 0x9546}}}, + {{{0x1b5ecce7, 0x0227abb5, 0x03484d4c, 0x102b1618, 0x059c8732, 0x0741e0cb, 0x1b16e13a, 0x1650ccda, 0x3744e9}}, + {{0x0a247721, 0x00990a0b, 0x09be0e48, 0x116be0a5, 0x1ec3c28e, 0x14ab7594, 0x1ea83839, 0x1f1b3208, 0x9546e0}}}, /* 15*16^57*G: */ - {{{0x05fef996, 0x0324a379, 0x04253515, 0x01a3d8e5, 0x33f2de14, 0x3342907b, 0x16d53324, 0x0f85f8d9, 0x1134}}, - {{0x1792aded, 0x00542b9d, 0x086f18e4, 0x33935968, 0x273765d0, 0x377e4c18, 0x28eeeb04, 0x212037ae, 0x4a9e}}} + {{{0x05fef996, 0x064946f2, 0x1094d454, 0x0d1ec728, 0x1f2de140, 0x08520f79, 0x154cc933, 0x02fc6cad, 0x11343e}}, + {{0x1792aded, 0x00a8573a, 0x01bc6390, 0x1c9acb41, 0x13765d0c, 0x0fc98313, 0x1bbac137, 0x101bd751, 0x4a9e84}}} }, { /* 1*16^58*G: */ - {{{0x0e6d8483, 0x3b26d35e, 0x2967f0dc, 0x3cb5ea11, 0x2ee94582, 0x23d27c6d, 0x1563d295, 0x32d828cf, 0x9c39}}, - {{0x2b2c50fb, 0x12ccd5bd, 0x1be43689, 0x2b794bcf, 0x216546bb, 0x065adef2, 0x3e51003d, 0x2fc7b924, 0xf097}}}, + {{{0x0e6d8483, 0x164da6bc, 0x059fc373, 0x05af508d, 0x0e94582f, 0x1a4f8db7, 0x18f4a563, 0x0c1467aa, 0x9c39cb}}, + {{0x0b2c50fb, 0x0599ab7b, 0x0f90da25, 0x1bca5e7b, 0x16546bba, 0x0b5bde50, 0x14400f46, 0x03dc927c, 0xf097bf}}}, /* 3*16^58*G: */ - {{{0x07a14dda, 0x1570c7e1, 0x34b4df3f, 0x1b410a59, 0x01308360, 0x1da3dc90, 0x2dad7443, 0x1eb3243a, 0x18f3}}, - {{0x25ac8364, 0x08bf370c, 0x28536cbe, 0x363df1e2, 0x1bcd0b77, 0x2fffb3b8, 0x12c26d7b, 0x12eeaa82, 0x2f94}}}, + {{{0x07a14dda, 0x0ae18fc2, 0x12d37cfd, 0x1a0852ce, 0x13083606, 0x147b9200, 0x0b5d10dd, 0x19921d5b, 0x18f37a}}, + {{0x05ac8364, 0x117e6e19, 0x014db2f8, 0x11ef8f15, 0x1cd0b77d, 0x1ff6770d, 0x109b5eef, 0x17554125, 0x2f944b}}}, /* 5*16^58*G: */ - {{{0x0c7d59be, 0x19d3a3a3, 0x20932fb5, 0x3a861623, 0x32736b98, 0x17ffb91d, 0x279da4ec, 0x0d630a07, 0x5413}}, - {{0x24f80590, 0x35fa87db, 0x100b3672, 0x3896c572, 0x24515a53, 0x123f4805, 0x0b024e7c, 0x3537a5a7, 0x680f}}}, + {{{0x0c7d59be, 0x13a74746, 0x024cbed5, 0x1430b11c, 0x0736b98e, 0x1ff723b9, 0x07693b17, 0x118503cf, 0x541335}}, + {{0x04f80590, 0x0bf50fb7, 0x002cd9cb, 0x04b62b92, 0x0515a53e, 0x07e900b2, 0x00939f12, 0x1bd2d396, 0x680fd4}}}, /* 7*16^58*G: */ - {{{0x076051a8, 0x3ae0327e, 0x2457ea58, 0x35dce58e, 0x385280be, 0x3f068f06, 0x194f05dc, 0x3449a46c, 0x4e2f}}, - {{0x29cc9005, 0x2bfb1d3f, 0x2c4fe2e6, 0x2e2ea964, 0x0a31bceb, 0x2cd68542, 0x0fbb2371, 0x2ef6fd7d, 0x122a}}}, + {{{0x076051a8, 0x15c064fc, 0x115fa963, 0x0ee72c74, 0x05280bed, 0x00d1e0dc, 0x13c1773f, 0x04d23632, 0x4e2fd1}}, + {{0x09cc9005, 0x17f63a7f, 0x113f8b9a, 0x11754b25, 0x031bcebb, 0x1ad0a845, 0x0ec8dc6c, 0x1b7ebe9f, 0x122abb}}}, /* 9*16^58*G: */ - {{{0x16a80e09, 0x19f2a3e9, 0x225f5fe3, 0x1d7c3dd9, 0x008fa0a2, 0x13d5a04f, 0x31b59200, 0x16352fbf, 0x2de7}}, - {{0x036a1cd3, 0x358bb7d5, 0x1dad6c99, 0x06b719a5, 0x1e64a07a, 0x00cac099, 0x0ee67d7c, 0x33cc5df6, 0xdd9a}}}, + {{{0x16a80e09, 0x13e547d2, 0x097d7f8d, 0x0be1eecc, 0x08fa0a27, 0x1ab409e0, 0x0d648013, 0x1a97dfe3, 0x2de758}}, + {{0x036a1cd3, 0x0b176faa, 0x16b5b267, 0x15b8cd2b, 0x064a07a1, 0x1958132f, 0x199f5f00, 0x062efb1d, 0xdd9acf}}}, /* 11*16^58*G: */ - {{{0x3a3628ac, 0x0940d6cb, 0x35b564ec, 0x22ee8b37, 0x2e12a456, 0x1685cf1b, 0x14a5728c, 0x282b3707, 0xf597}}, - {{0x2cd3550f, 0x3a80c435, 0x012106e7, 0x0bb3e475, 0x222cc077, 0x06edca25, 0x3d4557bb, 0x05a38cca, 0x0db9}}}, + {{{0x1a3628ac, 0x1281ad97, 0x16d593b0, 0x177459be, 0x012a4568, 0x10b9e377, 0x095ca316, 0x159b83a9, 0xf597a0}}, + {{0x0cd3550f, 0x1501886b, 0x04841b9f, 0x1d9f23a8, 0x02cc0772, 0x1db944b1, 0x1155eec6, 0x11c6657a, 0xdb916}}}, /* 13*16^58*G: */ - {{{0x2b75d6c3, 0x235a0f52, 0x13a28567, 0x0a9515f5, 0x3e40f3c4, 0x041c6086, 0x04fb908a, 0x0aa1b5bd, 0xaa22}}, - {{0x244cb028, 0x0c996939, 0x1a8c8f61, 0x1c7f252d, 0x22df4260, 0x122896bb, 0x28e76ce4, 0x21e4c006, 0x5637}}}, + {{{0x0b75d6c3, 0x06b41ea5, 0x0e8a159e, 0x14a8afaa, 0x040f3c42, 0x038c10df, 0x1ee42284, 0x10dade89, 0xaa222a}}, + {{0x044cb028, 0x1932d273, 0x0a323d84, 0x03f9296b, 0x0df42607, 0x0512d771, 0x19db3912, 0x12600351, 0x563787}}}, /* 15*16^58*G: */ - {{{0x235790c9, 0x3ea15ce4, 0x3f3c5037, 0x006e45dc, 0x335e2e9e, 0x03190e4b, 0x315b756f, 0x2c9af365, 0x8568}}, - {{0x26b1f5ac, 0x34fd54e0, 0x385479fd, 0x11797e3e, 0x363ce801, 0x1e382b90, 0x1d2ade90, 0x09869613, 0xd3f2}}} + {{{0x035790c9, 0x1d42b9c9, 0x1cf140df, 0x03722ee7, 0x15e2e9e0, 0x0321c979, 0x16dd5bc3, 0x0d79b2e2, 0x8568b2}}, + {{0x06b1f5ac, 0x09faa9c1, 0x0151e7f7, 0x0bcbf1f7, 0x03ce8014, 0x0705721b, 0x0ab7a41e, 0x034b09ba, 0xd3f226}}} }, { /* 1*16^59*G: */ - {{{0x1c38d4e4, 0x376a5f15, 0x1b173747, 0x3f597c6c, 0x181e25e2, 0x19b9d0c0, 0x29938975, 0x21498448, 0x3d92}}, - {{0x00ccf0d3, 0x3eabbc03, 0x17abc7f6, 0x02ac4e06, 0x2869eacc, 0x015c0d70, 0x0eab53ff, 0x2829751a, 0xd32c}}}, + {{{0x1c38d4e4, 0x0ed4be2a, 0x0c5cdd1f, 0x1acbe363, 0x01e25e2f, 0x173a180c, 0x04e25d59, 0x04c22453, 0x3d9285}}, + {{0x00ccf0d3, 0x1d577806, 0x1eaf1fdb, 0x15627032, 0x069eacc0, 0x0b81ae14, 0x0ad4ffc1, 0x14ba8d1d, 0xd32ca0}}}, /* 3*16^59*G: */ - {{{0x0dd7718a, 0x01c8c960, 0x1be4e4ed, 0x3206d946, 0x36dff891, 0x05668979, 0x02fc3f7c, 0x038dcae4, 0x3b18}}, - {{0x1afd82db, 0x099898a6, 0x02d14d07, 0x1244559c, 0x05211e58, 0x12f274a4, 0x358aafaa, 0x2c45fcda, 0xf2b6}}}, + {{{0x0dd7718a, 0x039192c0, 0x0f9393b4, 0x1036ca33, 0x0dff891c, 0x0cd12f3b, 0x1f0fdf05, 0x06e57205, 0x3b180e}}, + {{0x1afd82db, 0x1331314c, 0x0b45341c, 0x1222ace0, 0x1211e584, 0x1e4e9482, 0x02abea92, 0x02fe6d6b, 0xf2b6b1}}}, /* 5*16^59*G: */ - {{{0x13d3653d, 0x2a069446, 0x0e467d5f, 0x13b12c9d, 0x283eb213, 0x3d3d0262, 0x29c9f45e, 0x3fc0e475, 0xf352}}, - {{0x0a44f28e, 0x27999e32, 0x2c582d07, 0x06657e5c, 0x26d5055c, 0x2f5cf7f6, 0x05ebd020, 0x189b32db, 0x4472}}}, + {{{0x13d3653d, 0x140d288c, 0x1919f57e, 0x1d8964e9, 0x03eb2134, 0x07a04c54, 0x127d17bd, 0x00723ad3, 0xf352ff}}, + {{0x0a44f28e, 0x0f333c64, 0x1160b41e, 0x132bf2e5, 0x0d5055c1, 0x0b9efed3, 0x1af4082f, 0x0d996d8b, 0x447262}}}, /* 7*16^59*G: */ - {{{0x2d4478da, 0x19877c6b, 0x00e0154d, 0x173db089, 0x393ca1f1, 0x2d1736fd, 0x18c230af, 0x391c40d3, 0x670e}}, - {{0x34f563f0, 0x0a3ff93f, 0x3f247706, 0x30ee0583, 0x0750e81c, 0x19816c4e, 0x022ca254, 0x31d096e8, 0x5ca0}}}, + {{{0x0d4478da, 0x130ef8d7, 0x03805535, 0x19ed8448, 0x13ca1f15, 0x02e6dfbc, 0x108c2bed, 0x0e2069b1, 0x670ee4}}, + {{0x14f563f0, 0x147ff27f, 0x1c91dc18, 0x07702c1f, 0x150e81cc, 0x102d89c3, 0x0b289519, 0x084b7404, 0x5ca0c7}}}, /* 9*16^59*G: */ - {{{0x03dbd581, 0x3138a411, 0x0d6b35ba, 0x3face20a, 0x2c6fa93c, 0x2fe8c2b3, 0x19bdbefb, 0x38d50d27, 0x96f2}}, - {{0x28f59952, 0x36693ffb, 0x04f5d454, 0x2863c754, 0x0dbaf435, 0x17638e58, 0x126cf4fe, 0x36022175, 0x09fc}}}, + {{{0x03dbd581, 0x02714822, 0x15acd6eb, 0x1d671051, 0x06fa93cf, 0x1d185676, 0x0f6fbeef, 0x0a8693b3, 0x96f2e3}}, + {{0x08f59952, 0x0cd27ff7, 0x13d75153, 0x031e3aa0, 0x1baf435a, 0x0c71cb06, 0x1b3d3f97, 0x0110baa4, 0x9fcd8}}}, /* 11*16^59*G: */ - {{{0x24e9c2fc, 0x3acd0c92, 0x3bd706a1, 0x0b3c33cb, 0x209a35e7, 0x06082c51, 0x399ac804, 0x1b945fa0, 0xc494}}, - {{0x26398ce8, 0x10d1d8dd, 0x14623123, 0x22fce3b4, 0x3b8237e4, 0x283da3d1, 0x18a4ce99, 0x00482c61, 0x7489}}}, + {{{0x04e9c2fc, 0x159a1925, 0x0f5c1a87, 0x19e19e5f, 0x09a35e72, 0x01058a30, 0x06b20106, 0x0a2fd073, 0xc4946e}}, + {{0x06398ce8, 0x01a3b1bb, 0x1188c48d, 0x17e71da2, 0x18237e48, 0x07b47a3d, 0x0933a668, 0x041630b1, 0x748901}}}, /* 13*16^59*G: */ - {{{0x04960b03, 0x32e45cfa, 0x0808e8f5, 0x2b0eac32, 0x094d8fb6, 0x232315e0, 0x233dbfa4, 0x2d936a6f, 0x1653}}, - {{0x30f73c69, 0x201a953a, 0x1b564e7f, 0x0e383928, 0x15a8948b, 0x2caf60fa, 0x1d5609f4, 0x1c205a79, 0xa583}}}, + {{{0x04960b03, 0x05c8b9f4, 0x0023a3d7, 0x18756191, 0x14d8fb6a, 0x0462bc04, 0x0f6fe923, 0x09b537c6, 0x1653b6}}, + {{0x10f73c69, 0x00352a75, 0x0d5939fe, 0x11c1c943, 0x1a8948b3, 0x15ec1f4a, 0x15827d2c, 0x102d3cba, 0xa58370}}}, /* 15*16^59*G: */ - {{{0x3b63640e, 0x155df8c6, 0x0c72df2c, 0x26edfca4, 0x05cbf497, 0x319e729a, 0x3153f500, 0x1b75fb4b, 0x5107}}, - {{0x02e4476c, 0x3da5ca1e, 0x320ef021, 0x2fa93a79, 0x20fda6c8, 0x399405cb, 0x1df76aeb, 0x09d28b5b, 0xb397}}} + {{{0x1b63640e, 0x0abbf18d, 0x11cb7cb1, 0x176fe521, 0x1cbf4979, 0x13ce5342, 0x14fd4031, 0x1afda5e2, 0x51076d}}, + {{0x02e4476c, 0x1b4b943c, 0x083bc087, 0x1d49d3ce, 0x0fda6c8b, 0x1280b970, 0x1ddabaf9, 0x0945adbb, 0xb39727}}} }, { /* 1*16^60*G: */ - {{{0x244e8de3, 0x018c12c6, 0x2cc1e076, 0x02259a8b, 0x3d17915c, 0x29f73c22, 0x010b73a5, 0x266dd1a2, 0xf50b}}, - {{0x1b7f3588, 0x28fcee9b, 0x1721e854, 0x1d7c6348, 0x2dcebbe9, 0x265ce8b7, 0x18f0c878, 0x0187957c, 0xe2b5}}}, + {{{0x044e8de3, 0x0318258d, 0x130781d8, 0x112cd45d, 0x117915c0, 0x1ee7845e, 0x02dce969, 0x16e8d102, 0xf50b99}}, + {{0x1b7f3588, 0x11f9dd36, 0x1c87a152, 0x0be31a42, 0x1cebbe97, 0x0b9d16f6, 0x1c321e26, 0x03cabe31, 0xe2b506}}}, /* 3*16^60*G: */ - {{{0x02accf8b, 0x3771adae, 0x2816fa7d, 0x34a66460, 0x39430481, 0x3cc38944, 0x05770645, 0x1fd86954, 0x598d}}, - {{0x0f6cb808, 0x2e119cf0, 0x13540b91, 0x0a26a3cd, 0x33ebcad2, 0x31458ac9, 0x32609546, 0x087dd3e3, 0x9f31}}}, + {{{0x02accf8b, 0x0ee35b5c, 0x005be9f7, 0x05332305, 0x1430481d, 0x1871289c, 0x1dc1917c, 0x0c34aa0a, 0x598d7f}}, + {{0x0f6cb808, 0x1c2339e0, 0x0d502e46, 0x11351e6a, 0x1ebcad22, 0x08b15939, 0x182551b1, 0x1ee9f1e4, 0x9f3121}}}, /* 5*16^60*G: */ - {{{0x24aa7b3e, 0x3ece6951, 0x16c9cea9, 0x313bc6c1, 0x1c581013, 0x34824550, 0x34c4d64f, 0x0804bd27, 0x715a}}, - {{0x3c7d081d, 0x268ce512, 0x08b47d0d, 0x06f1622a, 0x113b6242, 0x24a23e2a, 0x06c0a1f7, 0x2cec6a98, 0x5922}}}, + {{{0x04aa7b3e, 0x1d9cd2a3, 0x1b273aa7, 0x09de360a, 0x0581013c, 0x1048aa0e, 0x113593f4, 0x025e93e9, 0x715a20}}, + {{0x1c7d081d, 0x0d19ca25, 0x02d1f436, 0x178b1151, 0x13b62421, 0x1447c548, 0x10287de4, 0x16354c0d, 0x5922b3}}}, /* 7*16^60*G: */ - {{{0x220db220, 0x06f6da5d, 0x287ace4d, 0x0732c405, 0x387876c7, 0x273a25fe, 0x1b125c40, 0x23179aaa, 0x49ec}}, - {{0x277338c2, 0x26e2b281, 0x13b9cce9, 0x0b0c1cf9, 0x1f542984, 0x2730d219, 0x2629b3da, 0x1f53f97a, 0x99a9}}}, + {{{0x020db220, 0x0dedb4bb, 0x01eb3934, 0x1996202d, 0x07876c71, 0x0744bfdc, 0x04971027, 0x0bcd5536, 0x49ec8c}}, + {{0x077338c2, 0x0dc56503, 0x0ee733a6, 0x1860e7ca, 0x15429842, 0x061a432f, 0x0a6cf6a7, 0x09fcbd4c, 0x99a97d}}}, /* 9*16^60*G: */ - {{{0x1e771268, 0x07af28c5, 0x10a65685, 0x13c529f6, 0x207b7a2f, 0x3c643817, 0x0b4483e6, 0x2dc35214, 0x1f8f}}, - {{0x0909c8dd, 0x2bf4c043, 0x092b3ab1, 0x074f0c47, 0x2192a14e, 0x0bb5d1c9, 0x3a2bf12c, 0x1eb6d186, 0xf53e}}}, + {{{0x1e771268, 0x0f5e518a, 0x02995a14, 0x1e294fb2, 0x07b7a2f4, 0x0c8702f0, 0x1120f9bc, 0x01a90a16, 0x1f8fb7}}, + {{0x0909c8dd, 0x17e98086, 0x04aceac6, 0x1a786239, 0x192a14e1, 0x16ba3930, 0x0afc4b0b, 0x1b68c374, 0xf53e7a}}}, /* 11*16^60*G: */ - {{{0x28d9819e, 0x17b03cac, 0x02dab1a5, 0x019e4bdd, 0x38732cd6, 0x3450ae99, 0x3f61fdd5, 0x31c69925, 0xb8d5}}, - {{0x29138ac4, 0x31e2fa3a, 0x1d45c3cd, 0x3d27c4d8, 0x23dc79e2, 0x3b90d66d, 0x37f823b6, 0x13bc4c84, 0x1cd1}}}, + {{{0x08d9819e, 0x0f607959, 0x0b6ac695, 0x0cf25ee8, 0x0732cd60, 0x0a15d33c, 0x187f7574, 0x034c92fe, 0xb8d5c7}}, + {{0x09138ac4, 0x03c5f475, 0x15170f37, 0x093e26c3, 0x1dc79e2f, 0x121acdb1, 0x1e08edbb, 0x1e26426f, 0x1cd14e}}}, /* 13*16^60*G: */ - {{{0x20bca3f3, 0x2a4f6f99, 0x16004906, 0x2cd0d451, 0x00d8c4ec, 0x0fad8722, 0x2ae3ddd6, 0x2d6b196e, 0x2265}}, - {{0x117409ff, 0x160a71b1, 0x2393d5a2, 0x202984b4, 0x0964983c, 0x0c4e8ec4, 0x0fe0f61a, 0x262fd72b, 0x97a1}}}, + {{{0x00bca3f3, 0x149edf33, 0x1801241a, 0x0686a28a, 0x0d8c4ecb, 0x15b0e440, 0x18f7758f, 0x158cb755, 0x2265b5}}, + {{0x117409ff, 0x0c14e362, 0x0e4f5689, 0x014c25a4, 0x164983c8, 0x09d1d884, 0x183d868c, 0x17eb959f, 0x97a198}}}, /* 15*16^60*G: */ - {{{0x05bac36e, 0x1cb48ffd, 0x175dcd03, 0x26265166, 0x09abcb59, 0x362a7d7f, 0x0492521f, 0x073440d6, 0xaf38}}, - {{0x31b119a9, 0x3cf621ea, 0x34d4a90f, 0x26e0bc7b, 0x1a264858, 0x15fc8a54, 0x30fbdc94, 0x021fedf7, 0x681a}}} + {{{0x05bac36e, 0x19691ffa, 0x1d77340d, 0x11328b32, 0x1abcb599, 0x054fafe4, 0x049487f6, 0x1a206b09, 0xaf381c}}, + {{0x11b119a9, 0x19ec43d5, 0x1352a43f, 0x1705e3de, 0x02648589, 0x1f914a8d, 0x1ef72515, 0x0ff6fbe1, 0x681a08}}} }, { /* 1*16^61*G: */ - {{{0x2037cfb4, 0x38665015, 0x3cdaa859, 0x003c91b0, 0x20b0e074, 0x1fd22036, 0x1ed0b0d7, 0x0c608ffd, 0x0425}}, - {{0x18775d23, 0x02dcc97b, 0x0ec5dd40, 0x28f93d4d, 0x261facee, 0x32934321, 0x00f7e628, 0x22f33eb8, 0xc90e}}}, + {{{0x0037cfb4, 0x10cca02b, 0x136aa167, 0x01e48d87, 0x0b0e0740, 0x1a4406d0, 0x142c35df, 0x1047febd, 0x42531}}, + {{0x18775d23, 0x05b992f6, 0x1b177500, 0x07c9ea69, 0x01faceea, 0x12686433, 0x1df98a32, 0x199f5c01, 0xc90e8b}}}, /* 3*16^61*G: */ - {{{0x06c34577, 0x213d9cd5, 0x2a52af77, 0x1027b239, 0x00e4bde6, 0x178c23a3, 0x3ca48b1f, 0x1ea838c2, 0x2755}}, - {{0x0416193c, 0x37fae6e0, 0x0c4380ba, 0x28b29cdd, 0x3d34f318, 0x235d6927, 0x05b3b77c, 0x31d61184, 0x8399}}}, + {{{0x06c34577, 0x027b39aa, 0x094abdde, 0x013d91cd, 0x0e4bde64, 0x11847460, 0x0922c7d7, 0x141c6179, 0x27557a}}, + {{0x0416193c, 0x0ff5cdc0, 0x110e02eb, 0x0594e6e9, 0x134f318a, 0x0bad24fe, 0x0ceddf23, 0x0b08c20b, 0x8399c7}}}, /* 5*16^61*G: */ - {{{0x2401f4d3, 0x3963f6da, 0x295b301e, 0x1b0b943a, 0x21d7decf, 0x01e0efd5, 0x073648e5, 0x1e05f496, 0x8e68}}, - {{0x0294d86b, 0x00a07a51, 0x2a191289, 0x02e5bc4b, 0x2d3cae90, 0x20268141, 0x09bfa62f, 0x2ae21b8b, 0x989c}}}, + {{{0x0401f4d3, 0x12c7edb5, 0x056cc07b, 0x185ca1d5, 0x1d7decf6, 0x1c1dfab0, 0x0d923941, 0x02fa4b0e, 0x8e6878}}, + {{0x0294d86b, 0x0140f4a2, 0x08644a24, 0x172de25d, 0x13cae900, 0x04d02836, 0x0fe98be0, 0x110dc593, 0x989cab}}}, /* 7*16^61*G: */ - {{{0x2d2aa8e6, 0x1658f789, 0x0effe2dc, 0x14d67f10, 0x27dbee20, 0x0da00f29, 0x25cf6d10, 0x05d1894f, 0x98a4}}, - {{0x206cf75b, 0x25d02fb5, 0x37ed2196, 0x0085feaa, 0x35cec9e3, 0x150bd68b, 0x063d6b11, 0x31a51f8d, 0x579a}}}, + {{{0x0d2aa8e6, 0x0cb1ef13, 0x1bff8b71, 0x06b3f881, 0x1dbee205, 0x1401e533, 0x13db440d, 0x08c4a7cb, 0x98a417}}, + {{0x006cf75b, 0x0ba05f6b, 0x1fb4865a, 0x042ff556, 0x1cec9e30, 0x017ad17a, 0x0f5ac455, 0x128fc68c, 0x579ac6}}}, /* 9*16^61*G: */ - {{{0x352c2d31, 0x328b323d, 0x061eecd7, 0x002aec23, 0x21a94618, 0x05b910f8, 0x140fd922, 0x151088c1, 0xe168}}, - {{0x24a50fec, 0x32e20da0, 0x09983941, 0x1d864afe, 0x2bc9343e, 0x0b990b40, 0x272142fb, 0x215724a3, 0x0700}}}, + {{{0x152c2d31, 0x0516647b, 0x187bb35f, 0x01576118, 0x1a946180, 0x17221f10, 0x03f64885, 0x084460a8, 0xe16854}}, + {{0x04a50fec, 0x05c41b41, 0x0660e507, 0x0c3257f1, 0x1c9343e7, 0x13216815, 0x0850becb, 0x0b9251ce, 0x70085}}}, /* 11*16^61*G: */ - {{{0x33a7cdad, 0x28ceeb8d, 0x10bcfaf4, 0x2b60f4b9, 0x0951a53c, 0x0a8b94ce, 0x113ea1ca, 0x0c52c275, 0xbfa6}}, - {{0x295cb953, 0x17e224c0, 0x04047a1c, 0x04643e32, 0x2ed1a726, 0x3e16eec7, 0x02c782a5, 0x3a065320, 0xb452}}}, + {{{0x13a7cdad, 0x119dd71b, 0x02f3ebd2, 0x1b07a5ca, 0x151a53ca, 0x117299c4, 0x0fa8728a, 0x09613aa2, 0xbfa631}}, + {{0x095cb953, 0x0fc44981, 0x1011e871, 0x0321f190, 0x0d1a7261, 0x02ddd8f7, 0x11e0a97e, 0x03299005, 0xb452e8}}}, /* 13*16^61*G: */ - {{{0x0ade0fb7, 0x36f32140, 0x26518d8e, 0x1b71d37a, 0x198e200c, 0x025d79b7, 0x21cd3ecf, 0x020b42a5, 0xe687}}, - {{0x1d4d6ece, 0x05e783cc, 0x08c22599, 0x307a17be, 0x11a72117, 0x3c394c87, 0x095555e5, 0x29121a13, 0x2135}}}, + {{{0x0ade0fb7, 0x0de64280, 0x1946363b, 0x1b8e9bd4, 0x18e200c6, 0x0baf36ec, 0x134fb3c2, 0x05a152c3, 0xe68708}}, + {{0x1d4d6ece, 0x0bcf0798, 0x03089664, 0x03d0bdf1, 0x1a72117c, 0x072990e8, 0x1555797c, 0x090d0992, 0x2135a4}}}, /* 15*16^61*G: */ - {{{0x0e432daf, 0x20f2d7c3, 0x2827ac9c, 0x2fb6822a, 0x074975f3, 0x30a35e54, 0x1a9e94bf, 0x1bbe18aa, 0x7ab1}}, - {{0x271bdc48, 0x045d622a, 0x34fdb013, 0x3a738eb9, 0x1ba7c5c7, 0x2460f8a3, 0x328b1a35, 0x0382a5f0, 0x584e}}} + {{{0x0e432daf, 0x01e5af86, 0x009eb272, 0x1db41155, 0x14975f3b, 0x146bca83, 0x07a52ff0, 0x1f0c5535, 0x7ab16e}}, + {{0x071bdc48, 0x08bac455, 0x13f6c04c, 0x139c75ce, 0x1a7c5c7e, 0x0c1f146d, 0x02c68d64, 0x0152f865, 0x584e0e}}} }, { /* 1*16^62*G: */ - {{{0x085fbd44, 0x01d1c4a6, 0x326267ac, 0x30b2a8e7, 0x15222c89, 0x11c7385b, 0x35905e05, 0x01b6b66a, 0x9bbf}}, - {{0x3a1d3e88, 0x0d11f7e9, 0x1036ed2a, 0x352f7705, 0x2f47e8c0, 0x176bcc29, 0x120a3675, 0x1fea1378, 0x1bcc}}}, + {{{0x085fbd44, 0x03a3894c, 0x09899eb0, 0x0595473e, 0x1222c89c, 0x18e70b6a, 0x04178151, 0x1b5b356b, 0x9bbf06}}, + {{0x1a1d3e88, 0x1a23efd3, 0x00dbb4a8, 0x097bb82a, 0x147e8c0d, 0x0d798537, 0x028d9d57, 0x1509bc24, 0x1bcc7f}}}, /* 3*16^62*G: */ - {{{0x34a7b506, 0x2deb9e4a, 0x3860be08, 0x1d62eeb9, 0x100ee922, 0x33ecab9d, 0x35bd3429, 0x3dfd96ce, 0x646f}}, - {{0x2b36f946, 0x25e70494, 0x08e6995c, 0x0b7f13f0, 0x0a8fe849, 0x078cc601, 0x218a55a6, 0x0aa74192, 0xbc11}}}, + {{{0x14a7b506, 0x1bd73c95, 0x0182f822, 0x0b1775cf, 0x00ee9227, 0x1d9573a8, 0x0f4d0a73, 0x1ecb676b, 0x646ff7}}, + {{0x0b36f946, 0x0bce0929, 0x039a6572, 0x1bf89f81, 0x08fe8492, 0x1198c025, 0x02956987, 0x13a0c943, 0xbc112a}}}, /* 5*16^62*G: */ - {{{0x0103b553, 0x152dc727, 0x3385a801, 0x183a89e0, 0x3e507ebe, 0x304002c9, 0x3d39a9d0, 0x151ea985, 0x7cc0}}, - {{0x0d45a526, 0x1e672e8f, 0x0228b7d5, 0x061682ab, 0x3c94c400, 0x1ca32ce7, 0x0045abdd, 0x27af48ca, 0x7b32}}}, + {{{0x0103b553, 0x0a5b8e4e, 0x0e16a005, 0x01d44f06, 0x0507ebe6, 0x0800593f, 0x0e6a7430, 0x0f54c2fa, 0x7cc054}}, + {{0x0d45a526, 0x1cce5d1e, 0x08a2df55, 0x10b41558, 0x094c4001, 0x14659cfe, 0x116af75c, 0x17a46500, 0x7b329e}}}, /* 7*16^62*G: */ - {{{0x19e717a4, 0x30bbd150, 0x0f01b81a, 0x368af6ab, 0x2ee15468, 0x0fb54db6, 0x1db4e056, 0x146642f0, 0x9468}}, - {{0x3526dea3, 0x1d7c3f46, 0x30acd9ca, 0x2665643d, 0x267dc057, 0x23439ac9, 0x191a8b3b, 0x1e108371, 0xca5c}}}, + {{{0x19e717a4, 0x0177a2a0, 0x1c06e06b, 0x1457b559, 0x0e15468d, 0x16a9b6d7, 0x0d38158f, 0x1321783b, 0x946851}}, + {{0x1526dea3, 0x1af87e8d, 0x02b36729, 0x132b21ee, 0x07dc0579, 0x08735933, 0x06a2cee3, 0x0841b8b2, 0xca5c78}}}, /* 9*16^62*G: */ - {{{0x08362735, 0x3e0b0dbc, 0x12b327bd, 0x3e2cdfbc, 0x12d1f5df, 0x163e3a91, 0x0e8fab12, 0x23c6f9f8, 0xe1b9}}, - {{0x0ecb11b7, 0x2584e327, 0x374090af, 0x067b8cf7, 0x3b2ba27e, 0x16d26a0e, 0x36a0b7e0, 0x3a6b66a5, 0xca83}}}, + {{{0x08362735, 0x1c161b78, 0x0acc9ef7, 0x1166fde2, 0x0d1f5dff, 0x07c75229, 0x03eac496, 0x037cfc1d, 0xe1b98f}}, + {{0x0ecb11b7, 0x0b09c64e, 0x1d0242be, 0x13dc67be, 0x12ba27e1, 0x1a4d41dd, 0x082df816, 0x15b352ed, 0xca83e9}}}, /* 11*16^62*G: */ - {{{0x39046346, 0x2d02ef60, 0x01440083, 0x296379cc, 0x27962d56, 0x2281af65, 0x207ef6d0, 0x3c9723f5, 0x3536}}, - {{0x0c14fea6, 0x100418af, 0x2d9b3e29, 0x1b0f47a8, 0x29e1c39e, 0x285a8694, 0x3509e73b, 0x07f85f78, 0x1e27}}}, + {{{0x19046346, 0x1a05dec1, 0x0510020e, 0x0b1bce60, 0x1962d56a, 0x1035ecb3, 0x1fbdb422, 0x0b91fac0, 0x3536f2}}, + {{0x0c14fea6, 0x0008315e, 0x166cf8a5, 0x187a3d45, 0x1e1c39e6, 0x0b50d294, 0x0279cee8, 0x1c2fbc6a, 0x1e271f}}}, /* 13*16^62*G: */ - {{{0x2847f6f8, 0x3ffe0fb5, 0x140ef530, 0x0a6d47ef, 0x3f8c3c10, 0x0547cd2d, 0x3d4de690, 0x0091af88, 0x0df5}}, - {{0x3b1633a6, 0x1332a29a, 0x1df3449b, 0x1b8599a2, 0x2174ab4c, 0x0cb13ef0, 0x2f1ca2b2, 0x011fca76, 0x2107}}}, + {{{0x0847f6f8, 0x1ffc1f6b, 0x103bd4c3, 0x136a3f7a, 0x18c3c102, 0x08f9a5bf, 0x1379a405, 0x08d7c47a, 0xdf502}}, + {{0x1b1633a6, 0x06654535, 0x17cd126d, 0x1c2ccd13, 0x174ab4c6, 0x1627de10, 0x0728ac8c, 0x0fe53b5e, 0x210704}}}, /* 15*16^62*G: */ - {{{0x3d4f1b81, 0x2173abb7, 0x0f4bb151, 0x1a69e923, 0x129330ad, 0x378eccd9, 0x13398f69, 0x3575133d, 0xca9d}}, - {{0x02b7c8bd, 0x3318b2b9, 0x2ada10f8, 0x325d82fe, 0x067b3e66, 0x11c7ed11, 0x22c56402, 0x2621946f, 0x6e4b}}} + {{{0x1d4f1b81, 0x02e7576f, 0x1d2ec546, 0x134f4919, 0x09330ad6, 0x11d99b29, 0x0e63da77, 0x1a899ea6, 0xca9dd5}}, + {{0x02b7c8bd, 0x06316572, 0x0b6843e3, 0x12ec17f5, 0x07b3e66c, 0x18fda223, 0x11590091, 0x10ca37c5, 0x6e4b98}}} }, { /* 1*16^63*G: */ - {{{0x044c0448, 0x3ab4c8cd, 0x10319e31, 0x0d5da1b0, 0x3893e796, 0x0ff32ced, 0x3dfa5494, 0x2b7d4a50, 0xb12f}}, - {{0x3369de57, 0x195d79da, 0x2fc4df29, 0x0179c0cc, 0x32a6a71d, 0x3e3d99de, 0x0f4ace96, 0x1165666c, 0x02e2}}}, + {{{0x044c0448, 0x1569919a, 0x00c678c7, 0x0aed0d82, 0x093e7963, 0x1e659dbc, 0x1e95250f, 0x1ea5287b, 0xb12fad}}, + {{0x1369de57, 0x12baf3b5, 0x1f137ca5, 0x0bce0665, 0x0a6a71d0, 0x07b33bd9, 0x12b3a5be, 0x12b3361e, 0x2e245}}}, /* 3*16^63*G: */ - {{{0x24e9151f, 0x14db1151, 0x00d8418f, 0x3a8ce672, 0x18fb3e67, 0x15776a47, 0x10568432, 0x238d3c71, 0x4838}}, - {{0x0d7a9434, 0x2fb927b7, 0x3de83101, 0x2c504454, 0x082bcc99, 0x14ce4c55, 0x04e9e6a2, 0x18eafd39, 0xb0ec}}}, + {{{0x04e9151f, 0x09b622a3, 0x0361063d, 0x14673390, 0x0fb3e67e, 0x0eed48ec, 0x15a10c95, 0x069e38a0, 0x48388e}}, + {{0x0d7a9434, 0x1f724f6e, 0x17a0c406, 0x028222a7, 0x02bcc99b, 0x19c98aa4, 0x1a79a894, 0x157e9c89, 0xb0ec63}}}, /* 5*16^63*G: */ - {{{0x0e5b833d, 0x1f7ed296, 0x20b2419d, 0x0e801cf2, 0x0109c959, 0x177e0414, 0x053da5e6, 0x1911eb85, 0xde8e}}, - {{0x214c5cc7, 0x03f3066a, 0x101c6c9f, 0x1f80c4ca, 0x2de26598, 0x08a232f5, 0x113d8e33, 0x118f0542, 0x05e1}}}, + {{{0x0e5b833d, 0x1efda52c, 0x02c90675, 0x1400e794, 0x109c9593, 0x0fc08280, 0x0f697997, 0x08f5c28a, 0xde8e64}}, + {{0x014c5cc7, 0x07e60cd5, 0x0071b27c, 0x1c062652, 0x1e265987, 0x14465eb6, 0x0f638cc8, 0x0782a122, 0x5e146}}}, /* 7*16^63*G: */ - {{{0x01f7df48, 0x38964fab, 0x071317b3, 0x19d1cfae, 0x18f385b2, 0x156d3939, 0x07e9e8e5, 0x04b4293b, 0xb18b}}, - {{0x2846b546, 0x06cf5643, 0x3d1e5599, 0x20fdf920, 0x2cc33b3c, 0x3109af16, 0x1fb445ce, 0x0648a8d6, 0xff53}}}, + {{{0x01f7df48, 0x112c9f56, 0x1c4c5ecf, 0x0e8e7d70, 0x0f385b26, 0x0da7272c, 0x1a7a3955, 0x1a149d8f, 0xb18b12}}, + {{0x0846b546, 0x0d9eac87, 0x14795664, 0x07efc907, 0x0c33b3c8, 0x0135e2d6, 0x0d1173b1, 0x04546b3f, 0xff5319}}}, /* 9*16^63*G: */ - {{{0x19c9fd24, 0x094eb71a, 0x1211e0df, 0x33762611, 0x28694402, 0x072a931c, 0x09433c7c, 0x2b5c7237, 0x5f51}}, - {{0x2d2ffd3a, 0x30eeba21, 0x224a9969, 0x087d8911, 0x2e4d0387, 0x0c17ef30, 0x2714a0cd, 0x3bc477df, 0x2bbb}}}, + {{{0x19c9fd24, 0x129d6e34, 0x0847837c, 0x1bb1308a, 0x0694402c, 0x05526394, 0x10cf1f07, 0x0e391b92, 0x5f51ad}}, + {{0x0d2ffd3a, 0x01dd7443, 0x092a65a7, 0x03ec488c, 0x04d03872, 0x02fde617, 0x0528334c, 0x023befce, 0x2bbbef}}}, /* 11*16^63*G: */ - {{{0x17cec42e, 0x0f1018ff, 0x2e3bdb7e, 0x0f724cfb, 0x06d8556f, 0x208bb90d, 0x01ebbfa5, 0x10364dcc, 0xfdf3}}, - {{0x0db6908b, 0x23d8d2df, 0x0de30c83, 0x1b9aafd4, 0x0ad2c445, 0x307f9ce3, 0x0c6e1d70, 0x2698e5a3, 0xa3e5}}}, + {{{0x17cec42e, 0x1e2031fe, 0x18ef6df8, 0x1b9267dd, 0x0d8556f3, 0x117721a3, 0x1aefe960, 0x1b26e603, 0xfdf340}}, + {{0x0db6908b, 0x07b1a5be, 0x178c320e, 0x1cd57ea1, 0x0d2c4456, 0x0ff39c65, 0x1b875c30, 0x0c72d198, 0xa3e59a}}}, /* 13*16^63*G: */ - {{{0x21dc4fe8, 0x30625153, 0x2072415f, 0x3a284ea5, 0x3dc983f9, 0x114a45ed, 0x25d79ec6, 0x3af22e7a, 0xe3ca}}, - {{0x1307b403, 0x1ad82dc8, 0x14f86a11, 0x0c00d968, 0x01f97651, 0x00d72e2c, 0x05928d22, 0x24f49efc, 0x97f0}}}, + {{{0x01dc4fe8, 0x00c4a2a7, 0x01c9057f, 0x1142752c, 0x1c983f9e, 0x0948bdbe, 0x15e7b191, 0x19173d4b, 0xe3caeb}}, + {{0x1307b403, 0x15b05b90, 0x13e1a845, 0x0006cb42, 0x1f976513, 0x1ae5c580, 0x04a34880, 0x1a4f7e0b, 0x97f093}}}, /* 15*16^63*G: */ - {{{0x3c119eff, 0x10535974, 0x29f9b846, 0x240b8302, 0x0fa00339, 0x10697396, 0x065b89af, 0x0b6e50aa, 0x0331}}, - {{0x38b1b950, 0x3a568ea7, 0x3515585f, 0x3b1676d7, 0x09e86f0a, 0x3ba8c5e0, 0x324df104, 0x36991acd, 0x6e3e}}} + {{{0x1c119eff, 0x00a6b2e9, 0x07e6e119, 0x005c1815, 0x1a003399, 0x0d2e72c7, 0x16e26bd0, 0x1728550c, 0x3312d}}, + {{0x18b1b950, 0x14ad1d4f, 0x1455617f, 0x18b3b6be, 0x1e86f0ae, 0x1518bc04, 0x137c413b, 0x0c8d66e4, 0x6e3eda}}} }, diff --git a/crypto/secp256k1.c b/crypto/secp256k1.c index 097c7cc170..34ccaaacbb 100644 --- a/crypto/secp256k1.c +++ b/crypto/secp256k1.c @@ -24,24 +24,25 @@ #include "secp256k1.h" const ecdsa_curve secp256k1 = { - /* .prime */ {/*.val =*/{0x3ffffc2f, 0x3ffffffb, 0x3fffffff, 0x3fffffff, - 0x3fffffff, 0x3fffffff, 0x3fffffff, 0x3fffffff, - 0xffff}}, + /* .prime */ {/*.val =*/{0x1ffffc2f, 0x1ffffff7, 0x1fffffff, 0x1fffffff, + 0x1fffffff, 0x1fffffff, 0x1fffffff, 0x1fffffff, + 0xffffff}}, /* G */ - {/*.x =*/{/*.val =*/{0x16f81798, 0x27ca056c, 0x1ce28d95, 0x26ff36cb, - 0x70b0702, 0x18a573a, 0xbbac55a, 0x199fbe77, 0x79be}}, - /*.y =*/{/*.val =*/{0x3b10d4b8, 0x311f423f, 0x28554199, 0x5ed1229, - 0x1108a8fd, 0x13eff038, 0x3c4655da, 0x369dc9a8, - 0x483a}}}, + {/*.x =*/{/*.val =*/{0x16f81798, 0x0f940ad8, 0x138a3656, 0x17f9b65b, + 0x10b07029, 0x114ae743, 0x0eb15681, 0x0fdf3b97, + 0x79be66}}, + /*.y =*/{/*.val =*/{0x1b10d4b8, 0x023e847f, 0x01550667, 0x0f68914d, + 0x108a8fd1, 0x1dfe0708, 0x11957693, 0x0ee4d478, + 0x483ada}}}, /* order */ - {/*.val =*/{0x10364141, 0x3f497a33, 0x348a03bb, 0x2bb739ab, 0x3ffffeba, - 0x3fffffff, 0x3fffffff, 0x3fffffff, 0xffff}}, + {/*.val =*/{0x10364141, 0x1e92f466, 0x12280eef, 0x1db9cd5e, 0x1fffebaa, + 0x1fffffff, 0x1fffffff, 0x1fffffff, 0xffffff}}, /* order_half */ - {/*.val =*/{0x281b20a0, 0x3fa4bd19, 0x3a4501dd, 0x15db9cd5, 0x3fffff5d, - 0x3fffffff, 0x3fffffff, 0x3fffffff, 0x7fff}}, + {/*.val =*/{0x081b20a0, 0x1f497a33, 0x09140777, 0x0edce6af, 0x1ffff5d5, + 0x1fffffff, 0x1fffffff, 0x1fffffff, 0x7fffff}}, /* a */ 0, diff --git a/crypto/secp256k1.table b/crypto/secp256k1.table index 9fd3c728ca..0fa87a8b16 100644 --- a/crypto/secp256k1.table +++ b/crypto/secp256k1.table @@ -1,1664 +1,1664 @@ { /* 1*16^0*G: */ - {{{0x16f81798, 0x27ca056c, 0x1ce28d95, 0x26ff36cb, 0x070b0702, 0x018a573a, 0x0bbac55a, 0x199fbe77, 0x79be}}, - {{0x3b10d4b8, 0x311f423f, 0x28554199, 0x05ed1229, 0x1108a8fd, 0x13eff038, 0x3c4655da, 0x369dc9a8, 0x483a}}}, + {{{0x16f81798, 0x0f940ad8, 0x138a3656, 0x17f9b65b, 0x10b07029, 0x114ae743, 0x0eb15681, 0x0fdf3b97, 0x79be66}}, + {{0x1b10d4b8, 0x023e847f, 0x01550667, 0x0f68914d, 0x108a8fd1, 0x1dfe0708, 0x11957693, 0x0ee4d478, 0x483ada}}}, /* 3*16^0*G: */ - {{{0x3ce036f9, 0x1807c44e, 0x36f99b08, 0x0c721160, 0x1d5229b5, 0x113e17e2, 0x0c310493, 0x22806496, 0xf930}}, - {{0x04b8e672, 0x32e7f5d6, 0x0c2231b6, 0x002a664d, 0x37f35665, 0x0cdf98a8, 0x1e8140fe, 0x1ec3d8cb, 0x388f}}}, + {{{0x1ce036f9, 0x100f889d, 0x1be66c21, 0x03908b06, 0x15229b53, 0x07c2fc4e, 0x0c4124d1, 0x00324b18, 0xf9308a}}, + {{0x04b8e672, 0x05cfebac, 0x1088c6db, 0x01533269, 0x1f356650, 0x1bf3151b, 0x00503f8c, 0x01ec65bd, 0x388f7b}}}, /* 5*16^0*G: */ - {{{0x3240efe4, 0x2ea355a6, 0x0619ab7c, 0x22e12f77, 0x1c5128e8, 0x129c9429, 0x3209355b, 0x37934681, 0x2f8b}}, - {{0x26ac62d6, 0x32a1f4ea, 0x30d6840d, 0x2209c6ea, 0x09c426f7, 0x2ea7769b, 0x1e3d6d4d, 0x08898db9, 0xd8ac}}}, + {{{0x1240efe4, 0x1d46ab4d, 0x1866adf2, 0x17097bb8, 0x05128e88, 0x1392852e, 0x024d56d2, 0x09a340e4, 0x2f8bde}}, + {{0x06ac62d6, 0x0543e9d5, 0x035a1037, 0x104e3756, 0x1c426f78, 0x14eed364, 0x0f5b536e, 0x04c6dcbc, 0xd8ac22}}}, /* 7*16^0*G: */ - {{{0x0ac4f9bc, 0x24af77b7, 0x330e39ce, 0x1066df80, 0x2a7a0e3d, 0x23cd97cb, 0x1b4eaa39, 0x3c191b97, 0x5cbd}}, - {{0x087264da, 0x142098a0, 0x3fde7b5a, 0x04f42e04, 0x1a54dba8, 0x1e35b618, 0x15960a31, 0x32902e89, 0x6aeb}}}, + {{{0x0ac4f9bc, 0x095eef6e, 0x0c38e73a, 0x0336fc06, 0x07a0e3d4, 0x19b2f975, 0x13aa8e63, 0x0c8dcbb6, 0x5cbdf0}}, + {{0x087264da, 0x08413140, 0x1f79ed69, 0x07a17027, 0x054dba81, 0x06b6c30d, 0x05828c5e, 0x081744ab, 0x6aebca}}}, /* 9*16^0*G: */ - {{{0x3c27ccbe, 0x0d7c4437, 0x057e714c, 0x25e5a5d3, 0x159abde0, 0x345e2a7d, 0x3f65309a, 0x2138bc31, 0xacd4}}, - {{0x064f9c37, 0x173098ab, 0x35f8e0f0, 0x3622290d, 0x3b61e9ad, 0x2025c5d8, 0x3d9fd643, 0x22486c29, 0xcc33}}}, + {{{0x1c27ccbe, 0x1af8886f, 0x15f9c530, 0x0f2d2e98, 0x19abde09, 0x0bc54faa, 0x194c26b4, 0x1c5e18fe, 0xacd484}}, + {{0x064f9c37, 0x0e613156, 0x17e383c1, 0x1111486e, 0x161e9add, 0x04b8bb1d, 0x07f590e0, 0x043614fb, 0xcc3389}}}, /* 11*16^0*G: */ - {{{0x1da008cb, 0x2fb05e25, 0x1c17891b, 0x126602f9, 0x065aac56, 0x1091adc3, 0x1411e5ef, 0x39fe162a, 0x774a}}, - {{0x0953c61b, 0x0075d327, 0x3f9d6a83, 0x0b6c78b7, 0x37b36537, 0x0f755b5e, 0x35e19024, 0x280cbada, 0xd984}}}, + {{{0x1da008cb, 0x1f60bc4a, 0x105e246e, 0x133017cb, 0x05aac564, 0x1235b863, 0x04797bd0, 0x1f0b1528, 0x774ae7}}, + {{0x0953c61b, 0x00eba64e, 0x1e75aa0c, 0x1b63c5bf, 0x1b365372, 0x0eab6bdb, 0x1864090f, 0x065d6d6b, 0xd984a0}}}, /* 13*16^0*G: */ - {{{0x19405aa8, 0x3bb77e3c, 0x10e58cdd, 0x1d7ef198, 0x348651b0, 0x0748170d, 0x1288bc7d, 0x1cf0b65d, 0xf287}}, - {{0x1b03ed81, 0x26d72d4b, 0x21fa91f2, 0x0681b694, 0x0daf473a, 0x084bad97, 0x00a89758, 0x240ba362, 0x0ab0}}}, + {{{0x19405aa8, 0x176efc78, 0x03963377, 0x0bf78cc2, 0x08651b07, 0x0902e1ba, 0x022f1f47, 0x185b2ea5, 0xf28773}}, + {{0x1b03ed81, 0x0dae5a96, 0x07ea47ca, 0x140db4a4, 0x1af473a1, 0x0975b2e6, 0x0a25d608, 0x05d1b101, 0xab090}}}, /* 15*16^0*G: */ - {{{0x227e080e, 0x12b6f3e3, 0x085f79e4, 0x39651bcf, 0x1ff41131, 0x196b8c25, 0x3ea965a4, 0x1353df50, 0xd792}}, - {{0x36a26b58, 0x1413727f, 0x096d3a5c, 0x102bcaf6, 0x0c6defea, 0x10bb08a3, 0x072a6838, 0x0a1caa1b, 0x581e}}} + {{{0x027e080e, 0x056de7c7, 0x017de791, 0x0b28de79, 0x1f41131e, 0x0d7184af, 0x0a596919, 0x09efa87d, 0xd7924d}}, + {{0x16a26b58, 0x0826e4ff, 0x05b4e971, 0x015e57b1, 0x06defea4, 0x17611466, 0x0a9a0e10, 0x0e550d8e, 0x581e28}}} }, { /* 1*16^1*G: */ - {{{0x2a6dec0a, 0x113ba278, 0x07a5ae9c, 0x28c4da6e, 0x023e97b2, 0x06aaf087, 0x29ec5301, 0x33a4ed67, 0xe60f}}, - {{0x29616821, 0x07ccb339, 0x0d23f0be, 0x25a24791, 0x39371012, 0x267cd3d5, 0x195929db, 0x141ce679, 0xf7e3}}}, + {{{0x0a6dec0a, 0x027744f1, 0x1e96ba71, 0x0626d370, 0x03e97b2a, 0x155e10e1, 0x1b14c046, 0x1276b3d3, 0xe60fce}}, + {{0x09616821, 0x0f996673, 0x148fc2f8, 0x0d123c89, 0x13710129, 0x0f9a7abc, 0x164a76e6, 0x0e733cb2, 0xf7e350}}}, /* 3*16^1*G: */ - {{{0x1118e5c3, 0x2f61c2a8, 0x12bebc19, 0x15e6c9d1, 0x265b4bfc, 0x0595bbd3, 0x1307db44, 0x0cd76591, 0x6eca}}, - {{0x05a08668, 0x2628bde0, 0x3f8ec344, 0x125a8e8e, 0x3875a03a, 0x3d5e41d2, 0x20710592, 0x08ed5e9e, 0xd501}}}, + {{{0x1118e5c3, 0x1ec38550, 0x0afaf066, 0x0f364e8a, 0x05b4bfc5, 0x12b77a73, 0x01f6d105, 0x0bb2c8a6, 0x6eca33}}, + {{0x05a08668, 0x0c517bc0, 0x1e3b0d12, 0x12d47477, 0x075a03a4, 0x0bc83a5c, 0x1c4164bd, 0x16af4f40, 0xd50123}}}, /* 5*16^1*G: */ - {{{0x0f87f62e, 0x3b34c785, 0x37161270, 0x39b98e18, 0x0659f010, 0x31d13b4d, 0x390ec0d7, 0x0eefbc6f, 0xe962}}, - {{0x244ee737, 0x0c04fabe, 0x168844e5, 0x1810f277, 0x1aa929fe, 0x3a54ea3b, 0x299e9e0f, 0x1d0ed2f0, 0x38a9}}}, + {{{0x0f87f62e, 0x16698f0a, 0x1c5849c3, 0x0dcc70c6, 0x059f010e, 0x1a2769a3, 0x03b035f1, 0x17de37f2, 0xe9623b}}, + {{0x044ee737, 0x1809f57d, 0x1a211394, 0x008793ba, 0x0a929fe6, 0x0a9d476d, 0x07a783fa, 0x07697853, 0x38a974}}}, /* 7*16^1*G: */ - {{{0x2a8d733c, 0x2c2ab7e0, 0x2fca8f9e, 0x309d2fd8, 0x00d682ff, 0x128dbc82, 0x21dba088, 0x375cf945, 0xbc82}}, - {{0x347797f0, 0x39e18413, 0x33897301, 0x24e82eb9, 0x1f02dfae, 0x26d2fdc6, 0x31cac54a, 0x230e8112, 0xe5f2}}}, + {{{0x0a8d733c, 0x18556fc1, 0x1f2a3e7a, 0x04e97ec5, 0x0d682ffc, 0x11b79040, 0x16e82212, 0x0e7ca2c3, 0xbc82dd}}, + {{0x147797f0, 0x13c30827, 0x0e25cc07, 0x074175ce, 0x102dfae9, 0x1a5fb8cf, 0x12b152a6, 0x07408963, 0xe5f28c}}}, /* 9*16^1*G: */ - {{{0x1fbc7671, 0x1fbf88c5, 0x2858e32d, 0x0fc6f214, 0x18f49074, 0x0a47385e, 0x17211d20, 0x049231d9, 0x8e3d}}, - {{0x18717dec, 0x3bc77190, 0x23e144a7, 0x0d4aeaa9, 0x13e90eb9, 0x1203864e, 0x3cb81f64, 0x123843b3, 0x099a}}}, + {{{0x1fbc7671, 0x1f7f118a, 0x01638cb5, 0x1e3790a5, 0x0f490743, 0x08e70bcc, 0x0847480a, 0x0918ecae, 0x8e3d12}}, + {{0x18717dec, 0x178ee320, 0x0f85129f, 0x0a57554c, 0x1e90eb93, 0x0070c9c9, 0x0e07d912, 0x1c21d9f9, 0x99a48}}}, /* 11*16^1*G: */ - {{{0x3eb31db2, 0x0ca1d0ca, 0x0f506a0f, 0x32ba09e2, 0x08a2b68f, 0x2864fb42, 0x0a498896, 0x246a888d, 0x78a8}}, - {{0x39fa4343, 0x01a7588e, 0x000b82d3, 0x0de6f376, 0x302df654, 0x17c9549c, 0x035cbfcf, 0x28d6fad4, 0x6912}}}, + {{{0x1eb31db2, 0x1943a195, 0x1d41a83c, 0x15d04f11, 0x0a2b68fc, 0x0c9f6844, 0x126225a8, 0x15444694, 0x78a891}}, + {{0x19fa4343, 0x034eb11d, 0x002e0b4c, 0x0f379bb0, 0x02df6543, 0x192a9398, 0x172ff3d7, 0x0b7d6a06, 0x6912a3}}}, /* 13*16^1*G: */ - {{{0x0db0e595, 0x14d23dde, 0x3a082bb6, 0x058f2e7e, 0x2076eba7, 0x38dd9605, 0x31b17d7c, 0x1e061576, 0x7d86}}, - {{0x3c733de8, 0x265478ea, 0x225d5329, 0x0de11383, 0x0f883829, 0x18b8afb5, 0x2f8772e5, 0x26b7fb21, 0xe2b9}}}, + {{{0x0db0e595, 0x09a47bbc, 0x0820aed9, 0x0c7973f7, 0x076eba71, 0x1bb2c0b0, 0x0c5f5f38, 0x030abb63, 0x7d8678}}, + {{0x1c733de8, 0x0ca8f1d5, 0x09754ca6, 0x0f089c1c, 0x18838293, 0x1715f6a7, 0x01dcb958, 0x1bfd90df, 0xe2b99a}}}, /* 15*16^1*G: */ - {{{0x16060dfc, 0x023fbe14, 0x05e6a2a0, 0x1517e108, 0x1ab08676, 0x252e7710, 0x02ac8484, 0x0c43c016, 0xddc5}}, - {{0x27820ca8, 0x2d7e2adb, 0x3d04730f, 0x36ebf1aa, 0x0f0e9041, 0x06adb732, 0x19692019, 0x0bcebc83, 0xba0d}}} + {{{0x16060dfc, 0x047f7c28, 0x179a8a80, 0x08bf0840, 0x0b086765, 0x05cee20d, 0x0b212125, 0x01e00b05, 0xddc531}}, + {{0x07820ca8, 0x1afc55b7, 0x1411cc3e, 0x175f8d57, 0x10e9041d, 0x15b6e647, 0x1a480646, 0x075e41b2, 0xba0d2f}}} }, { /* 1*16^2*G: */ - {{{0x15f51508, 0x191b88ff, 0x1ac1ca10, 0x30e72af5, 0x2de238d8, 0x29b8f85c, 0x209d9ea2, 0x098c84b1, 0x8282}}, - {{0x36e26caf, 0x0c6dbabf, 0x37b17bed, 0x3584eb0b, 0x360ace62, 0x095ba0c2, 0x3dfe45e8, 0x2a026155, 0x11f8}}}, + {{{0x15f51508, 0x123711fe, 0x0b072841, 0x073957ab, 0x1e238d8c, 0x171f0b96, 0x0767a8a9, 0x064258c1, 0x828226}}, + {{0x16e26caf, 0x18db757f, 0x1ec5efb4, 0x0c27585e, 0x00ace62d, 0x0b74185b, 0x1f917a09, 0x0130aafb, 0x11f8a8}}}, /* 3*16^2*G: */ - {{{0x257e8dfa, 0x33f032e7, 0x3c7e184f, 0x20246468, 0x298ca009, 0x28c3e2b2, 0x19c4c0d9, 0x33cbfc1e, 0x8262}}, - {{0x3bac376a, 0x173fe363, 0x314c4783, 0x2dbb4cca, 0x334f3457, 0x3b88bb16, 0x09e4e66f, 0x25788244, 0x83fd}}}, + {{{0x057e8dfa, 0x07e065cf, 0x11f8613f, 0x01232347, 0x18ca0098, 0x187c5654, 0x11303668, 0x05fe0f33, 0x8262cf}}, + {{0x1bac376a, 0x0e7fc6c7, 0x05311e0d, 0x0dda6656, 0x14f3457b, 0x111762d9, 0x19399bfb, 0x1c412213, 0x83fd95}}}, /* 5*16^2*G: */ - {{{0x026bdb6f, 0x014b922c, 0x3734b949, 0x2906f51e, 0x299c877c, 0x0416c933, 0x0ddd5168, 0x1722c768, 0x1982}}, - {{0x049cfc9b, 0x177dc213, 0x0f6d3a6b, 0x3a7bb323, 0x359f6ceb, 0x09873253, 0x0878f320, 0x0c43c353, 0x6294}}}, + {{{0x026bdb6f, 0x02972458, 0x1cd2e524, 0x0837a8f6, 0x19c877ca, 0x02d92674, 0x17545a04, 0x1163b41b, 0x19825c}}, + {{0x049cfc9b, 0x0efb8426, 0x1db4e9ad, 0x13dd9919, 0x19f6cebe, 0x10e64a7a, 0x1e3cc809, 0x01e1a990, 0x629431}}}, /* 7*16^2*G: */ - {{{0x3d82824c, 0x03b42548, 0x21534e65, 0x29638d17, 0x02999edf, 0x17d5bb1b, 0x0191443c, 0x361b0458, 0x6f12}}, - {{0x06eb34d0, 0x15e70d20, 0x054bc5b8, 0x07249042, 0x22376939, 0x2653cff5, 0x3bfa0875, 0x3dfd12ac, 0x5c4f}}}, + {{{0x1d82824c, 0x07684a91, 0x054d3994, 0x0b1c68bc, 0x0999edfa, 0x1ab76361, 0x04510f17, 0x0d822c03, 0x6f12d8}}, + {{0x06eb34d0, 0x0bce1a40, 0x152f16e1, 0x19248210, 0x03769391, 0x0a79feb1, 0x1e821d66, 0x1e895677, 0x5c4ff7}}}, /* 9*16^2*G: */ - {{{0x1b453629, 0x1db7700b, 0x359e6030, 0x33f73703, 0x3abef645, 0x189c5a88, 0x2aa5d142, 0x231be682, 0x203a}}, - {{0x3ff89f84, 0x25c71e14, 0x1285ed45, 0x1b7ac971, 0x01061268, 0x31db457d, 0x1d9b936c, 0x02d4f797, 0x3b0f}}}, + {{{0x1b453629, 0x1b6ee016, 0x167980c1, 0x1fb9b81e, 0x0bef645c, 0x138b511d, 0x09745098, 0x0df34155, 0x203a8c}}, + {{0x1ff89f84, 0x0b8e3c29, 0x0a17b516, 0x1bd64b8a, 0x10612686, 0x1b68afa0, 0x06e4db31, 0x0a7bcbbb, 0x3b0f0b}}}, /* 11*16^2*G: */ - {{{0x246c7ecb, 0x20c4c377, 0x1bb4ce97, 0x0ebb4ff9, 0x26e1ec9d, 0x3bdccd21, 0x34181c81, 0x32bacf40, 0x6e2a}}, - {{0x2ebc8720, 0x1124807b, 0x367512c8, 0x31c1ae46, 0x3b643afa, 0x03136bc3, 0x3ee149d8, 0x2919e5fb, 0x9e61}}}, + {{{0x046c7ecb, 0x018986ef, 0x0ed33a5e, 0x15da7fcb, 0x0e1ec9d3, 0x1b99a433, 0x0607207b, 0x1d67a068, 0x6e2aca}}, + {{0x0ebc8720, 0x024900f7, 0x19d44b21, 0x0e0d7236, 0x1643afac, 0x026d787d, 0x18527603, 0x0cf2fdfd, 0x9e61a4}}}, /* 13*16^2*G: */ - {{{0x30a4147e, 0x2dc063cf, 0x375f201e, 0x11f762fd, 0x090a5827, 0x05c5fa29, 0x1156baf6, 0x0124ba7a, 0xd5a7}}, - {{0x33fb65ff, 0x392cf2e0, 0x167f57f8, 0x3136611e, 0x1e0532f4, 0x242641d9, 0x389c6fc4, 0x09bd76ea, 0x9db5}}}, + {{{0x10a4147e, 0x1b80c79f, 0x1d7c807a, 0x0fbb17ee, 0x10a58274, 0x18bf4524, 0x15aebd85, 0x125d3d22, 0xd5a704}}, + {{0x13fb65ff, 0x1259e5c1, 0x19fd5fe3, 0x09b308f2, 0x00532f4c, 0x04c83b2f, 0x071bf124, 0x1ebb7571, 0x9db526}}}, /* 15*16^2*G: */ - {{{0x18edcec6, 0x3b76d1af, 0x3634f454, 0x018730b4, 0x2cdac6a1, 0x0fbf18c0, 0x18ba8052, 0x0466aaf8, 0x38c5}}, - {{0x1933db08, 0x15b82fec, 0x35530a64, 0x285b208a, 0x1f282f28, 0x32cb689d, 0x1732a668, 0x3748a176, 0xe649}}} + {{{0x18edcec6, 0x16eda35e, 0x18d3d153, 0x0c3985a6, 0x0dac6a10, 0x17e31816, 0x0ea0148f, 0x13557c31, 0x38c511}}, + {{0x1933db08, 0x0b705fd8, 0x154c2991, 0x02d90456, 0x1282f28a, 0x196d13af, 0x0ca99a32, 0x0450bb2e, 0xe649dd}}} }, { /* 1*16^3*G: */ - {{{0x11e5b739, 0x0ff396d5, 0x12222ed7, 0x2e4e0cff, 0x3c846de0, 0x26731b1b, 0x3865a72f, 0x0567dca2, 0x175e}}, - {{0x29fed695, 0x3be9bffb, 0x124345c6, 0x2d6556b7, 0x371f5eac, 0x3e5e947f, 0x079eba4e, 0x1b83678f, 0xd350}}}, + {{{0x11e5b739, 0x1fe72daa, 0x0888bb5c, 0x127067fa, 0x0846de0b, 0x0e63637e, 0x1969cbe6, 0x13ee5170, 0x175e15}}, + {{0x09fed695, 0x17d37ff7, 0x090d171b, 0x0b2ab5ba, 0x11f5eacb, 0x0bd28ffb, 0x07ae93be, 0x01b3c78f, 0xd3506e}}}, /* 3*16^3*G: */ - {{{0x05041216, 0x16dfe3c7, 0x02b836a6, 0x1ccd7da1, 0x2fed523f, 0x2d67bf70, 0x3acf4128, 0x0c5ec87d, 0xda75}}, - {{0x2e708572, 0x2bb4ca61, 0x37acedad, 0x2ab01eb9, 0x2d7fc6e9, 0x27886cd0, 0x2d5f0df1, 0x2811afdc, 0x73f8}}}, + {{{0x05041216, 0x0dbfc78e, 0x0ae0da99, 0x066bed08, 0x1ed523f7, 0x0cf7ee17, 0x13d04a2d, 0x0f643ef5, 0xda7531}}, + {{0x0e708572, 0x176994c3, 0x1eb3b6b6, 0x1580f5ce, 0x17fc6e9a, 0x110d9a16, 0x17c37c67, 0x08d7ee5a, 0x73f8a0}}}, /* 5*16^3*G: */ - {{{0x2465a930, 0x0050f9c7, 0x31352fdb, 0x21fc705a, 0x02eb1e25, 0x0f16312a, 0x349d7057, 0x316d23a5, 0x1c71}}, - {{0x034638b5, 0x361cfdb3, 0x3174d471, 0x0d178fed, 0x0bb68c79, 0x0fc7ca09, 0x1fa0c271, 0x30cd3a3d, 0x4a91}}}, + {{{0x0465a930, 0x00a1f38f, 0x04d4bf6c, 0x0fe382d6, 0x0eb1e258, 0x02c62541, 0x075c15cf, 0x1691d2e9, 0x1c71c5}}, + {{0x034638b5, 0x0c39fb66, 0x05d351c7, 0x08bc7f6e, 0x1b68c793, 0x18f94125, 0x08309c4f, 0x069d1ebf, 0x4a91c3}}}, /* 7*16^3*G: */ - {{{0x3adb6ee7, 0x0c636b96, 0x344a077e, 0x143750c9, 0x1b4c9c78, 0x3a0dea42, 0x1a566936, 0x12bf07cc, 0xd84e}}, - {{0x142ebed2, 0x0b555b9b, 0x2a3e6498, 0x362b25d2, 0x25de4dfd, 0x0e3563d5, 0x379ce12a, 0x20269f1e, 0xe525}}}, + {{{0x1adb6ee7, 0x18c6d72d, 0x11281df8, 0x01ba864e, 0x14c9c785, 0x01bd484d, 0x159a4dba, 0x1f83e634, 0xd84e4a}}, + {{0x142ebed2, 0x16aab736, 0x08f99260, 0x11592e95, 0x1de4dfdd, 0x06ac7ab2, 0x07384a8e, 0x134f8f6f, 0xe52580}}}, /* 9*16^3*G: */ - {{{0x249e6d10, 0x253a7b3e, 0x2ac99d23, 0x02b7fceb, 0x3f6ed3f6, 0x08ae4a17, 0x2814d41b, 0x1112f799, 0xf3d4}}, - {{0x1347da3f, 0x280e3301, 0x29d6c630, 0x06b69433, 0x0a4b5bfc, 0x2e56b066, 0x0163d4ba, 0x0937e9bc, 0x0a43}}}, + {{{0x049e6d10, 0x0a74f67d, 0x0b26748e, 0x15bfe75d, 0x16ed3f60, 0x15c942ff, 0x053506c8, 0x097bccd0, 0xf3d444}}, + {{0x1347da3f, 0x101c6602, 0x075b18c2, 0x15b4a19d, 0x04b5bfc1, 0x0ad60cc5, 0x18f52eae, 0x1bf4de02, 0xa4324}}}, /* 11*16^3*G: */ - {{{0x29d33a07, 0x232cd01b, 0x239bcab4, 0x1cbb822a, 0x3df4044e, 0x21548336, 0x01d89f90, 0x194b2767, 0xae30}}, - {{0x20a0b2a6, 0x121c303d, 0x3d7e95c7, 0x270dfd77, 0x38d5cf1c, 0x339f4cf6, 0x3fe57efc, 0x3670e358, 0x6cb9}}}, + {{{0x09d33a07, 0x0659a037, 0x0e6f2ad2, 0x05dc1154, 0x1f4044e7, 0x0a9066de, 0x1627e421, 0x0593b383, 0xae3065}}, + {{0x00a0b2a6, 0x0438607b, 0x15fa571d, 0x186febbf, 0x0d5cf1c9, 0x13e99edc, 0x195fbf33, 0x1871ac7f, 0x6cb9d9}}}, /* 13*16^3*G: */ - {{{0x0c28caca, 0x165952e4, 0x08281da7, 0x1a71eef3, 0x388c9a18, 0x05f9d60c, 0x1e1c815e, 0x06ca96f5, 0xd8dc}}, - {{0x23b3ec7a, 0x36d9dba8, 0x08128f6c, 0x0c574b3b, 0x247d947d, 0x36369080, 0x2c7d58c6, 0x02b649f3, 0x8cec}}}, + {{{0x0c28caca, 0x0cb2a5c8, 0x00a0769d, 0x138f7799, 0x08c9a186, 0x1f3ac19c, 0x07205785, 0x054b7abc, 0xd8dc1b}}, + {{0x03b3ec7a, 0x0db3b751, 0x004a3db3, 0x02ba59d9, 0x07d947d3, 0x06d21012, 0x1f5631b6, 0x1b24f9d8, 0x8cec0a}}}, /* 15*16^3*G: */ - {{{0x3bc4416f, 0x2487ed98, 0x30b04028, 0x2bbf48fc, 0x32f31da7, 0x1096a340, 0x04eccd59, 0x38a4b17e, 0x2749}}, - {{0x3c6bbd8e, 0x3a62f78b, 0x2e961057, 0x27a7ed97, 0x0adb3ef5, 0x3652643f, 0x32bc4403, 0x0b538dd9, 0x50cc}}} + {{{0x1bc4416f, 0x090fdb31, 0x02c100a2, 0x1dfa47e6, 0x0f31da7a, 0x12d46819, 0x1b335650, 0x1258bf09, 0x2749e2}}, + {{0x1c6bbd8e, 0x14c5ef17, 0x1a58415f, 0x1d3f6cbd, 0x0db3ef59, 0x0a4c87e5, 0x0f1100f6, 0x09c6ece5, 0x50cc2d}}} }, { /* 1*16^4*G: */ - {{{0x03ff4640, 0x09aeb63e, 0x1552ffe5, 0x11071f95, 0x262ee053, 0x3ab016d8, 0x00c9c99c, 0x243511ec, 0x363d}}, - {{0x3bee9de9, 0x0800f1fc, 0x0199ecb6, 0x2e6a2402, 0x33363145, 0x2d114e5f, 0x32221953, 0x1ceb7f1c, 0x04e2}}}, + {{{0x03ff4640, 0x135d6c7c, 0x154bff94, 0x0838fcaa, 0x02ee0534, 0x1602db13, 0x1272673a, 0x1a88f601, 0x363d90}}, + {{0x1bee9de9, 0x1001e3f9, 0x0667b2d8, 0x13512010, 0x1363145b, 0x0229cbf9, 0x088654ed, 0x15bf8e64, 0x4e273}}}, /* 3*16^4*G: */ - {{{0x36e55dc8, 0x2e24485b, 0x2ca04394, 0x3e56adba, 0x1094426f, 0x12910301, 0x1ffb2ba8, 0x1011e431, 0x4431}}, - {{0x1be323b3, 0x076512bb, 0x2aa2e503, 0x1a8a6de7, 0x02fed7a6, 0x260dfd59, 0x366f8fe9, 0x3050b994, 0x96b0}}}, + {{{0x16e55dc8, 0x1c4890b7, 0x12810e52, 0x12b56dd5, 0x094426ff, 0x12206028, 0x1ecaea12, 0x08f218bf, 0x443140}}, + {{0x1be323b3, 0x0eca2576, 0x0a8b940c, 0x14536f3d, 0x0fed7a66, 0x01bfab21, 0x1be3fa66, 0x085cca6c, 0x96b0c1}}}, /* 5*16^4*G: */ - {{{0x301b23a8, 0x3fa52175, 0x287ee0ad, 0x1edf51c2, 0x21089dab, 0x090f56e4, 0x0a87c126, 0x3fa3619b, 0x9e22}}, - {{0x0884edae, 0x1e904f14, 0x3511cecf, 0x3df2527e, 0x1c1533c0, 0x3cfc0826, 0x22d10177, 0x3c3a7284, 0xfd2f}}}, + {{{0x101b23a8, 0x1f4a42eb, 0x01fb82b7, 0x16fa8e15, 0x1089dab7, 0x01eadc90, 0x01f04989, 0x11b0cd95, 0x9e22fe}}, + {{0x0884edae, 0x1d209e28, 0x14473b3d, 0x0f9293f6, 0x01533c0f, 0x1f8104ce, 0x14405dfc, 0x1d394245, 0xfd2ff0}}}, /* 7*16^4*G: */ - {{{0x071a70e4, 0x35d022fc, 0x35cf475d, 0x17b947d7, 0x05306dcd, 0x35a7991c, 0x22a8d2ed, 0x3db540f3, 0x508d}}, - {{0x29950984, 0x3cb96fdc, 0x28aadfed, 0x300c8a3b, 0x3e49c54e, 0x0c12a9cc, 0x3c42d777, 0x10e6e4ce, 0x154c}}}, + {{{0x071a70e4, 0x0ba045f8, 0x173d1d77, 0x1dca3ebe, 0x1306dcd5, 0x14f32382, 0x0a34bb75, 0x1aa079c5, 0x508df6}}, + {{0x09950984, 0x1972dfb9, 0x02ab7fb7, 0x006451dd, 0x049c54ec, 0x0255399f, 0x10b5ddcc, 0x13726778, 0x154c43}}}, /* 9*16^4*G: */ - {{{0x0e1abe11, 0x3abf69db, 0x1cb220f6, 0x2e487096, 0x0125b2da, 0x37d6064c, 0x09763338, 0x3fe11544, 0xe3db}}, - {{0x1fa8de63, 0x2d26b552, 0x06b5c414, 0x325f640f, 0x0a8ef3d3, 0x23e9d76e, 0x01421643, 0x3e42668d, 0x06f2}}}, + {{{0x0e1abe11, 0x157ed3b6, 0x12c883db, 0x124384b3, 0x125b2dab, 0x1ac0c980, 0x1d8cce37, 0x108aa212, 0xe3dbff}}, + {{0x1fa8de63, 0x1a4d6aa4, 0x1ad71052, 0x12fb2078, 0x08ef3d3c, 0x1d3aedc5, 0x108590e3, 0x01334682, 0x6f2f9}}}, /* 11*16^4*G: */ - {{{0x03593449, 0x33c6c8d8, 0x02a46ffd, 0x06df04b9, 0x3d014af6, 0x36704e81, 0x2940d878, 0x381931f7, 0x19ac}}, - {{0x2df83631, 0x29052e4e, 0x084068a3, 0x1c42e7d0, 0x002c46ac, 0x2f5ce765, 0x0a333bfe, 0x2480d49a, 0xe379}}}, + {{{0x03593449, 0x078d91b0, 0x0a91bff7, 0x16f825c8, 0x1014af61, 0x0e09d03e, 0x10361e36, 0x0c98fbd2, 0x19ace0}}, + {{0x0df83631, 0x120a5c9d, 0x0101a28e, 0x02173e81, 0x02c46ac7, 0x0b9ceca0, 0x0cceffaf, 0x006a4d14, 0xe37992}}}, /* 13*16^4*G: */ - {{{0x0cba6b63, 0x38fa624b, 0x10b3bb5e, 0x03f99d3f, 0x288e310a, 0x30cc8a3a, 0x07daa108, 0x033b083e, 0xd874}}, - {{0x2934c5f3, 0x3ba8db01, 0x381694ab, 0x0413d730, 0x3ac37d40, 0x29bba640, 0x132bf378, 0x304cf1ae, 0x6472}}}, + {{{0x0cba6b63, 0x11f4c496, 0x02ceed7b, 0x1fcce9fa, 0x08e310a0, 0x19914754, 0x16a84230, 0x1d841f0f, 0xd8740c}}, + {{0x0934c5f3, 0x1751b603, 0x005a52af, 0x009eb987, 0x0c37d401, 0x1774c81d, 0x0afcde29, 0x0678d726, 0x6472c1}}}, /* 15*16^4*G: */ - {{{0x1b3ec038, 0x0653fcb0, 0x20c6b276, 0x3f545ab9, 0x290a50d9, 0x20f9d8bc, 0x06083648, 0x0cce46d4, 0x58ac}}, - {{0x10246279, 0x1baa8fc4, 0x34fbbca1, 0x06410f02, 0x11fe9702, 0x1e4927a6, 0x092d9787, 0x35c1b557, 0x9163}}} + {{{0x1b3ec038, 0x0ca7f960, 0x031ac9d8, 0x1aa2d5cc, 0x10a50d9f, 0x1f3b1794, 0x020d9220, 0x07236a0c, 0x58ac33}}, + {{0x10246279, 0x17551f88, 0x13eef285, 0x12087816, 0x1fe97021, 0x0924f4c8, 0x0b65e1de, 0x00daab92, 0x9163d7}}} }, { /* 1*16^5*G: */ - {{{0x1ffdf80c, 0x27de6957, 0x15bcd1b6, 0x3929e068, 0x05638843, 0x0912d6dd, 0x3c2be8c6, 0x17c5977c, 0x8b4b}}, - {{0x1fd4fd36, 0x0fbfc319, 0x162ee56b, 0x38cd9518, 0x30da04f9, 0x2f5e04ea, 0x308b4b3f, 0x029bda34, 0x4aad}}}, + {{{0x1ffdf80c, 0x0fbcd2ae, 0x16f346da, 0x094f0342, 0x1638843e, 0x025adba2, 0x0afa3189, 0x02cbbe78, 0x8b4b5f}}, + {{0x1fd4fd36, 0x1f7f8632, 0x18bb95ac, 0x066ca8c2, 0x0da04f9e, 0x0bc09d58, 0x02d2cfef, 0x0ded1a61, 0x4aad0a}}}, /* 3*16^5*G: */ - {{{0x355812dd, 0x028a960b, 0x12d30e2a, 0x1119c8d5, 0x18f78e3d, 0x2afb5b01, 0x3352f0b6, 0x2f5ea4bf, 0x7029}}, - {{0x1a2d2927, 0x087319ac, 0x3b2c73c7, 0x36ba1090, 0x0683ac47, 0x19512b8c, 0x0b3d27dd, 0x3eb6bf7a, 0xb0ee}}}, + {{{0x155812dd, 0x05152c17, 0x0b4c38a8, 0x08ce46aa, 0x0f78e3d4, 0x1f6b602c, 0x14bc2daa, 0x0f525fe6, 0x7029bd}}, + {{0x1a2d2927, 0x10e63358, 0x0cb1cf1c, 0x15d08487, 0x083ac47d, 0x0a257183, 0x0f49f759, 0x1b5fbd16, 0xb0eefa}}}, /* 5*16^5*G: */ - {{{0x3d486ed1, 0x27395a0e, 0x1565b6a4, 0x116fae92, 0x0f756057, 0x35042763, 0x25c99009, 0x3b72bab9, 0x9ccf}}, - {{0x35e95d8d, 0x3db567b5, 0x1592aa24, 0x0859d65a, 0x0b341124, 0x08920480, 0x232cfb61, 0x135c4f5a, 0x7c2f}}}, + {{{0x1d486ed1, 0x0e72b41d, 0x1596da92, 0x0b7d7492, 0x17560574, 0x0084ec67, 0x12640275, 0x195d5ccb, 0x9ccfed}}, + {{0x15e95d8d, 0x1b6acf6b, 0x164aa893, 0x02ceb2d2, 0x13411242, 0x12409005, 0x0b3ed848, 0x0e27ad46, 0x7c2f4d}}}, /* 7*16^5*G: */ - {{{0x1bd0eaca, 0x081ac69d, 0x22d4ab7a, 0x31d15dae, 0x24df19d0, 0x23f78cf2, 0x1414335a, 0x12e1d8d0, 0xcd9a}}, - {{0x2bff4acc, 0x39bebed6, 0x16f634f6, 0x09ece3bb, 0x3ea08b01, 0x1222ba4c, 0x0f23e815, 0x161e687a, 0xf045}}}, + {{{0x1bd0eaca, 0x10358d3a, 0x0b52ade8, 0x0e8aed74, 0x0df19d0c, 0x1ef19e52, 0x050cd6a3, 0x10ec6828, 0xcd9a4b}}, + {{0x0bff4acc, 0x137d7dad, 0x1bd8d3db, 0x0f671dda, 0x0a08b012, 0x0457499f, 0x08fa0552, 0x0f343d1e, 0xf04558}}}, /* 9*16^5*G: */ - {{{0x07bc57c6, 0x08254e8f, 0x2b276cbf, 0x00f5e88f, 0x16309449, 0x3cb4ba4f, 0x19bea884, 0x220be23b, 0xad09}}, - {{0x2e4a0ab8, 0x28cb03b6, 0x190e2d3c, 0x0c474dcd, 0x1abe5f7b, 0x061b1ca7, 0x3a52ba28, 0x302310be, 0x7243}}}, + {{{0x07bc57c6, 0x104a9d1e, 0x0c9db2fc, 0x07af447d, 0x03094490, 0x169749eb, 0x0faa213c, 0x05f11db3, 0xad0988}}, + {{0x0e4a0ab8, 0x1196076d, 0x0438b4f2, 0x023a6e6b, 0x0be5f7b3, 0x036394ed, 0x14ae8a06, 0x11885f74, 0x7243c0}}}, /* 11*16^5*G: */ - {{{0x2ba56302, 0x2a0c31ca, 0x30f1862e, 0x01aa4deb, 0x3ad2e0f5, 0x368b4aa7, 0x0a41f1ea, 0x0a42bacf, 0xd9d1}}, - {{0x08291c29, 0x2ab76bea, 0x3a74f2ae, 0x0e6bb367, 0x2386e417, 0x1c5719c9, 0x13eed029, 0x0c44fb0b, 0x7eb5}}}, + {{{0x0ba56302, 0x14186395, 0x03c618ba, 0x0d526f5e, 0x0d2e0f50, 0x116954fd, 0x107c7ab6, 0x015d6794, 0xd9d129}}, + {{0x08291c29, 0x156ed7d4, 0x09d3caba, 0x135d9b3f, 0x186e4173, 0x0ae33931, 0x1bb40a5c, 0x027d85a7, 0x7eb531}}}, /* 13*16^5*G: */ - {{{0x34d1243a, 0x2b34dc13, 0x354a5fdb, 0x2c49808f, 0x3f558402, 0x3486b018, 0x16cef91c, 0x1e7794e7, 0xbc50}}, - {{0x055db68a, 0x172545a2, 0x1f47169f, 0x1fb93d6c, 0x3fc8d75f, 0x31cae537, 0x05cbb8ee, 0x0a8ece9c, 0x6506}}}, + {{{0x14d1243a, 0x1669b827, 0x15297f6e, 0x024c047e, 0x1558402b, 0x10d6031f, 0x13be4734, 0x1bca73ad, 0xbc5079}}, + {{0x055db68a, 0x0e4a8b44, 0x1d1c5a7d, 0x1dc9eb63, 0x1c8d75f7, 0x195ca6ff, 0x12ee3bb1, 0x07674e0b, 0x65062a}}}, /* 15*16^5*G: */ - {{{0x374a3f9f, 0x2349139a, 0x00981690, 0x21e99977, 0x32625ac2, 0x37aab9f6, 0x3c7e8913, 0x29df9417, 0x4d31}}, - {{0x301e0ba7, 0x3f2c0904, 0x2e00a754, 0x3dbed46d, 0x002753cb, 0x063ce31e, 0x0575b06b, 0x07b25826, 0x2224}}} + {{{0x174a3f9f, 0x06922735, 0x02605a42, 0x0f4ccbb8, 0x0625ac28, 0x15573ed9, 0x1fa244f7, 0x0fca0bf8, 0x4d31a7}}, + {{0x101e0ba7, 0x1e581209, 0x18029d53, 0x0df6a36d, 0x02753cbf, 0x079c63c0, 0x1d6c1ac6, 0x192c130a, 0x22241e}}} }, { /* 1*16^6*G: */ - {{{0x1232fcda, 0x2d845649, 0x2c0e77bc, 0x0036ffe9, 0x1548c7b7, 0x1dc7002f, 0x3996d6bf, 0x2ea9b976, 0x723c}}, - {{0x1eb39f5f, 0x07701a76, 0x37949480, 0x1828194d, 0x024d6e26, 0x044dd222, 0x0c498a92, 0x19ed5657, 0x96e8}}}, + {{{0x1232fcda, 0x1b08ac92, 0x1039def2, 0x01b7ff4d, 0x148c7b70, 0x18e005ea, 0x05b5afdd, 0x14dcbb73, 0x723cba}}, + {{0x1eb39f5f, 0x0ee034ec, 0x1e525200, 0x0140ca6e, 0x04d6e266, 0x09ba4441, 0x1262a484, 0x16ab2b98, 0x96e867}}}, /* 3*16^6*G: */ - {{{0x00633cb1, 0x159f827a, 0x1d021132, 0x168892da, 0x181fcb57, 0x189cc848, 0x2cad400c, 0x273cc5ea, 0x6dde}}, - {{0x27ce6b34, 0x1f7526a9, 0x3859ef35, 0x2c9ff6b3, 0x3a66a880, 0x27be1a86, 0x3e41d5c9, 0x3ef9e9c1, 0x9188}}}, + {{{0x00633cb1, 0x0b3f04f4, 0x140844c9, 0x144496d3, 0x01fcb575, 0x1399090c, 0x0b500318, 0x1e62f559, 0x6dde9c}}, + {{0x07ce6b34, 0x1eea4d53, 0x0167bcd5, 0x04ffb59f, 0x066a880b, 0x17c350dd, 0x10757267, 0x1cf4e0fc, 0x9188fb}}}, /* 5*16^6*G: */ - {{{0x2933f3c5, 0x06694634, 0x1f125224, 0x1683dc45, 0x07b85008, 0x12edfe39, 0x1cde813c, 0x29cb356d, 0x486f}}, - {{0x0afb0f53, 0x2b529c6b, 0x30f23b79, 0x366de0f3, 0x08f19f62, 0x3122ebb3, 0x3dd43e48, 0x08c67d5a, 0x62e1}}}, + {{{0x0933f3c5, 0x0cd28c69, 0x1c494890, 0x141ee22b, 0x1b850085, 0x1dbfc723, 0x17a04f12, 0x059ab6b9, 0x486fa7}}, + {{0x0afb0f53, 0x16a538d6, 0x03c8ede6, 0x136f079e, 0x0f19f62d, 0x045d7664, 0x150f9231, 0x033ead7b, 0x62e123}}}, /* 7*16^6*G: */ - {{{0x1e99f728, 0x2f565089, 0x2f12204e, 0x1cdd7ef9, 0x2a530367, 0x13fc9edd, 0x0af4fb66, 0x1a5d2a25, 0x2479}}, - {{0x2baaebff, 0x1e80145b, 0x175a2d83, 0x36fcf025, 0x0d664a5a, 0x0ba1f9f6, 0x33001ec5, 0x23511a23, 0xe3d7}}}, + {{{0x1e99f728, 0x1eaca112, 0x1c48813a, 0x06ebf7cd, 0x05303677, 0x1f93dbb5, 0x1d3ed993, 0x0e951295, 0x247969}}, + {{0x0baaebff, 0x1d0028b7, 0x1d68b60d, 0x17e7812a, 0x1664a5ad, 0x143f3ec6, 0x0007b14b, 0x088d11e6, 0xe3d78d}}}, /* 9*16^6*G: */ - {{{0x2fb0079a, 0x27831b50, 0x3926049c, 0x1be7bdc8, 0x33832491, 0x2967b9da, 0x15ff0631, 0x32f6a8f5, 0x2f39}}, - {{0x2c5690ba, 0x388a5cc0, 0x02a0230f, 0x3ecfef22, 0x0da58b9b, 0x24db409e, 0x239834da, 0x36f784e1, 0xabea}}}, + {{{0x0fb0079a, 0x0f0636a1, 0x04981272, 0x1f3dee47, 0x18324916, 0x0cf73b59, 0x1fc18c69, 0x1b547aab, 0x2f39cb}}, + {{0x0c5690ba, 0x1114b981, 0x0a808c3f, 0x167f7910, 0x1a58b9bf, 0x1b6813c6, 0x060d36a4, 0x1bc270c7, 0xabeadb}}}, /* 11*16^6*G: */ - {{{0x24f7ab73, 0x24cc02cb, 0x14443a77, 0x38f53aa7, 0x34aed262, 0x0e7a1b14, 0x161ba56a, 0x075b0c9f, 0xe5a3}}, - {{0x30561f42, 0x244e8ff1, 0x00cba213, 0x2311126a, 0x0ece5dbf, 0x062a5de9, 0x29d7a0c1, 0x230f6347, 0x3778}}}, + {{{0x04f7ab73, 0x09980597, 0x1110e9de, 0x07a9d53a, 0x0aed262e, 0x0f43629a, 0x06e95a8e, 0x0d864fac, 0xe5a31d}}, + {{0x10561f42, 0x089d1fe3, 0x032e884e, 0x18889350, 0x0ce5dbf8, 0x054bbd27, 0x15e83046, 0x07b1a3d3, 0x37788c}}}, /* 13*16^6*G: */ - {{{0x014dcd86, 0x23e4a68f, 0x2bf71b58, 0x31750825, 0x11dcf11f, 0x03766081, 0x13447df5, 0x27528345, 0xcc38}}, - {{0x08f0a873, 0x23adb767, 0x27e78746, 0x315f863f, 0x2910ca05, 0x1a2f6efa, 0x2bbed9b5, 0x13f5983d, 0x93ae}}}, + {{{0x014dcd86, 0x07c94d1e, 0x0fdc6d62, 0x0ba8412d, 0x1dcf11fc, 0x0ecc1028, 0x111f7d43, 0x0941a2a6, 0xcc389d}}, + {{0x08f0a873, 0x075b6ece, 0x1f9e1d1a, 0x0afc31fc, 0x110ca05c, 0x05eddf54, 0x0fb66d5a, 0x1acc1ed7, 0x93ae4f}}}, /* 15*16^6*G: */ - {{{0x38819311, 0x13e71bad, 0x08771472, 0x0f87b884, 0x35ed1f0b, 0x0285f833, 0x1e902375, 0x2472275c, 0x7f92}}, - {{0x2c2eb125, 0x2a7e6d5e, 0x086a174a, 0x02aa9027, 0x2415b612, 0x037a3114, 0x03ef0f5d, 0x034418fb, 0x9da0}}} + {{{0x18819311, 0x07ce375b, 0x01dc51c9, 0x1c3dc421, 0x1ed1f0b3, 0x10bf067a, 0x0408dd42, 0x1913ae3d, 0x7f9291}}, + {{0x0c2eb125, 0x14fcdabd, 0x01a85d2a, 0x15548139, 0x015b6120, 0x0f462292, 0x1bc3d743, 0x020c7d87, 0x9da00d}}} }, { /* 1*16^7*G: */ - {{{0x0e7dd7fa, 0x294cfb28, 0x3a919839, 0x11e5848d, 0x02d3b509, 0x3fbb204b, 0x2bf98ba5, 0x293524ef, 0xeebf}}, - {{0x21de8999, 0x37f53f6b, 0x311f712d, 0x393370e9, 0x38089d9a, 0x39fb6bc5, 0x2f0f269e, 0x2328e5c3, 0x5d9a}}}, + {{{0x0e7dd7fa, 0x1299f650, 0x0a4660e6, 0x0f2c246f, 0x0d3b5094, 0x17640961, 0x1e62e97f, 0x1a9277d7, 0xeebfa4}}, + {{0x01de8999, 0x0fea7ed7, 0x047dc4b7, 0x099b874e, 0x0089d9ae, 0x1f6d78bc, 0x03c9a7b9, 0x1472e1de, 0x5d9a8c}}}, /* 3*16^7*G: */ - {{{0x3b7ceceb, 0x0fd9e3fe, 0x097faf0f, 0x2967e4e2, 0x2e681473, 0x3ee049bd, 0x2d45036f, 0x2188109d, 0x437a}}, - {{0x16c181e1, 0x0d8ef30d, 0x08f97827, 0x0883f3f7, 0x1297ff87, 0x23fada67, 0x2c32f69b, 0x1ae84fba, 0x0b91}}}, + {{{0x1b7ceceb, 0x1fb3c7fd, 0x05febc3c, 0x0b3f2711, 0x0681473a, 0x1c0937b7, 0x1140dbfe, 0x04084eda, 0x437a86}}, + {{0x16c181e1, 0x1b1de61a, 0x03e5e09c, 0x041f9fb9, 0x097ff872, 0x1f5b4ce9, 0x0cbda6e3, 0x1427dd58, 0xb916b}}}, /* 5*16^7*G: */ - {{{0x097f96f2, 0x1635ca78, 0x2c8735cd, 0x208d4a74, 0x3cc27335, 0x2df8ee68, 0x089bc83c, 0x27c4f8a9, 0xa9ef}}, - {{0x16c04be4, 0x00f556c1, 0x29b4702c, 0x13e26bd6, 0x3b613db7, 0x1bb8583a, 0x19d7cd95, 0x33396515, 0xe814}}}, + {{{0x097f96f2, 0x0c6b94f0, 0x121cd735, 0x046a53a5, 0x0c273358, 0x1f1dcd1e, 0x06f20f2d, 0x027c5491, 0xa9ef9f}}, + {{0x16c04be4, 0x01eaad82, 0x06d1c0b0, 0x1f135eb5, 0x1613db74, 0x170b075d, 0x15f3655b, 0x1cb28ab3, 0xe814cc}}}, /* 7*16^7*G: */ - {{{0x350cf77e, 0x302ad684, 0x0a8ab0db, 0x36fd5d15, 0x2a064207, 0x209f5a7e, 0x135be553, 0x01507b87, 0x66d8}}, - {{0x20eaa3a6, 0x297e5ebe, 0x3b1b76d2, 0x112d0ead, 0x1613f694, 0x0750814d, 0x3fb42c3f, 0x37f9ccbf, 0x51cf}}}, + {{{0x150cf77e, 0x0055ad09, 0x0a2ac36f, 0x17eae8a9, 0x0064207d, 0x13eb4fd5, 0x16f954e0, 0x083dc3a6, 0x66d805}}, + {{0x00eaa3a6, 0x12fcbd7d, 0x0c6ddb4a, 0x0968756f, 0x013f6944, 0x0a1029ab, 0x0d0b0fc7, 0x1ce65fff, 0x51cfdf}}}, /* 9*16^7*G: */ - {{{0x07213a5a, 0x0d5218a2, 0x05fa62b9, 0x1cc8129e, 0x0cc3c80b, 0x14228719, 0x03fa2bf3, 0x01784d94, 0x62ac}}, - {{0x346a9e45, 0x04348703, 0x17994efc, 0x16424060, 0x292579e5, 0x179e781e, 0x1a6e4d39, 0x2f7ce834, 0x236f}}}, + {{{0x07213a5a, 0x1aa43144, 0x17e98ae4, 0x064094f0, 0x0c3c80b7, 0x0450e326, 0x1e8afcd4, 0x1c26ca07, 0x62ac05}}, + {{0x146a9e45, 0x08690e07, 0x1e653bf0, 0x12120302, 0x12579e55, 0x13cf03d4, 0x1b934e57, 0x1e741a34, 0x236fbd}}}, /* 11*16^7*G: */ - {{{0x27bad12b, 0x0c3f5261, 0x2f66e1ec, 0x357a803a, 0x2f2db385, 0x184ebd71, 0x08f5b5bf, 0x31125c91, 0xca13}}, - {{0x1723b0f2, 0x25a67d1a, 0x1a575668, 0x1c2adc44, 0x2da3d663, 0x17e993aa, 0x287c8ac1, 0x0260d870, 0x83aa}}}, + {{{0x07bad12b, 0x187ea4c3, 0x1d9b87b0, 0x0bd401d5, 0x12db385d, 0x09d7ae37, 0x1d6d6fd8, 0x092e4891, 0xca13c4}}, + {{0x1723b0f2, 0x0b4cfa34, 0x095d59a2, 0x0156e223, 0x1a3d6637, 0x1d327556, 0x1f22b057, 0x106c3850, 0x83aa09}}}, /* 13*16^7*G: */ - {{{0x1c80414e, 0x36bb97e5, 0x166cf7fd, 0x3be2a18b, 0x209e4914, 0x04713d11, 0x12ae85ac, 0x2c4069c1, 0x1cec}}, - {{0x12169a3b, 0x32ba524b, 0x07231d0d, 0x1d55f951, 0x2dad1690, 0x2a8ca0d7, 0x17cfb4e5, 0x1819a582, 0xf343}}}, + {{{0x1c80414e, 0x0d772fca, 0x19b3dff7, 0x1f150c5a, 0x09e4914e, 0x0e27a230, 0x0ba16b04, 0x0034e0a5, 0x1cecb1}}, + {{0x12169a3b, 0x0574a496, 0x1c8c7437, 0x0aafca88, 0x1ad16907, 0x11941af6, 0x13ed396a, 0x0cd2c12f, 0xf34360}}}, /* 15*16^7*G: */ - {{{0x0ed810a9, 0x13d6f231, 0x0700155c, 0x22274fcf, 0x1f23924f, 0x036bd7c7, 0x38f9cc95, 0x241d4135, 0x2a69}}, - {{0x3a9b4728, 0x3e1ace23, 0x2c145c7c, 0x1f51fa5f, 0x3b04fc66, 0x3161a553, 0x1ffdac3e, 0x00e6db0f, 0x54f9}}} + {{{0x0ed810a9, 0x07ade462, 0x1c005571, 0x113a7e78, 0x123924f8, 0x0d7af8ef, 0x1e732543, 0x0ea09af1, 0x2a6990}}, + {{0x1a9b4728, 0x1c359c47, 0x105171f3, 0x1a8fd2fd, 0x104fc667, 0x0c34aa7d, 0x1f6b0fb1, 0x136d87bf, 0x54f903}}} }, { /* 1*16^8*G: */ - {{{0x39a48db0, 0x3f5e0d6c, 0x33c03bfe, 0x048568a6, 0x3bde459f, 0x0742826d, 0x27167279, 0x11369a5b, 0x100f}}, - {{0x2bc65a09, 0x3ef57358, 0x35195ac0, 0x3fd2863f, 0x090666b7, 0x23ccc030, 0x00b772ec, 0x384c64a8, 0xcdd9}}}, + {{{0x19a48db0, 0x1ebc1ad9, 0x0f00effb, 0x042b4536, 0x1de459f1, 0x08504dbd, 0x059c9e47, 0x1b4d2dce, 0x100f44}}, + {{0x0bc65a09, 0x1deae6b1, 0x14656b03, 0x1e9431fe, 0x10666b7f, 0x19980604, 0x0ddcbb23, 0x06325401, 0xcdd9e1}}}, /* 3*16^8*G: */ - {{{0x15bc15b4, 0x32e684d2, 0x25a2ee69, 0x1d40a391, 0x17ca8d92, 0x163ba73b, 0x2adc9ed8, 0x038b947b, 0x10e9}}, - {{0x18aa258d, 0x13af9825, 0x2bb6a883, 0x296258c0, 0x2d1f754c, 0x1ea3185a, 0x1e0424d5, 0x0dc0e035, 0xc68a}}}, + {{{0x15bc15b4, 0x05cd09a4, 0x168bb9a7, 0x0a051c8c, 0x1ca8d927, 0x0774e76b, 0x1727b616, 0x05ca3dd5, 0x10e90e}}, + {{0x18aa258d, 0x075f304a, 0x0edaa20d, 0x0b12c605, 0x11f754ca, 0x14630b56, 0x0109355e, 0x00701abc, 0xc68a37}}}, /* 5*16^8*G: */ - {{{0x3fe75269, 0x374ff0c0, 0x13d33182, 0x1de8f301, 0x0b7dcda3, 0x16e42dc5, 0x01638457, 0x0bd0b695, 0xf742}}, - {{0x17e49bd5, 0x22603a1c, 0x0a398e01, 0x2ce88dfd, 0x3635977f, 0x339f72e7, 0x3093fd18, 0x0bc68cc4, 0x406c}}}, + {{{0x1fe75269, 0x0e9fe181, 0x0f4cc60b, 0x0f47980a, 0x17dcda37, 0x1c85b8a5, 0x18e115d6, 0x085b4a82, 0xf7422f}}, + {{0x17e49bd5, 0x04c07438, 0x08e63806, 0x07446fe9, 0x035977fb, 0x13ee5cfb, 0x04ff4633, 0x03466261, 0x406c2f}}}, /* 7*16^8*G: */ - {{{0x35a7175f, 0x14ed9a5b, 0x31cf42a6, 0x2e39dc74, 0x15debbed, 0x1e69560b, 0x03cff728, 0x2b4105f5, 0x2d8c}}, - {{0x3b9d592a, 0x3cdeee46, 0x0b5e5e0c, 0x211aff67, 0x2c9d377a, 0x08cbe984, 0x0a94a7bb, 0x0ee0cc63, 0xc73f}}}, + {{{0x15a7175f, 0x09db34b7, 0x073d0a99, 0x11cee3a6, 0x1debbedb, 0x0d2ac16a, 0x13fdca1e, 0x0082fa87, 0x2d8cad}}, + {{0x1b9d592a, 0x19bddc8d, 0x0d797833, 0x08d7fb39, 0x09d377a8, 0x197d3096, 0x0529eec8, 0x10663195, 0xc73f3b}}}, /* 9*16^8*G: */ - {{{0x14b51045, 0x0d326f0e, 0x31c25b3e, 0x31b225bc, 0x28cf73bb, 0x1cf53ac7, 0x26ea58ae, 0x3f476e62, 0x1ecb}}, - {{0x02c70026, 0x0e99c404, 0x036422d5, 0x240191ad, 0x1a9b38b1, 0x342ec612, 0x1c3a6447, 0x388c22e6, 0x1cf6}}}, + {{{0x14b51045, 0x1a64de1c, 0x07096cf8, 0x0d912de6, 0x0cf73bbc, 0x1ea758f4, 0x1a962b9c, 0x03b7314d, 0x1ecbfd}}, + {{0x02c70026, 0x1d338808, 0x0d908b54, 0x000c8d68, 0x09b38b19, 0x05d8c24d, 0x0e9911f4, 0x06117338, 0x1cf6e2}}}, /* 11*16^8*G: */ - {{{0x29358533, 0x1eb35d9b, 0x0fb4b9df, 0x2a4cfe75, 0x132a8c10, 0x25568a47, 0x3752883e, 0x25317f95, 0x9a08}}, - {{0x0360ba08, 0x2cf87177, 0x380ddadf, 0x29b96f6e, 0x0fc32165, 0x05f57e55, 0x38fc31f9, 0x20f10806, 0xa798}}}, + {{{0x09358533, 0x1d66bb37, 0x1ed2e77d, 0x1267f3a9, 0x12a8c10a, 0x0ad148e9, 0x14a20fa5, 0x18bfcaee, 0x9a0894}}, + {{0x0360ba08, 0x19f0e2ee, 0x00376b7e, 0x0dcb7b77, 0x1c32165a, 0x1eafcaa7, 0x1f0c7e45, 0x18840371, 0xa79883}}}, /* 13*16^8*G: */ - {{{0x198ef7f6, 0x25101758, 0x2078f9f6, 0x08fcfdde, 0x38aea659, 0x272149ce, 0x3d2e35bd, 0x361276d3, 0x664d}}, - {{0x1d1eac94, 0x1d25bfcd, 0x38e6ecee, 0x0f4eacc6, 0x0458cffc, 0x12339774, 0x27932a14, 0x0805c5fc, 0xad51}}}, + {{{0x198ef7f6, 0x0a202eb0, 0x01e3e7da, 0x07e7eef4, 0x0aea6592, 0x042939dc, 0x0b8d6f67, 0x093b69fa, 0x664dd8}}, + {{0x1d1eac94, 0x1a4b7f9a, 0x039bb3b9, 0x1a756637, 0x058cffc3, 0x0672ee82, 0x04ca8512, 0x02e2fe4f, 0xad5120}}}, /* 15*16^8*G: */ - {{{0x03c934b3, 0x03029adf, 0x30ae2c4e, 0x0c7d6016, 0x11a7022b, 0x07659a60, 0x0b863823, 0x0ea4ddf4, 0x8211}}, - {{0x042c6a0f, 0x1f9798ab, 0x24468037, 0x07df09a6, 0x20c628aa, 0x19b3cad6, 0x23666084, 0x2e36b26b, 0x8da1}}} + {{{0x03c934b3, 0x060535be, 0x02b8b138, 0x03eb00b6, 0x1a7022b3, 0x0cb34c08, 0x018e08c7, 0x126efa17, 0x82113a}}, + {{0x042c6a0f, 0x1f2f3156, 0x111a00dd, 0x1ef84d34, 0x0c628aa1, 0x16795ad0, 0x19982119, 0x1b5935c6, 0x8da1b8}}} }, { /* 1*16^9*G: */ - {{{0x2534fd2d, 0x322b379b, 0x0f3b3852, 0x1fe35119, 0x04c017a7, 0x2489e928, 0x3ed1b1dc, 0x06f898b1, 0xe103}}, - {{0x1456a00d, 0x113c63ca, 0x21ced79a, 0x24b75067, 0x17535af2, 0x1a905d96, 0x0405e6bb, 0x1864a250, 0x9d70}}}, + {{{0x0534fd2d, 0x04566f37, 0x1cece14b, 0x1f1a88c9, 0x0c017a77, 0x113d2502, 0x146c7724, 0x1c4c58fd, 0xe1031b}}, + {{0x1456a00d, 0x0278c794, 0x073b5e69, 0x05ba833c, 0x1535af29, 0x120bb2cb, 0x0179aeda, 0x12512808, 0x9d7061}}}, /* 3*16^9*G: */ - {{{0x2f028d83, 0x1e588ebb, 0x27439615, 0x25649b6e, 0x1e69db61, 0x2af96857, 0x385ec6a5, 0x3df138f1, 0xa7eb}}, - {{0x19d0bed1, 0x1900e4ae, 0x30539199, 0x28e249d2, 0x04804b47, 0x271cddc1, 0x362d5cfd, 0x054beff8, 0x6205}}}, + {{{0x0f028d83, 0x1cb11d77, 0x1d0e5855, 0x0b24db74, 0x069db619, 0x1f2d0aef, 0x17b1a96a, 0x189c78f0, 0xa7ebf7}}, + {{0x19d0bed1, 0x1201c95c, 0x014e4665, 0x07124e96, 0x0804b47a, 0x039bb822, 0x0b573f67, 0x05f7fc6c, 0x620515}}}, /* 5*16^9*G: */ - {{{0x27dd5cfa, 0x2b839008, 0x309d4b5b, 0x227144df, 0x2346336a, 0x31a94d09, 0x24f4c1cd, 0x282372c0, 0x5b5c}}, - {{0x1e48e98c, 0x19929be6, 0x33269d3e, 0x3419f32b, 0x069094bf, 0x07c33aa2, 0x15825e99, 0x2dbdc2a8, 0x3ecc}}}, + {{{0x07dd5cfa, 0x17072011, 0x02752d6e, 0x138a26fe, 0x146336a8, 0x1529a131, 0x1d307371, 0x11b96049, 0x5b5ca0}}, + {{0x1e48e98c, 0x132537cc, 0x0c9a74f9, 0x00cf995e, 0x09094bfd, 0x18675443, 0x0097a647, 0x1ee1542b, 0x3eccb6}}}, /* 7*16^9*G: */ - {{{0x23531f82, 0x2e54a38c, 0x10c2c9f2, 0x144c9aec, 0x022c29ff, 0x3cf9d227, 0x14bb5cce, 0x09ab3044, 0x046f}}, - {{0x0bceda07, 0x1417f22c, 0x2b55c7fa, 0x09651736, 0x032579d0, 0x0dc2b0bf, 0x382eace2, 0x12cc58d6, 0x6b80}}}, + {{{0x03531f82, 0x1ca94719, 0x030b27ca, 0x0264d762, 0x02c29ff5, 0x1f3a44e1, 0x0ed733bc, 0x15982229, 0x46f26}}, + {{0x0bceda07, 0x082fe458, 0x0d571fe9, 0x0b28b9b5, 0x12579d02, 0x185617e1, 0x0bab388d, 0x062c6b70, 0x6b804b}}}, /* 9*16^9*G: */ - {{{0x10432711, 0x02c550dc, 0x1916b906, 0x0502cbf7, 0x19645acf, 0x25bc3c22, 0x0efb535f, 0x09b64c78, 0xc119}}, - {{0x2fe2610c, 0x1249878b, 0x0f34055e, 0x2ae48b28, 0x0cc6cf83, 0x252fc61b, 0x1b689184, 0x3e331f49, 0x8be1}}}, + {{{0x10432711, 0x058aa1b8, 0x045ae418, 0x08165fbb, 0x1645acf1, 0x1787844c, 0x1ed4d7e5, 0x1b263c1d, 0xc11926}}, + {{0x0fe2610c, 0x04930f17, 0x1cd01579, 0x17245941, 0x0c6cf83a, 0x05f8c366, 0x1a246125, 0x198fa4b6, 0x8be1f8}}}, /* 11*16^9*G: */ - {{{0x21257963, 0x05e61d3e, 0x34aa861c, 0x006354b0, 0x0979c45b, 0x2ed52d4e, 0x08f2e6cd, 0x11ba7ada, 0x6908}}, - {{0x066f9835, 0x295d9665, 0x1c92b253, 0x2f0f2a08, 0x2fbb7f6c, 0x05c093e4, 0x3ebc5b40, 0x17f2dfcf, 0xe248}}}, + {{{0x01257963, 0x0bcc3a7d, 0x12aa1870, 0x031aa586, 0x179c45b0, 0x1aa5a9c4, 0x1cb9b36e, 0x1d3d6d11, 0x690846}}, + {{0x066f9835, 0x12bb2cca, 0x124ac94e, 0x18795043, 0x1bb7f6cb, 0x18127c97, 0x0f16d005, 0x196fe7fd, 0xe2485f}}}, /* 13*16^9*G: */ - {{{0x1ee23ace, 0x3444e52f, 0x14dd2fd2, 0x321f196d, 0x232915de, 0x1d54b7d2, 0x220babba, 0x3dfee324, 0xfb3d}}, - {{0x1722e8de, 0x0277bd32, 0x2d27f5ee, 0x1c9c50bf, 0x3ab58a9e, 0x09455036, 0x33c5652a, 0x0a6f0471, 0x510e}}}, + {{{0x1ee23ace, 0x0889ca5e, 0x1374bf4b, 0x10f8cb6a, 0x12915dec, 0x0a96fa51, 0x02eaee9d, 0x1f719244, 0xfb3df7}}, + {{0x1722e8de, 0x04ef7a64, 0x149fd7b8, 0x04e285fd, 0x0b58a9e7, 0x08aa06dd, 0x11594a89, 0x178238e7, 0x510e29}}}, /* 15*16^9*G: */ - {{{0x10272351, 0x181f3fbd, 0x19ff1098, 0x1cd2cf7e, 0x31cd4170, 0x228facea, 0x0518b3eb, 0x17b093d7, 0x6dd8}}, - {{0x3fc7664b, 0x2c1fe8ad, 0x3e0817c9, 0x1f1bfdf0, 0x1c41b787, 0x101fe6bd, 0x3427e09d, 0x19fd0487, 0x16ea}}} + {{{0x10272351, 0x103e7f7a, 0x07fc4261, 0x06967bf3, 0x1cd41707, 0x11f59d58, 0x062cfae2, 0x1849eb8a, 0x6dd85e}}, + {{0x1fc7664b, 0x183fd15b, 0x18205f26, 0x18dfef87, 0x041b7877, 0x03fcd7ae, 0x09f82750, 0x1e8243e8, 0x16ea67}}} }, { /* 1*16^10*G: */ - {{{0x1094696d, 0x3579a236, 0x01d6af52, 0x3e2c99a9, 0x3bd7ec5c, 0x0a0e7c50, 0x15b530ac, 0x1b2b91b5, 0xfeea}}, - {{0x18090088, 0x05577afc, 0x041442d3, 0x072255f3, 0x3ecd5c98, 0x39384afc, 0x0e1bab06, 0x1adb25f7, 0xe57c}}}, + {{{0x1094696d, 0x0af3446c, 0x075abd4b, 0x1164cd48, 0x1d7ec5cf, 0x01cf8a1d, 0x0d4c2b0a, 0x15c8daab, 0xfeea6c}}, + {{0x18090088, 0x0aaef5f8, 0x10510b4c, 0x1912af98, 0x0cd5c981, 0x07095f9f, 0x06eac1b9, 0x0d92fb9c, 0xe57c6b}}}, /* 3*16^10*G: */ - {{{0x08dfd587, 0x1e4d86ed, 0x1b026560, 0x312e8e32, 0x35a12d5e, 0x19eaa8b3, 0x0508b348, 0x2d06eb3d, 0x5084}}, - {{0x11470e89, 0x39e7a5fe, 0x091f5606, 0x2dbd581a, 0x2927475d, 0x2a9b2154, 0x00d31619, 0x18c68766, 0x34a9}}}, + {{{0x08dfd587, 0x1c9b0dda, 0x0c099581, 0x09747193, 0x1a12d5ec, 0x1d55167a, 0x022cd219, 0x03759e8a, 0x5084b4}}, + {{0x11470e89, 0x13cf4bfc, 0x047d581b, 0x0deac0d1, 0x127475db, 0x13642a94, 0x14c5866a, 0x0343b301, 0x34a963}}}, /* 5*16^10*G: */ - {{{0x3ab34cc6, 0x0208c985, 0x0f30a12d, 0x030a5d9f, 0x0d7128c8, 0x2cfc7f46, 0x2d5ea53f, 0x300f8190, 0x4f14}}, - {{0x187e681f, 0x17b094be, 0x281dd022, 0x378f33a3, 0x262540b9, 0x0e9c3d0e, 0x0e894c65, 0x342a32a9, 0x7b53}}}, + {{{0x1ab34cc6, 0x0411930b, 0x1cc284b4, 0x1852ecf9, 0x17128c80, 0x1f8fe8c6, 0x17a94fec, 0x07c0c85a, 0x4f14c0}}, + {{0x187e681f, 0x0f61297c, 0x00774089, 0x1c799d1d, 0x02540b9d, 0x1387a1d3, 0x0253194e, 0x1519549d, 0x7b53d0}}}, /* 7*16^10*G: */ - {{{0x1241d90d, 0x109dc404, 0x32444f83, 0x073c5076, 0x1dd363e8, 0x10d8257b, 0x39ed1d41, 0x2e1f9271, 0xa74d}}, - {{0x3f7adad4, 0x0c9462e0, 0x0a0a313f, 0x3b9424d1, 0x0171c8a9, 0x37422962, 0x3eef327f, 0x24736bc8, 0xf786}}}, + {{{0x1241d90d, 0x013b8808, 0x09113e0d, 0x19e283b6, 0x1d363e81, 0x1b04af6e, 0x1b475050, 0x0fc938f3, 0xa74db8}}, + {{0x1f7adad4, 0x1928c5c1, 0x0828c4fc, 0x1ca12689, 0x171c8a9e, 0x08452c40, 0x1bcc9ff7, 0x19b5e47d, 0xf78691}}}, /* 9*16^10*G: */ - {{{0x31c1ae1f, 0x17b32888, 0x2cd40b2a, 0x1b9631a2, 0x23565845, 0x373513ae, 0x2a2cf9ac, 0x3e95d12e, 0x6901}}, - {{0x122838b0, 0x3e0cc197, 0x1c77a930, 0x27cee979, 0x1c900dd7, 0x2d4e030a, 0x3c212461, 0x1722089c, 0x35de}}}, + {{{0x11c1ae1f, 0x0f665111, 0x13502ca9, 0x1cb18d15, 0x15658456, 0x06a275d1, 0x0b3e6b37, 0x0ae89754, 0x6901fa}}, + {{0x122838b0, 0x1c19832e, 0x11dea4c3, 0x1e774bcb, 0x0900dd79, 0x09c0614e, 0x0849186d, 0x11044e78, 0x35de5c}}}, /* 11*16^10*G: */ - {{{0x327a4bdb, 0x2c0c4206, 0x1494cac4, 0x1a9b410d, 0x3ba35d04, 0x12d90fc6, 0x38127a24, 0x360b4750, 0x8d3c}}, - {{0x269a8a2c, 0x0f4d31f3, 0x30ad296c, 0x38e01f4d, 0x36236ed4, 0x3efe7401, 0x241f470c, 0x0958603b, 0x9bd4}}}, + {{{0x127a4bdb, 0x1818840d, 0x12532b12, 0x14da086a, 0x1a35d046, 0x1b21f8dd, 0x049e8912, 0x05a3a870, 0x8d3cd8}}, + {{0x069a8a2c, 0x1e9a63e7, 0x02b4a5b0, 0x0700fa6e, 0x0236ed4e, 0x1fce803b, 0x07d1c33e, 0x0c301dc8, 0x9bd425}}}, /* 13*16^10*G: */ - {{{0x34ec1d2d, 0x10334f1a, 0x27d8f454, 0x0267d71b, 0x3b691fd9, 0x2759ca59, 0x24739afe, 0x20d8f581, 0xeaf9}}, - {{0x0c838452, 0x33f9d581, 0x3e84b53f, 0x3d4b5515, 0x3199aaa9, 0x08a2839a, 0x38d22775, 0x060e9ff9, 0xe518}}}, + {{{0x14ec1d2d, 0x00669e35, 0x1f63d151, 0x133eb8dc, 0x1691fd90, 0x0b394b3d, 0x1ce6bfa7, 0x0c7ac0c8, 0xeaf983}}, + {{0x0c838452, 0x07f3ab02, 0x1a12d4ff, 0x0a5aa8af, 0x199aaa9f, 0x14507358, 0x1489dd48, 0x074ffcf1, 0xe51818}}}, /* 15*16^10*G: */ - {{{0x045ae767, 0x32cd6fdc, 0x289771cb, 0x1cea72e7, 0x06e5d8c2, 0x103814b0, 0x1b63466f, 0x2f458ebb, 0xfb95}}, - {{0x3bbf0e11, 0x214fa82b, 0x259f1341, 0x05bd1c62, 0x02275bb8, 0x013674da, 0x0ddbc520, 0x0536046a, 0x664c}}} + {{{0x045ae767, 0x059adfb8, 0x025dc72f, 0x0753973d, 0x0e5d8c27, 0x07029603, 0x18d19bd0, 0x02c75db6, 0xfb95bd}}, + {{0x1bbf0e11, 0x029f5057, 0x167c4d06, 0x0de8e314, 0x0275bb81, 0x06ce9b41, 0x16f14801, 0x1b02351b, 0x664c14}}} }, { /* 1*16^11*G: */ - {{{0x01ec6cb1, 0x0fea5e2f, 0x08583de3, 0x3b595f60, 0x3fca3cfe, 0x1ef92f9b, 0x09cdcb36, 0x2a476441, 0xda67}}, - {{0x3a68be1d, 0x3a7aa389, 0x0f740a17, 0x31eb7142, 0x1780e5de, 0x118fdfb2, 0x242bc41f, 0x2a8d5205, 0x9bac}}}, + {{{0x01ec6cb1, 0x1fd4bc5e, 0x0160f78c, 0x1acafb01, 0x1ca3cfee, 0x1f25f37f, 0x1372cd9e, 0x03b22093, 0xda67a9}}, + {{0x1a68be1d, 0x14f54713, 0x1dd0285f, 0x0f5b8a11, 0x180e5dec, 0x11fbf64b, 0x0af107d1, 0x06a902c8, 0x9bacaa}}}, /* 3*16^11*G: */ - {{{0x15bc8a44, 0x3bf74194, 0x3e151a19, 0x10405df2, 0x1a5fc768, 0x159692e9, 0x0eda3d38, 0x20160f3f, 0x4d01}}, - {{0x1adbc09e, 0x3c7e5324, 0x182da362, 0x250811a1, 0x16381396, 0x26ea001f, 0x0f5d367e, 0x31b0632d, 0x3a33}}}, + {{{0x15bc8a44, 0x17ee8328, 0x18546867, 0x0202ef97, 0x05fc7684, 0x12d25d2d, 0x168f4e15, 0x0b079f9d, 0x4d0180}}, + {{0x1adbc09e, 0x18fca648, 0x00b68d8b, 0x08408d0b, 0x03813969, 0x1d4003eb, 0x174d9fa6, 0x1831969e, 0x3a33c6}}}, /* 5*16^11*G: */ - {{{0x25daeb00, 0x306ad4a1, 0x2645f76b, 0x08fac933, 0x36e9d159, 0x32da89ce, 0x0f957082, 0x0541f7d7, 0x2f66}}, - {{0x033992c0, 0x089d9e26, 0x15d308c1, 0x337b89c6, 0x00add06e, 0x254dea08, 0x2b33f6ef, 0x0484dbd4, 0xfd5c}}}, + {{{0x05daeb00, 0x00d5a943, 0x1917ddaf, 0x07d6499c, 0x0e9d1592, 0x1b5139db, 0x055c20b2, 0x00fbeb9f, 0x2f6615}}, + {{0x033992c0, 0x113b3c4c, 0x174c2304, 0x1bdc4e32, 0x0add06ec, 0x09bd4100, 0x0cfdbbe5, 0x026dea56, 0xfd5c12}}}, /* 7*16^11*G: */ - {{{0x116aa6d9, 0x20aa4282, 0x3702dcf1, 0x18b22d91, 0x035a3836, 0x3c5d3686, 0x247d2254, 0x045f417f, 0xf594}}, - {{0x3f2e50cf, 0x1f41a5ba, 0x26b5b86c, 0x249de20f, 0x14bceb7a, 0x176f6ac2, 0x31b12cf6, 0x18695ba5, 0xcaa7}}}, + {{{0x116aa6d9, 0x01548504, 0x1c0b73c6, 0x05916c8e, 0x15a38366, 0x0ba6d0c1, 0x1f48953c, 0x0fa0bfc8, 0xf59411}}, + {{0x1f2e50cf, 0x1e834b75, 0x1ad6e1b1, 0x04ef107c, 0x0bceb7a9, 0x0ded584a, 0x0c4b3d97, 0x14add2e3, 0xcaa761}}}, /* 9*16^11*G: */ - {{{0x3ac6f4c0, 0x2ab80e55, 0x04bdc4cc, 0x13a37a33, 0x16711dda, 0x070e2f9a, 0x19cdec4e, 0x135fc7d3, 0x0f2d}}, - {{0x32339b58, 0x1f9eeeb5, 0x0242656e, 0x1a8429e4, 0x01e71e8f, 0x2c9ff7ce, 0x3de4d17f, 0x27e15fa4, 0x3ec8}}}, + {{{0x1ac6f4c0, 0x15701cab, 0x12f71332, 0x1d1bd198, 0x0711dda4, 0x01c5f34b, 0x137b1387, 0x0fe3e9b3, 0xf2d4d}}, + {{0x12339b58, 0x1f3ddd6b, 0x090995b9, 0x14214f20, 0x1e71e8f6, 0x13fef9c0, 0x19345fec, 0x10afd27b, 0x3ec89f}}}, /* 11*16^11*G: */ - {{{0x1f428cb2, 0x215414ff, 0x2a22b55d, 0x0e08bf59, 0x18d0f123, 0x1e860565, 0x14bbd1eb, 0x33b0b8a8, 0x1d5d}}, - {{0x095b189b, 0x397b4402, 0x36044a51, 0x0fa44be1, 0x2f0b88bd, 0x1e1e0921, 0x2c8c50d0, 0x1020ec50, 0x6e5c}}}, + {{{0x1f428cb2, 0x02a829fe, 0x088ad576, 0x1045facd, 0x0d0f1233, 0x10c0acac, 0x0ef47ade, 0x185c5429, 0x1d5dce}}, + {{0x095b189b, 0x12f68804, 0x18112947, 0x1d225f0e, 0x10b88bd3, 0x03c12437, 0x0314341e, 0x10762859, 0x6e5c40}}}, /* 13*16^11*G: */ - {{{0x28381273, 0x2c3aa23e, 0x293dae5f, 0x10dda581, 0x0126ced8, 0x3aa6cb31, 0x167439fd, 0x28bf4c02, 0x89d9}}, - {{0x1309773d, 0x00facfbb, 0x1127324a, 0x1875a02b, 0x0f62f58f, 0x2abc81db, 0x26f50377, 0x096d1475, 0xdfca}}}, + {{{0x08381273, 0x1875447d, 0x04f6b97e, 0x06ed2c0d, 0x126ced84, 0x14d96620, 0x1d0e7f7a, 0x1fa6012c, 0x89d9a2}}, + {{0x1309773d, 0x01f59f76, 0x049cc928, 0x03ad015a, 0x162f58f6, 0x17903b67, 0x1d40ddea, 0x168a3acd, 0xdfca25}}}, /* 15*16^11*G: */ - {{{0x35c71d91, 0x330cacb2, 0x2894fd21, 0x25178b8a, 0x1afece23, 0x28704c45, 0x10ae1c52, 0x06e1e0e9, 0x8319}}, - {{0x22148a61, 0x02e7b023, 0x10445ee7, 0x2847d45d, 0x3cae8a17, 0x1b784f45, 0x01b709e0, 0x1fc55ce0, 0xe0ac}}} + {{{0x15c71d91, 0x06195965, 0x0253f487, 0x08bc5c55, 0x0fece239, 0x0e0988ad, 0x0b8714a8, 0x10f074a1, 0x83191b}}, + {{0x02148a61, 0x05cf6047, 0x01117b9c, 0x023ea2ea, 0x0ae8a17a, 0x0f09e8be, 0x0dc2781b, 0x02ae7003, 0xe0ac7f}}} }, { /* 1*16^12*G: */ - {{{0x1a37b7c0, 0x1d517330, 0x311069f5, 0x02343dee, 0x322151ec, 0x00024d7b, 0x34cdda6e, 0x13ea82cc, 0x5390}}, - {{0x022771c8, 0x372c25ac, 0x14434699, 0x26666078, 0x0d3c1c13, 0x27b32b08, 0x0106d88c, 0x21f42f20, 0x5bc0}}}, + {{{0x1a37b7c0, 0x1aa2e660, 0x0441a7d5, 0x11a1ef76, 0x02151ec0, 0x0049af79, 0x13769b80, 0x15416669, 0x53904f}}, + {{0x022771c8, 0x0e584b58, 0x110d1a67, 0x133303c2, 0x13c1c139, 0x16656106, 0x01b62327, 0x1a179002, 0x5bc087}}}, /* 3*16^12*G: */ - {{{0x08a2050e, 0x06b10bf9, 0x15f8a677, 0x0bbd55d8, 0x079b8974, 0x1da731b9, 0x0731896b, 0x093f492f, 0x6737}}, - {{0x061d3d70, 0x24326924, 0x3349cc2b, 0x1aeb3f50, 0x086b6dbe, 0x120b026a, 0x24a20203, 0x2095e25a, 0xe4cf}}}, + {{{0x08a2050e, 0x0d6217f2, 0x17e299dc, 0x1deaaec2, 0x19b89742, 0x14e63723, 0x0c625add, 0x1fa4978e, 0x673724}}, + {{0x061d3d70, 0x0864d248, 0x0d2730ae, 0x1759fa86, 0x06b6dbe6, 0x01604d44, 0x088080d2, 0x0af12d49, 0xe4cf82}}}, /* 5*16^12*G: */ - {{{0x02de63bf, 0x2fdb920e, 0x3261c66c, 0x0ebd4ca1, 0x2166a8e0, 0x26298c7d, 0x34c309e5, 0x3be91cb7, 0x4366}}, - {{0x217924cd, 0x0b1a9023, 0x2aa6d6b0, 0x0ec31496, 0x0268eaf3, 0x094df84c, 0x2d7ce2ee, 0x36426fb8, 0x2e7d}}}, + {{{0x02de63bf, 0x1fb7241c, 0x098719b2, 0x15ea650e, 0x166a8e03, 0x05318fb0, 0x10c27966, 0x148e5be9, 0x4366ef}}, + {{0x017924cd, 0x16352047, 0x0a9b5ac0, 0x1618a4b5, 0x068eaf33, 0x09bf0981, 0x1f38bb89, 0x0137dc5a, 0x2e7dd9}}}, /* 7*16^12*G: */ - {{{0x06f96190, 0x04149ffc, 0x3c9525ef, 0x3c0b7a41, 0x3aa75fd1, 0x3955a599, 0x1ab1f97b, 0x14d89e64, 0x7bd7}}, - {{0x2bda00f6, 0x0f45c812, 0x20ea695a, 0x03f31707, 0x3827d6ce, 0x3591d250, 0x26309d5e, 0x3cacf6ee, 0x8336}}}, + {{{0x06f96190, 0x08293ff8, 0x125497bc, 0x005bd20f, 0x0a75fd1f, 0x0ab4b33d, 0x0c7e5ef9, 0x0c4f3235, 0x7bd753}}, + {{0x0bda00f6, 0x1e8b9025, 0x03a9a568, 0x1f98b83c, 0x027d6ce0, 0x123a4a1c, 0x0c2757b5, 0x167b774c, 0x8336f2}}}, /* 9*16^12*G: */ - {{{0x16ad41ed, 0x0ec54c55, 0x0f035243, 0x022b0d7d, 0x18dc9203, 0x0d067a24, 0x2d5c1afa, 0x249ef76a, 0x4f7e}}, - {{0x3e642d57, 0x3d0d5e19, 0x2af775bd, 0x1cc51c53, 0x28f6a62e, 0x26037d4e, 0x08b10552, 0x1d1455aa, 0xdfe7}}}, + {{{0x16ad41ed, 0x1d8a98aa, 0x1c0d490c, 0x11586be9, 0x0dc92030, 0x00cf448c, 0x1706be8d, 0x0f7bb55a, 0x4f7e92}}, + {{0x1e642d57, 0x1a1abc33, 0x0bddd6f7, 0x0628e29d, 0x0f6a62e7, 0x006fa9d4, 0x0c4154a6, 0x0a2ad511, 0xdfe774}}}, /* 11*16^12*G: */ - {{{0x27748690, 0x3e981449, 0x0630b01c, 0x15e41376, 0x133d007d, 0x114ac7b7, 0x11ccc94b, 0x32e19f4a, 0x2355}}, - {{0x0c89582b, 0x1f11d4c5, 0x11c93914, 0x0a1a1633, 0x2a7c5858, 0x2e17b056, 0x1e1f8f55, 0x3c62969c, 0x21c2}}}, + {{{0x07748690, 0x1d302893, 0x18c2c073, 0x0f209bb0, 0x13d007d5, 0x0958f6e9, 0x133252d1, 0x10cfa523, 0x2355cb}}, + {{0x0c89582b, 0x1e23a98a, 0x0724e451, 0x10d0b19a, 0x07c58582, 0x02f60ad5, 0x07e3d56e, 0x114b4e3c, 0x21c2f1}}}, /* 13*16^12*G: */ - {{{0x0ade7f16, 0x36ba8858, 0x0be028c6, 0x272eba4f, 0x275d24ae, 0x164aadb0, 0x1a56c013, 0x2096e6cf, 0x0b66}}, - {{0x08c56217, 0x251109a1, 0x3e7cd2bd, 0x090f037c, 0x17a97fb7, 0x29daea2d, 0x09b3fef3, 0x282e0638, 0xa1fb}}}, + {{{0x0ade7f16, 0x0d7510b0, 0x0f80a31b, 0x1975d279, 0x15d24ae9, 0x0955b613, 0x15b004d6, 0x0b7367b4, 0xb6682}}, + {{0x08c56217, 0x0a221342, 0x19f34af6, 0x08781be7, 0x1a97fb72, 0x1b5d45ab, 0x0cffbce9, 0x17031c13, 0xa1fba0}}}, /* 15*16^12*G: */ - {{{0x19060d5b, 0x241ac08a, 0x03a3a7c2, 0x1184ec47, 0x3951cb90, 0x026cbf67, 0x1022cb61, 0x010f3c2f, 0xf602}}, - {{0x1af88f13, 0x1bdbd42c, 0x3dd1a3f7, 0x2a95b4ad, 0x0f7bea37, 0x2a3d92b1, 0x0cf19881, 0x2dc1b07c, 0xf036}}} + {{{0x19060d5b, 0x08358114, 0x0e8e9f0a, 0x0c276238, 0x151cb904, 0x0d97ecfc, 0x08b2d842, 0x079e17a0, 0xf60204}}, + {{0x1af88f13, 0x17b7a858, 0x17468fdd, 0x14ada56f, 0x17bea37a, 0x07b25627, 0x1c66206a, 0x00d83e19, 0xf036b7}}} }, { /* 1*16^13*G: */ - {{{0x3ad86047, 0x3fe567d0, 0x29b8bcae, 0x2d4e810e, 0x0a906779, 0x3329dd93, 0x183a7719, 0x3342f4d6, 0x8e7b}}, - {{0x0460372a, 0x284011fa, 0x3fd68b3e, 0x3a238b91, 0x29514579, 0x0c410832, 0x1a4b3940, 0x1dc2ca8f, 0x10b7}}}, + {{{0x1ad86047, 0x1fcacfa1, 0x06e2f2bb, 0x0a740875, 0x0906779b, 0x053bb265, 0x0e9dc673, 0x017a6b30, 0x8e7bcd}}, + {{0x0460372a, 0x108023f4, 0x1f5a2cfa, 0x111c5c8f, 0x1514579e, 0x08210654, 0x12ce500c, 0x016547b4, 0x10b777}}}, /* 3*16^13*G: */ - {{{0x041ead4b, 0x3fa21e68, 0x11b03c1f, 0x1d7b7eda, 0x3e76be3a, 0x11cd3beb, 0x3337ec71, 0x03032323, 0xbfc9}}, - {{0x06fedaed, 0x114b1bc2, 0x2e0ae3e7, 0x11a3bfcc, 0x042d36fb, 0x29c63754, 0x0ded24db, 0x206c7827, 0x7a94}}}, + {{{0x041ead4b, 0x1f443cd0, 0x06c0f07f, 0x0bdbf6d2, 0x076be3a7, 0x19a77d7f, 0x0dfb1c51, 0x019191e6, 0xbfc90c}}, + {{0x06fedaed, 0x02963784, 0x182b8f9d, 0x0d1dfe65, 0x02d36fb4, 0x18c6ea82, 0x1b4936e9, 0x163c139b, 0x7a9481}}}, /* 5*16^13*G: */ - {{{0x35bb3b3e, 0x1b9ef41d, 0x39f73cb2, 0x1d4d85fb, 0x2d3f5b50, 0x1664fa30, 0x3aaa4dca, 0x3c472f8f, 0x732d}}, - {{0x17366693, 0x315df87b, 0x0c58436c, 0x276b5b59, 0x253916e6, 0x38956100, 0x39977cb7, 0x240fb7a3, 0x7f41}}}, + {{{0x15bb3b3e, 0x173de83b, 0x07dcf2c9, 0x0a6c2fdf, 0x13f5b507, 0x0c9f4616, 0x0a937296, 0x0397c7f5, 0x732df1}}, + {{0x17366693, 0x02bbf0f6, 0x11610db3, 0x1b5adac9, 0x13916e69, 0x12ac2012, 0x05df2df8, 0x07dbd1f3, 0x7f4190}}}, /* 7*16^13*G: */ - {{{0x088dc3b9, 0x17d6cf06, 0x1774c99c, 0x299a493a, 0x17ef6019, 0x2a210332, 0x147b428d, 0x252e580e, 0x4ce0}}, - {{0x25c0de52, 0x3053dedb, 0x1ea06502, 0x0816c832, 0x36aca216, 0x2d360329, 0x29b3ed57, 0x03eeafc6, 0x0539}}}, + {{{0x088dc3b9, 0x0fad9e0c, 0x1dd32671, 0x0cd249d2, 0x1ef6019a, 0x0420664b, 0x1ed0a36a, 0x172c0728, 0x4ce094}}, + {{0x05c0de52, 0x00a7bdb7, 0x1a81940b, 0x00b64193, 0x0aca2162, 0x06c0653b, 0x0cfb55ed, 0x1757e353, 0x5390f}}}, /* 9*16^13*G: */ - {{{0x0aaafe5a, 0x30dd782c, 0x109aedd4, 0x151c2ce9, 0x023fd0e2, 0x229aa56c, 0x267de96d, 0x23addbf1, 0x9a96}}, - {{0x0ed975c0, 0x39aff509, 0x1e70cc0c, 0x2d620299, 0x061d0ee7, 0x319b40f6, 0x3ba2954f, 0x3ec1e9b4, 0xabf6}}}, + {{{0x0aaafe5a, 0x01baf058, 0x026bb753, 0x08e1674a, 0x03fd0e25, 0x1354ad81, 0x1f7a5b62, 0x16edf8cc, 0x9a968e}}, + {{0x0ed975c0, 0x135fea12, 0x19c33033, 0x0b1014cb, 0x01d0ee7b, 0x13681ec3, 0x08a553f1, 0x00f4da77, 0xabf6fb}}}, /* 11*16^13*G: */ - {{{0x334c6397, 0x1d472fe7, 0x074cd093, 0x374f6d40, 0x36b22107, 0x2bbe0094, 0x161954f0, 0x3efb405c, 0xd3c6}}, - {{0x28cb3f9c, 0x07f23415, 0x05e0e00b, 0x031dc224, 0x2ab6468a, 0x20e5364b, 0x22af1945, 0x34b15797, 0x4a0d}}}, + {{{0x134c6397, 0x1a8e5fcf, 0x1d33424d, 0x1a7b6a00, 0x0b22107d, 0x17c0129b, 0x06553c2b, 0x1da02e2c, 0xd3c6fb}}, + {{0x08cb3f9c, 0x0fe4682b, 0x1783802c, 0x18ee1120, 0x0b6468a0, 0x1ca6c975, 0x0bc65160, 0x18abcbc5, 0x4a0dd2}}}, /* 13*16^13*G: */ - {{{0x0ac3137e, 0x26e0964c, 0x1af64461, 0x2496d8a9, 0x2b3953fe, 0x3c1a9daa, 0x243b8e02, 0x38e604a4, 0x4cbd}}, - {{0x2ec02fe6, 0x0023c573, 0x08ead60c, 0x24e9eb96, 0x14c370d1, 0x24a84d2e, 0x36159500, 0x151823c4, 0x6ce5}}}, + {{{0x0ac3137e, 0x0dc12c98, 0x0bd91186, 0x04b6c54b, 0x13953fe9, 0x0353b555, 0x0ee380bc, 0x13025248, 0x4cbde3}}, + {{0x0ec02fe6, 0x00478ae7, 0x03ab5830, 0x074f5cb1, 0x0c370d19, 0x1509a5ca, 0x05654024, 0x0c11e26c, 0x6ce554}}}, /* 15*16^13*G: */ - {{{0x20fbf84b, 0x1e88c1b3, 0x03f0b8a4, 0x3123f2ef, 0x14cebb03, 0x3671cc30, 0x16247b8b, 0x0ccf20ac, 0x4b9d}}, - {{0x236c3c48, 0x0e7b92d2, 0x2f5b5e62, 0x19b550f8, 0x39b7eb67, 0x04f66099, 0x0c152553, 0x31fef893, 0xfd7f}}} + {{{0x00fbf84b, 0x1d118367, 0x0fc2e291, 0x091f9778, 0x0cebb03c, 0x0e39860a, 0x091ee2f6, 0x0790562c, 0x4b9d33}}, + {{0x036c3c48, 0x1cf725a5, 0x1d6d7988, 0x0daa87c5, 0x1b7eb676, 0x1ecc133c, 0x054954c4, 0x1f7c4998, 0xfd7fc7}}} }, { /* 1*16^14*G: */ - {{{0x19c43862, 0x2a107856, 0x397e6690, 0x29fd3c60, 0x381bde71, 0x02061a26, 0x1ff21e6d, 0x3b4d3073, 0x385e}}, - {{0x142e5453, 0x01163f95, 0x086dc8cc, 0x0c13bb08, 0x2bf4576b, 0x077867a7, 0x223f5670, 0x3af0fa3a, 0x283b}}}, + {{{0x19c43862, 0x1420f0ac, 0x05f99a42, 0x0fe9e307, 0x01bde71a, 0x00c344dc, 0x1c879b42, 0x069839bf, 0x385eed}}, + {{0x142e5453, 0x022c7f2a, 0x01b72330, 0x009dd841, 0x1f4576b3, 0x0f0cf4f5, 0x0fd59c07, 0x187d1d44, 0x283beb}}}, /* 3*16^14*G: */ - {{{0x36e2d9b3, 0x12f4c1aa, 0x338d6351, 0x36e4a0c6, 0x0f845641, 0x0ba984e7, 0x305e75e1, 0x053ce5f1, 0x19a3}}, - {{0x0baaaf33, 0x154bb897, 0x004be56d, 0x00874749, 0x3528b3a5, 0x2597e21f, 0x328dd234, 0x363d76b1, 0x6cac}}}, + {{{0x16e2d9b3, 0x05e98355, 0x0e358d45, 0x17250636, 0x1845641d, 0x15309ce7, 0x179d784b, 0x1e72f8e0, 0x19a314}}, + {{0x0baaaf33, 0x0a97712e, 0x012f95b5, 0x043a3a48, 0x128b3a50, 0x12fc43fa, 0x03748d25, 0x1ebb58e5, 0x6cacd8}}}, /* 5*16^14*G: */ - {{{0x12f00480, 0x36161fac, 0x100dcee7, 0x0d620128, 0x36721920, 0x32618d93, 0x0daa355d, 0x3b52e56a, 0x5840}}, - {{0x3e22cf9e, 0x164b578a, 0x2ae38721, 0x1d489514, 0x1dd8daba, 0x1a37aa85, 0x3f141079, 0x369ac882, 0x670c}}}, + {{{0x12f00480, 0x0c2c3f58, 0x00373b9f, 0x0b100942, 0x07219203, 0x0c31b27b, 0x0a8d5772, 0x0972b51b, 0x5840ed}}, + {{0x1e22cf9e, 0x0c96af15, 0x0b8e1c85, 0x0a44a8a5, 0x1d8daba7, 0x06f550ae, 0x05041e5a, 0x0d64417e, 0x670cda}}}, /* 7*16^14*G: */ - {{{0x23f54c42, 0x12137ba0, 0x29a3dc8e, 0x37068f09, 0x0e532545, 0x16307d3b, 0x118fb1dc, 0x00694d1a, 0x9f57}}, - {{0x2feb6a21, 0x18387124, 0x219e5278, 0x3b9e12ac, 0x29bfdd89, 0x256dad5c, 0x19e57bfb, 0x23ee2007, 0xce7b}}}, + {{{0x03f54c42, 0x0426f741, 0x068f7239, 0x1834784d, 0x0532545d, 0x060fa767, 0x03ec7716, 0x14a68d23, 0x9f5701}}, + {{0x0feb6a21, 0x1070e249, 0x067949e1, 0x1cf09564, 0x1bfdd89e, 0x0db5ab94, 0x195efee5, 0x171003b3, 0xce7b8f}}}, /* 9*16^14*G: */ - {{{0x1522461a, 0x3a504cca, 0x3c718327, 0x2cc28996, 0x3ef9a0bc, 0x2e1c0419, 0x28cfc01b, 0x045a48d6, 0x27f6}}, - {{0x07301a2d, 0x2a932be7, 0x28639446, 0x2606c836, 0x028ee8e4, 0x2315849d, 0x26ad2ea4, 0x3c6a6402, 0xe512}}}, + {{{0x1522461a, 0x14a09994, 0x11c60c9f, 0x06144cb7, 0x0f9a0bcb, 0x0380833f, 0x13f006ee, 0x0d246b51, 0x27f611}}, + {{0x07301a2d, 0x152657ce, 0x018e511a, 0x103641b5, 0x08ee8e49, 0x02b093a1, 0x0b4ba923, 0x1532014d, 0xe512f1}}}, /* 11*16^14*G: */ - {{{0x114f36b9, 0x338b26cb, 0x3b9f390c, 0x2632aed8, 0x34a98125, 0x2fcbd0d7, 0x2f941261, 0x1e615b3b, 0x6407}}, - {{0x24b4b50a, 0x252c7ba7, 0x19ceeb28, 0x36821c12, 0x1a7b6c8c, 0x035d7f61, 0x16efaef9, 0x24a3d139, 0xda61}}}, + {{{0x114f36b9, 0x07164d96, 0x0e7ce433, 0x119576c7, 0x0a981259, 0x197a1afa, 0x0504986f, 0x10ad9ddf, 0x640779}}, + {{0x04b4b50a, 0x0a58f74f, 0x073baca2, 0x1410e093, 0x07b6c8cd, 0x0bafec2d, 0x1bebbe43, 0x11e89cad, 0xda6192}}}, /* 13*16^14*G: */ - {{{0x14d6b76f, 0x3bd8f7e6, 0x0c815dbc, 0x396a7eed, 0x1dfeae7f, 0x3dc22f02, 0x1669f452, 0x1438c721, 0xa237}}, - {{0x0dcca8da, 0x0764b332, 0x1b848d14, 0x1c1f047f, 0x011113e7, 0x0be8f935, 0x3de6dac3, 0x26c529b9, 0xf733}}}, + {{{0x14d6b76f, 0x17b1efcc, 0x120576f3, 0x0b53f769, 0x1feae7fe, 0x1845e04e, 0x1a7d14bd, 0x1c6390ac, 0xa23750}}, + {{0x0dcca8da, 0x0ec96664, 0x0e123450, 0x00f823fb, 0x11113e77, 0x1d1f26a0, 0x19b6b0cb, 0x0294dcfb, 0xf7339b}}}, /* 15*16^14*G: */ - {{{0x3ceee475, 0x0bba7193, 0x0ed782b1, 0x1ab20a10, 0x0aff41ab, 0x0f0087cf, 0x2378d5ed, 0x2b01e8fc, 0xbbf1}}, - {{0x07fe5067, 0x1188a802, 0x38b41d68, 0x3ae76250, 0x315fe324, 0x20f320da, 0x060e6108, 0x2e37bab5, 0xb4bf}}} + {{{0x1ceee475, 0x1774e327, 0x1b5e0ac4, 0x15905081, 0x0ff41ab6, 0x0010f9e5, 0x1e357b4f, 0x00f47e46, 0xbbf1ac}}, + {{0x07fe5067, 0x03115004, 0x02d075a1, 0x173b1287, 0x15fe324e, 0x1e641b58, 0x03984220, 0x1bdd5a8c, 0xb4bfb8}}} }, { /* 1*16^15*G: */ - {{{0x03fac3a7, 0x181bb61b, 0x147fbc9c, 0x377e1296, 0x3dfa180f, 0x31ce9104, 0x0f191637, 0x366e00fb, 0x06f9}}, - {{0x3a842160, 0x21a24180, 0x0281002d, 0x29374bd7, 0x05c4d47e, 0x238a8c39, 0x059ba69b, 0x31a3980c, 0x7c80}}}, + {{{0x03fac3a7, 0x10376c36, 0x11fef271, 0x1bf094b2, 0x1fa180fd, 0x19d2209e, 0x06458df1, 0x17007d9e, 0x6f9d9}}, + {{0x1a842160, 0x03448301, 0x0a0400b6, 0x09ba5eb8, 0x1c4d47ea, 0x11518722, 0x06e9a6e3, 0x11cc060b, 0x7c80c6}}}, /* 3*16^15*G: */ - {{{0x121ce204, 0x13b5d7a3, 0x26763d52, 0x29c96390, 0x26f72fb2, 0x1d361672, 0x3c64fb83, 0x107458ac, 0x43ca}}, - {{0x134a8f6b, 0x1494113a, 0x2a4a468e, 0x2db1eccf, 0x1ba31f9a, 0x143e4863, 0x023fa1c6, 0x16a0b8dc, 0xdcea}}}, + {{{0x121ce204, 0x076baf46, 0x19d8f549, 0x0e4b1c84, 0x0f72fb2a, 0x06c2ce53, 0x193ee0dd, 0x1a2c5678, 0x43ca41}}, + {{0x134a8f6b, 0x09282274, 0x09291a39, 0x0d8f667d, 0x1a31f9ab, 0x07c90c6d, 0x0fe87194, 0x105c6e04, 0xdcea5a}}}, /* 5*16^15*G: */ - {{{0x2be6efda, 0x13f3a4b3, 0x07280596, 0x0b53fcfe, 0x1a506d92, 0x1bdc8de1, 0x12bf5b66, 0x01bbc8a2, 0x9c3e}}, - {{0x27aefc7d, 0x3c503cca, 0x336fdf7d, 0x0ef21a1e, 0x226fd5d4, 0x02cb5133, 0x2923d8af, 0x027979d8, 0xa7b7}}}, + {{{0x0be6efda, 0x07e74967, 0x1ca01659, 0x1a9fe7f0, 0x0506d922, 0x1b91bc2d, 0x0fd6d99b, 0x1de45125, 0x9c3e06}}, + {{0x07aefc7d, 0x18a07995, 0x0dbf7df7, 0x1790d0f6, 0x06fd5d43, 0x196a2671, 0x08f62bc2, 0x1cbcec52, 0xa7b709}}}, /* 7*16^15*G: */ - {{{0x06c88be2, 0x2449ead7, 0x06ee5e27, 0x0b1e0834, 0x30775bea, 0x1c9d6760, 0x20f033bb, 0x22a8c4f8, 0x5d6f}}, - {{0x0d7ad75d, 0x24b954fc, 0x2bf92c28, 0x2adbe3a9, 0x08bc20ed, 0x2abcceac, 0x2d4e8c71, 0x2c636355, 0xadc4}}}, + {{{0x06c88be2, 0x0893d5ae, 0x1bb9789e, 0x18f041a0, 0x0775bea2, 0x13acec18, 0x1c0ceedc, 0x14627c41, 0x5d6f8a}}, + {{0x0d7ad75d, 0x0972a9f8, 0x0fe4b0a2, 0x16df1d4d, 0x0bc20eda, 0x1799d584, 0x13a31c6a, 0x11b1aada, 0xadc4b1}}}, /* 9*16^15*G: */ - {{{0x12d1b844, 0x0a24d46e, 0x173e484f, 0x2700e0b0, 0x388bc5c6, 0x2c570f04, 0x20d5fc86, 0x0d70c129, 0xf57d}}, - {{0x21266837, 0x192eaef5, 0x0915c6a4, 0x01a5c80c, 0x24634c70, 0x134fd6a7, 0x2f4d9790, 0x0f67aa63, 0x707f}}}, + {{{0x12d1b844, 0x1449a8dc, 0x1cf9213c, 0x18070582, 0x08bc5c69, 0x0ae1e09c, 0x157f21ac, 0x186094c1, 0xf57d35}}, + {{0x01266837, 0x125d5deb, 0x04571a91, 0x0d2e4061, 0x0634c700, 0x09fad4f2, 0x1365e413, 0x13d531de, 0x707f3d}}}, /* 11*16^15*G: */ - {{{0x3cc7cb09, 0x0d3401fc, 0x1d1b4352, 0x31fada28, 0x1871463b, 0x1b87fb8f, 0x194a5f59, 0x181e8e99, 0x13e7}}, - {{0x08079160, 0x2f9d6a28, 0x2b576411, 0x3ab8aed9, 0x34299d65, 0x17f7616c, 0x3b8b1e32, 0x32237a3e, 0x284d}}}, + {{{0x1cc7cb09, 0x1a6803f9, 0x146d0d48, 0x0fd6d143, 0x071463bc, 0x10ff71ec, 0x1297d65b, 0x0f474cb2, 0x13e760}}, + {{0x08079160, 0x1f3ad450, 0x0d5d9046, 0x15c576cd, 0x0299d65e, 0x1eec2d9a, 0x02c78c97, 0x11bd1f77, 0x284dc8}}}, /* 13*16^15*G: */ - {{{0x18cdee05, 0x01833849, 0x32ec3b90, 0x1d87ec85, 0x06901da8, 0x00942c6c, 0x182e6240, 0x28c895a0, 0x29be}}, - {{0x262651c8, 0x39280d66, 0x0c698e39, 0x3f0c6db2, 0x305ec7f9, 0x026cfee1, 0x29a0ea90, 0x36689a43, 0x7c40}}}, + {{{0x18cdee05, 0x03067092, 0x0bb0ee40, 0x0c3f642e, 0x0901da87, 0x12858d83, 0x0b989000, 0x044ad030, 0x29bea3}}, + {{0x062651c8, 0x12501acd, 0x11a638e7, 0x18636d91, 0x05ec7f9f, 0x0d9fdc38, 0x083aa402, 0x144d21d3, 0x7c40d9}}}, /* 15*16^15*G: */ - {{{0x12f18ada, 0x06db1d58, 0x3dbdbcc1, 0x182f64ee, 0x3d4a59d4, 0x0dbebfcc, 0x288e7d9c, 0x1e1b48e0, 0xf521}}, - {{0x23953516, 0x375a2bf4, 0x05bf0981, 0x17bd28db, 0x11d1d6aa, 0x09840af3, 0x0db57ecc, 0x1befd80e, 0xe068}}} + {{{0x12f18ada, 0x0db63ab0, 0x16f6f304, 0x017b2777, 0x14a59d46, 0x17d7f99e, 0x039f670d, 0x0da47051, 0xf52178}}, + {{0x03953516, 0x0eb457e9, 0x16fc2607, 0x1de946d8, 0x1d1d6aa5, 0x10815e68, 0x0d5fb309, 0x17ec071b, 0xe0686f}}} }, { /* 1*16^16*G: */ - {{{0x02d0e6bd, 0x0edf839d, 0x30f5e531, 0x1d3458f6, 0x0d6ecbf7, 0x0851f041, 0x04e2582a, 0x3500490f, 0x3322}}, - {{0x2c28b2a0, 0x13ce8ba5, 0x2873af62, 0x017d8fa8, 0x1af9b728, 0x0066f137, 0x24ef5bfb, 0x01e5fa59, 0x56e7}}}, + {{{0x02d0e6bd, 0x1dbf073a, 0x03d794c4, 0x09a2c7b6, 0x16ecbf77, 0x0a3e0826, 0x18960a88, 0x00248789, 0x3322d4}}, + {{0x0c28b2a0, 0x079d174b, 0x01cebd89, 0x0bec7d45, 0x0f9b7280, 0x0cde26ed, 0x1bd6fec0, 0x12fd2cc9, 0x56e707}}}, /* 3*16^16*G: */ - {{{0x059ab499, 0x2f674fc8, 0x273c330a, 0x04ca671b, 0x3f01bc0b, 0x065acf19, 0x005ba5d2, 0x2bfcc057, 0x78ba}}, - {{0x3ee097fd, 0x20748c63, 0x11251996, 0x18cbbba3, 0x02082e91, 0x2a1383b6, 0x2c0afafc, 0x3736f6c1, 0xad4b}}}, + {{{0x059ab499, 0x1ece9f90, 0x1cf0cc2a, 0x065338dc, 0x101bc0b1, 0x0b59e33f, 0x16e97486, 0x1e602b80, 0x78baaf}}, + {{0x1ee097fd, 0x00e918c7, 0x0494665a, 0x065ddd1a, 0x0082e916, 0x027076c1, 0x02bebf2a, 0x1b7b60d8, 0xad4bdc}}}, /* 5*16^16*G: */ - {{{0x3d06ace6, 0x124f85b3, 0x03a20ca4, 0x1c26cdbe, 0x29ab1a23, 0x2e126124, 0x2e3d4c20, 0x3c846852, 0x6f70}}, - {{0x3602d5de, 0x122fb4d2, 0x25ac5ee0, 0x0ca559af, 0x399f5075, 0x1763cd1e, 0x27b736f9, 0x228c2500, 0x791e}}}, + {{{0x1d06ace6, 0x049f0b67, 0x0e883291, 0x01366df0, 0x1ab1a237, 0x024c2494, 0x0f53082e, 0x0234295c, 0x6f70f2}}, + {{0x1602d5de, 0x045f69a5, 0x16b17b81, 0x052acd7c, 0x19f50753, 0x0c79a3dc, 0x0dcdbe57, 0x0612804f, 0x791e8a}}}, /* 7*16^16*G: */ - {{{0x20ee1b40, 0x323b8fb9, 0x1e96247d, 0x3b5216dc, 0x03ccd48c, 0x2527c644, 0x2a415f80, 0x276ca75a, 0xe159}}, - {{0x178f93a6, 0x0758997b, 0x032999de, 0x0d8e9d2f, 0x2fc7cfa6, 0x3e252aa8, 0x1d4a0efa, 0x1888caa0, 0x7933}}}, + {{{0x00ee1b40, 0x04771f73, 0x1a5891f7, 0x1a90b6e3, 0x1ccd48ce, 0x04f8c881, 0x1057e025, 0x1653ad54, 0xe1599d}}, + {{0x178f93a6, 0x0eb132f6, 0x0ca66778, 0x0c74e978, 0x1c7cfa63, 0x04a55517, 0x1283bebe, 0x0465503a, 0x793362}}}, /* 9*16^16*G: */ - {{{0x09c00c3e, 0x2077e8a1, 0x11208e2f, 0x03a3c0f2, 0x051859f0, 0x158b4cf5, 0x06956436, 0x0125c110, 0xbb0b}}, - {{0x11955a35, 0x266a60b4, 0x05dc90a7, 0x19c113a4, 0x31b052fe, 0x34be85ea, 0x39f63655, 0x391614eb, 0x4067}}}, + {{{0x09c00c3e, 0x00efd142, 0x048238be, 0x1d1e0792, 0x11859f00, 0x11699ea2, 0x05590d95, 0x12e0880d, 0xbb0b04}}, + {{0x11955a35, 0x0cd4c168, 0x1772429e, 0x0e089d20, 0x1b052fe6, 0x17d0bd58, 0x1d8d9574, 0x0b0a75f3, 0x4067e4}}}, /* 11*16^16*G: */ - {{{0x05dd32e6, 0x039d6e70, 0x13e5ee7e, 0x18ed546d, 0x1a5fbfc6, 0x1276f81d, 0x1789e9b6, 0x10555065, 0xdc5a}}, - {{0x354a99b9, 0x039f6de9, 0x2e49bcf8, 0x3cbba41d, 0x3f59442f, 0x3a978806, 0x367a76dc, 0x2a298fe7, 0x4af3}}}, + {{{0x05dd32e6, 0x073adce0, 0x0f97b9f8, 0x076aa36a, 0x05fbfc66, 0x0edf03ad, 0x027a6d92, 0x0aa832af, 0xdc5a41}}, + {{0x154a99b9, 0x073edbd3, 0x1926f3e0, 0x05dd20ed, 0x159442ff, 0x12f100df, 0x1e9db73a, 0x14c7f3ec, 0x4af3a8}}}, /* 13*16^16*G: */ - {{{0x0544e7cb, 0x3b516eb1, 0x12960359, 0x0190896d, 0x014e99a1, 0x0d5295c4, 0x33b9dbe3, 0x065c0e61, 0x156e}}, - {{0x2d250a37, 0x354e4b02, 0x2b439cd6, 0x25b56357, 0x034be894, 0x255ca98e, 0x1907da93, 0x2367e3cc, 0x6bc0}}}, + {{{0x0544e7cb, 0x16a2dd62, 0x0a580d67, 0x0c844b6a, 0x14e99a10, 0x0a52b880, 0x0e76f8cd, 0x0e0730e7, 0x156e19}}, + {{0x0d250a37, 0x0a9c9605, 0x0d0e735b, 0x0dab1abd, 0x14be8949, 0x0b9531c1, 0x01f6a4e5, 0x13f1e632, 0x6bc08d}}}, /* 15*16^16*G: */ - {{{0x059853ca, 0x2fef0a73, 0x319bf54d, 0x3a589ae7, 0x27161348, 0x29da88a3, 0x043826bc, 0x2f33b2da, 0x4269}}, - {{0x35b8d367, 0x2a563bd4, 0x1e5a8a3d, 0x0e50297e, 0x31a409fd, 0x2132a710, 0x016b723c, 0x0706a0b0, 0xed2b}}} + {{{0x059853ca, 0x1fde14e6, 0x066fd536, 0x12c4d73e, 0x1161348e, 0x1b511473, 0x0e09af29, 0x19d96d08, 0x4269bc}}, + {{0x15b8d367, 0x14ac77a9, 0x196a28f6, 0x12814bf3, 0x1a409fd3, 0x0654e218, 0x1adc8f21, 0x03505802, 0xed2b1c}}} }, { /* 1*16^17*G: */ - {{{0x0134ab83, 0x0875d34a, 0x36433977, 0x06cfe6bd, 0x26586874, 0x05dc3625, 0x0b7da2bd, 0x0b1f4b78, 0x8567}}, - {{0x390313a6, 0x238c253d, 0x1298f44c, 0x1fc5ff31, 0x22c2e5e7, 0x10126fe9, 0x3b2eb637, 0x06e6d6d0, 0x7c48}}}, + {{{0x0134ab83, 0x10eba694, 0x190ce5dc, 0x167f35ee, 0x05868741, 0x1b86c4b3, 0x1f68af45, 0x0fa5bc16, 0x85672c}}, + {{0x190313a6, 0x07184a7b, 0x0a63d132, 0x1e2ff98a, 0x0c2e5e77, 0x024dfd31, 0x0bad8dd0, 0x136b6876, 0x7c481b}}}, /* 3*16^17*G: */ - {{{0x03ba9000, 0x37c1c8ea, 0x025e8b6f, 0x21cbe71a, 0x00143dc4, 0x21d81d61, 0x1d8c1684, 0x1d3e7ffc, 0xac38}}, - {{0x2f10cf0a, 0x368f1f65, 0x366e9fa4, 0x178d435f, 0x117f9308, 0x0b77a250, 0x1c069b86, 0x3a48c228, 0xaa65}}}, + {{{0x03ba9000, 0x0f8391d4, 0x097a2dbf, 0x0e5f38d0, 0x0143dc48, 0x1b03ac20, 0x0305a121, 0x1f3ffe3b, 0xac3874}}, + {{0x0f10cf0a, 0x0d1e3ecb, 0x19ba7e93, 0x1c6a1afe, 0x17f93085, 0x0ef44a08, 0x01a6e18b, 0x04611438, 0xaa65e9}}}, /* 5*16^17*G: */ - {{{0x2d06dbd4, 0x2981bd9b, 0x0a20d081, 0x038fe15e, 0x23e729ec, 0x0501d7a6, 0x070139ad, 0x1739ea9a, 0x570d}}, - {{0x3d1ed495, 0x2996fb3a, 0x2460bed5, 0x20e8db71, 0x101bbbb6, 0x19b99c47, 0x202f605b, 0x14d25083, 0xa6ae}}}, + {{{0x0d06dbd4, 0x13037b37, 0x08834206, 0x1c7f0af1, 0x1e729ec0, 0x003af4d1, 0x004e6b45, 0x1cf54d0e, 0x570d5c}}, + {{0x1d1ed495, 0x132df675, 0x1182fb56, 0x0746db8c, 0x01bbbb68, 0x173388e8, 0x0bd816d9, 0x092841c0, 0xa6ae53}}}, /* 7*16^17*G: */ - {{{0x092d230e, 0x0d307e48, 0x29339284, 0x3b8ca834, 0x366ef5da, 0x308a7b80, 0x28bb6f87, 0x3e1c0a09, 0x75b5}}, - {{0x151570b8, 0x0df2f7ef, 0x111f8fb0, 0x19e92c01, 0x1dfa8e02, 0x1e1d1553, 0x3852363d, 0x338878e9, 0x527c}}}, + {{{0x092d230e, 0x1a60fc90, 0x04ce4a10, 0x1c6541a5, 0x06ef5dae, 0x114f701b, 0x0edbe1f0, 0x0e0504d1, 0x75b5f8}}, + {{0x151570b8, 0x1be5efde, 0x047e3ec0, 0x0f49600a, 0x1fa8e026, 0x03a2aa6e, 0x148d8f5e, 0x043c74f0, 0x527cce}}}, /* 9*16^17*G: */ - {{{0x034fcc0e, 0x1edafdab, 0x3e3884c4, 0x1fc4290a, 0x1259c892, 0x16e0389f, 0x1dec2b0a, 0x23beb87b, 0x44fc}}, - {{0x319c420a, 0x33fc0c79, 0x0d0489d9, 0x03a5292f, 0x33d3d772, 0x099f9e20, 0x31367e49, 0x37a52ea6, 0xd2c7}}}, + {{{0x034fcc0e, 0x1db5fb56, 0x18e21311, 0x1e214857, 0x059c8927, 0x1c0713e9, 0x1b0ac296, 0x1f5c3dbb, 0x44fc8e}}, + {{0x119c420a, 0x07f818f3, 0x14122767, 0x1d294979, 0x1d3d7720, 0x13f3c419, 0x0d9f9249, 0x12975362, 0xd2c7de}}}, /* 11*16^17*G: */ - {{{0x0bb69991, 0x169207f2, 0x3307175d, 0x3ecfe8b0, 0x02f535ff, 0x28598838, 0x27bc6866, 0x2e91eeb3, 0xdea2}}, - {{0x316fe2df, 0x019d0aa7, 0x21ed9bc7, 0x27736cd8, 0x37b9e722, 0x32ffb213, 0x028e4ac5, 0x2ff5b643, 0xae28}}}, + {{{0x0bb69991, 0x0d240fe4, 0x0c1c5d75, 0x167f4586, 0x0f535fff, 0x0b310701, 0x0f1a19a8, 0x08f759cf, 0xdea2ba}}, + {{0x116fe2df, 0x033a154f, 0x07b66f1c, 0x1b9b66c4, 0x1b9e7229, 0x1ff6427b, 0x0392b172, 0x1adb2185, 0xae28bf}}}, /* 13*16^17*G: */ - {{{0x114fc9cc, 0x30903409, 0x1a461658, 0x3402af0a, 0x38a83626, 0x073db312, 0x168d6efc, 0x3f2629b8, 0x3968}}, - {{0x1fad37dd, 0x064e5225, 0x388f3340, 0x05195dbf, 0x2d32c91a, 0x1e60b46a, 0x35928123, 0x2ef436d2, 0x789c}}}, + {{{0x114fc9cc, 0x01206812, 0x09185963, 0x00157853, 0x0a83626d, 0x07b6625c, 0x035bbf07, 0x1314dc2d, 0x3968fc}}, + {{0x1fad37dd, 0x0c9ca44a, 0x023ccd00, 0x08caedff, 0x132c91a1, 0x0c168d56, 0x04a048de, 0x1a1b696b, 0x789cbb}}}, /* 15*16^17*G: */ - {{{0x2e0c85f1, 0x2bb08646, 0x03a3a250, 0x294b94d8, 0x3945d5a6, 0x0977c255, 0x06a2926b, 0x2441a638, 0x6896}}, - {{0x2dc1de21, 0x31d208cc, 0x0d503922, 0x10306768, 0x05d72d1f, 0x0c170761, 0x0979256f, 0x0fed2ce3, 0xaefd}}} + {{{0x0e0c85f1, 0x17610c8d, 0x0e8e8942, 0x0a5ca6c0, 0x145d5a6a, 0x0ef84abc, 0x08a49ac9, 0x00d31c0d, 0x689691}}, + {{0x0dc1de21, 0x03a41199, 0x1540e48b, 0x01833b41, 0x1d72d1f4, 0x02e0ec22, 0x1e495bcc, 0x16967192, 0xaefd3f}}} }, { /* 1*16^18*G: */ - {{{0x20c82a0a, 0x3f6566bd, 0x3668832f, 0x2489b183, 0x1413b10f, 0x1b27c646, 0x188a46b0, 0x2fe026c6, 0x0948}}, - {{0x18c8e589, 0x132dfe23, 0x17cd2bed, 0x137fc232, 0x03418c6d, 0x2dd31747, 0x36646dc6, 0x18a15b72, 0x53a5}}}, + {{{0x00c82a0a, 0x1ecacd7b, 0x19a20cbf, 0x044d8c1e, 0x013b10f9, 0x04f8c8ca, 0x0291ac1b, 0x10136331, 0x948bf}}, + {{0x18c8e589, 0x065bfc46, 0x1f34afb5, 0x1bfe1192, 0x1418c6d4, 0x1a62e8e1, 0x191b71ad, 0x10adb96c, 0x53a562}}}, /* 3*16^18*G: */ - {{{0x38c8ac7f, 0x0a0bf97e, 0x1e2aa527, 0x0490bb99, 0x16f84964, 0x0ce5b481, 0x22bbcb5c, 0x2cbef8e0, 0x9945}}, - {{0x29aea3b0, 0x1b650e85, 0x2dacdfa9, 0x0bde88fb, 0x28eff528, 0x36d13fec, 0x3282d607, 0x3b6092c3, 0x3eef}}}, + {{{0x18c8ac7f, 0x1417f2fd, 0x18aa949c, 0x0485dccb, 0x0f849641, 0x1cb6902b, 0x0ef2d70c, 0x1f7c7045, 0x9945b2}}, + {{0x09aea3b0, 0x16ca1d0b, 0x16b37ea5, 0x1ef447dd, 0x0eff5282, 0x1a27fd94, 0x00b581f6, 0x104961e5, 0x3eefed}}}, /* 5*16^18*G: */ - {{{0x169e353a, 0x3475e78e, 0x2bbe1f6e, 0x28110214, 0x07d5fe10, 0x3e0889c4, 0x070e6235, 0x131ac816, 0x2a31}}, - {{0x25746067, 0x09649b87, 0x32658bfc, 0x22952ab6, 0x2a1ba013, 0x18f91dae, 0x227ac1a4, 0x2b02fcd6, 0x15a4}}}, + {{{0x169e353a, 0x08ebcf1c, 0x0ef87dbb, 0x008810a5, 0x1d5fe10a, 0x01113883, 0x03988d7e, 0x0d640b0e, 0x2a314c}}, + {{0x05746067, 0x12c9370f, 0x09962ff0, 0x14a955b6, 0x01ba0138, 0x1f23b5d5, 0x1eb06918, 0x017e6b44, 0x15a4ac}}}, /* 7*16^18*G: */ - {{{0x29b84966, 0x278bd27b, 0x17f3ff98, 0x13d041b7, 0x2b6c911b, 0x2dbebce9, 0x3fc2d498, 0x29402dc0, 0x5959}}, - {{0x07473a6a, 0x02998c86, 0x0fe24264, 0x00373023, 0x082a7091, 0x0c4a0837, 0x0a897f94, 0x399d07d7, 0x0370}}}, + {{{0x09b84966, 0x0f17a4f7, 0x1fcffe62, 0x1e820dba, 0x16c911b4, 0x17d79d35, 0x10b5262d, 0x0016e07f, 0x5959a5}}, + {{0x07473a6a, 0x0533190c, 0x1f890990, 0x01b98119, 0x02a70910, 0x094106e4, 0x025fe50c, 0x0e83eb95, 0x370e6}}}, /* 9*16^18*G: */ - {{{0x2bc6b173, 0x2c326e48, 0x2ed3feb3, 0x36188f1f, 0x1b5f9d7d, 0x183118c1, 0x22fe8e11, 0x0c4e4dc8, 0x9eeb}}, - {{0x1723a71d, 0x14e58836, 0x0e70c4b9, 0x29c6afb4, 0x3a1ae30e, 0x2aaff6ee, 0x2d58d952, 0x3c780443, 0xe121}}}, + {{{0x0bc6b173, 0x1864dc91, 0x1b4fface, 0x10c478fd, 0x15f9d7dd, 0x0623182d, 0x1fa38458, 0x0726e445, 0x9eeb31}}, + {{0x1723a71d, 0x09cb106c, 0x19c312e5, 0x0e357da1, 0x01ae30ea, 0x15fedddd, 0x163654aa, 0x1c0221da, 0xe121f1}}}, /* 11*16^18*G: */ - {{{0x3ec805f3, 0x1dc910fd, 0x1d995915, 0x3903dd42, 0x2e97887d, 0x2ec8e201, 0x318f516e, 0x13f931fd, 0x39cc}}, - {{0x3a3c48d3, 0x06468304, 0x3c912e4d, 0x2e55cdcf, 0x02de7dbb, 0x399a4f3d, 0x2f8f3151, 0x11cb1691, 0xecb1}}}, + {{{0x1ec805f3, 0x1b9221fb, 0x16656455, 0x081eea13, 0x097887de, 0x191c4037, 0x03d45bae, 0x1c98fee3, 0x39cc4f}}, + {{0x1a3c48d3, 0x0c8d0609, 0x1244b934, 0x12ae6e7f, 0x0de7dbbb, 0x1349e7a1, 0x03cc5479, 0x058b48df, 0xecb147}}}, /* 13*16^18*G: */ - {{{0x0e22580e, 0x0f58bed7, 0x2d6f8879, 0x04ca25b4, 0x1bd4d2c7, 0x0bff7993, 0x0dc69689, 0x201d19bb, 0xf94c}}, - {{0x3127db82, 0x07948fd9, 0x2371d4e8, 0x21fb114c, 0x1a81f698, 0x12ffdaad, 0x1225a919, 0x1ff719e1, 0x5e9c}}}, + {{{0x0e22580e, 0x1eb17dae, 0x15be21e4, 0x06512da5, 0x1d4d2c71, 0x1fef326d, 0x11a5a24b, 0x0e8cdd9b, 0xf94c80}}, + {{0x1127db82, 0x0f291fb3, 0x0dc753a0, 0x0fd88a64, 0x081f6988, 0x1ffb55ad, 0x096a4652, 0x1b8cf0a4, 0x5e9c7f}}}, /* 15*16^18*G: */ - {{{0x10c4f21f, 0x2f902eb4, 0x103da7a6, 0x092a5653, 0x1999d250, 0x0081a36c, 0x1d162fcc, 0x2e1b1ab5, 0x8ccc}}, - {{0x329dfea0, 0x1fc49ba9, 0x264be28f, 0x24b72b20, 0x0758a54b, 0x2fbd5272, 0x11c43699, 0x2596189d, 0x57f8}}} + {{{0x10c4f21f, 0x1f205d68, 0x00f69e9a, 0x0952b29a, 0x199d2502, 0x10346d8c, 0x058bf300, 0x0d8d5aba, 0x8cccb8}}, + {{0x129dfea0, 0x1f893753, 0x192f8a3d, 0x05b95904, 0x158a54b9, 0x17aa4e43, 0x110da66f, 0x0b0c4ea3, 0x57f896}}} }, { /* 1*16^19*G: */ - {{{0x338fd8e8, 0x33b36067, 0x069752ac, 0x2c39137f, 0x2873a8f1, 0x19f383c0, 0x001c34f0, 0x339fd186, 0x6260}}, - {{0x32b4ae17, 0x06a13a56, 0x051c198c, 0x34a488e0, 0x2a1ef7ec, 0x024125dd, 0x1b571a7f, 0x2a0adbe9, 0xbc2d}}}, + {{{0x138fd8e8, 0x0766c0cf, 0x1a5d4ab3, 0x01c89bf8, 0x073a8f1b, 0x1e707814, 0x070d3c19, 0x0fe8c300, 0x6260ce}}, + {{0x12b4ae17, 0x0d4274ad, 0x14706630, 0x05244700, 0x01ef7ecd, 0x0824bbb5, 0x15c69fc2, 0x056df4b6, 0xbc2da8}}}, /* 3*16^19*G: */ - {{{0x01136602, 0x2c2e9195, 0x19e3a5bb, 0x311bd203, 0x333b3d38, 0x1624dfc8, 0x2dfc33d0, 0x09ca0120, 0x87d1}}, - {{0x18af6aac, 0x3da0f107, 0x3d3bf7c4, 0x2a211d1b, 0x27745387, 0x289db3fd, 0x203de926, 0x0921c296, 0x71ce}}}, + {{{0x01136602, 0x185d232a, 0x078e96ee, 0x08de901b, 0x13b3d38c, 0x049bf919, 0x1f0cf416, 0x0500905b, 0x87d127}}, + {{0x18af6aac, 0x1b41e20e, 0x14efdf13, 0x1108e8df, 0x1745387a, 0x13b67fb3, 0x0f7a49a8, 0x10e14b40, 0x71ce24}}}, /* 5*16^19*G: */ - {{{0x08c5a916, 0x2c8175cd, 0x35610f25, 0x17110354, 0x354aa13f, 0x2b318f6a, 0x1e9746b0, 0x1f4ff898, 0xfd5d}}, - {{0x3adb8bda, 0x052cdec1, 0x1cf6faab, 0x35ce052f, 0x07b52fe5, 0x10f299e7, 0x15b07d2b, 0x0fb43bad, 0x0dd8}}}, + {{{0x08c5a916, 0x1902eb9a, 0x15843c96, 0x18881aa6, 0x14aa13f5, 0x0631ed5a, 0x05d1ac2b, 0x07fc4c3d, 0xfd5d7d}}, + {{0x1adb8bda, 0x0a59bd83, 0x13dbeaac, 0x0e70297b, 0x1b52fe5d, 0x1e533ce3, 0x0c1f4ad0, 0x1a1dd6ab, 0xdd83e}}}, /* 7*16^19*G: */ - {{{0x35f7529c, 0x17664258, 0x1bd51dd4, 0x1d96e62d, 0x34438138, 0x114f0cb4, 0x026122ba, 0x35042607, 0xde0d}}, - {{0x24cd88fe, 0x0f08300b, 0x09b77406, 0x224931a2, 0x3a357017, 0x042608b5, 0x2145f9b2, 0x1ba74428, 0xd70a}}}, + {{{0x15f7529c, 0x0ecc84b1, 0x0f547751, 0x0cb7316b, 0x04381387, 0x09e1969a, 0x1848ae91, 0x02130384, 0xde0dd4}}, + {{0x04cd88fe, 0x1e106017, 0x06ddd018, 0x12498d11, 0x03570178, 0x04c116bd, 0x117e6c84, 0x13a21442, 0xd70a6e}}}, /* 9*16^19*G: */ - {{{0x38f76d11, 0x320bd234, 0x38515573, 0x044003ef, 0x0292a215, 0x16fbf0e7, 0x0f44e69c, 0x0822b693, 0xb26c}}, - {{0x23b7356b, 0x307002c7, 0x182624bd, 0x000c1967, 0x0d643305, 0x13a1f643, 0x1d33cf0c, 0x3e208252, 0x1f1c}}}, + {{{0x18f76d11, 0x0417a469, 0x014555cf, 0x02001f7f, 0x092a2151, 0x1f7e1ce1, 0x1139a716, 0x115b499e, 0xb26c20}}, + {{0x03b7356b, 0x00e0058f, 0x009892f7, 0x0060cb3b, 0x16433050, 0x143ec866, 0x0cf3c313, 0x1041293a, 0x1f1cf8}}}, /* 11*16^19*G: */ - {{{0x269e22db, 0x2538ec19, 0x39c8933f, 0x264ffd67, 0x0c294eac, 0x0ef4a406, 0x3f523a7e, 0x052e3f1f, 0xfceb}}, - {{0x1c2260a1, 0x3d5cb6c9, 0x24ebe4cb, 0x15439e4e, 0x1f0924ad, 0x22969d49, 0x2b8d1fcd, 0x1ace9035, 0x64aa}}}, + {{{0x069e22db, 0x0a71d833, 0x07224cfe, 0x127feb3f, 0x0294eac9, 0x1e9480c6, 0x148e9f8e, 0x171f8ffe, 0xfceb14}}, + {{0x1c2260a1, 0x1ab96d92, 0x13af932f, 0x0a1cf274, 0x10924ad5, 0x12d3a92f, 0x0347f362, 0x07481ad7, 0x64aa6b}}}, /* 13*16^19*G: */ - {{{0x238a2755, 0x3c2105e6, 0x149c5506, 0x1c869c59, 0x107faa53, 0x05d5dd2d, 0x15cac55c, 0x26988f33, 0x4e90}}, - {{0x23cca3de, 0x3de927d8, 0x229800ca, 0x3354e534, 0x3559dbb6, 0x091b7541, 0x235aecef, 0x36a1e333, 0xae56}}}, + {{{0x038a2755, 0x18420bcd, 0x1271541b, 0x0434e2ca, 0x07faa537, 0x1abba5a8, 0x12b15705, 0x0c4799ab, 0x4e909a}}, + {{0x03cca3de, 0x1bd24fb1, 0x0a60032b, 0x1aa729a4, 0x159dbb6c, 0x036ea83a, 0x16bb3bc9, 0x10f199c6, 0xae56da}}}, /* 15*16^19*G: */ - {{{0x183ba64d, 0x20962566, 0x0c595a3a, 0x3983dde2, 0x0e40e2bd, 0x028517ae, 0x04c03bfb, 0x115708b8, 0xc367}}, - {{0x2a2181fd, 0x053323e5, 0x1778f146, 0x189aab28, 0x1964c742, 0x3839ba13, 0x36033080, 0x02b41a72, 0x3a52}}} + {{{0x183ba64d, 0x012c4acc, 0x116568ea, 0x0c1eef11, 0x040e2bde, 0x10a2f5c7, 0x100efec2, 0x0b845c09, 0xc36745}}, + {{0x0a2181fd, 0x0a6647cb, 0x1de3c518, 0x04d55942, 0x164c7426, 0x0737426c, 0x00cc2038, 0x1a0d396c, 0x3a520a}}} }, { /* 1*16^20*G: */ - {{{0x2037fa2d, 0x254f3234, 0x1bfdc432, 0x0fb23d5d, 0x3f410304, 0x0d21052e, 0x1d8d43d8, 0x1f782bf0, 0xe503}}, - {{0x1d755bda, 0x03977210, 0x0481f10e, 0x17d6c0fb, 0x190bddbd, 0x263427ee, 0x0d3b5f9f, 0x14d2eaa5, 0x4571}}}, + {{{0x0037fa2d, 0x0a9e6469, 0x0ff710ca, 0x1d91eaeb, 0x14103043, 0x0420a5df, 0x0350f60d, 0x1c15f83b, 0xe5037d}}, + {{0x1d755bda, 0x072ee420, 0x1207c438, 0x1eb607d8, 0x10bddbd5, 0x0684fdcc, 0x0ed7e7e6, 0x0975529a, 0x457153}}}, /* 3*16^20*G: */ - {{{0x177e7775, 0x222a29b8, 0x0ed95f63, 0x385564e2, 0x1291aeb5, 0x150eeb3d, 0x233cee58, 0x1a8ebfe5, 0x9d89}}, - {{0x3a056691, 0x3f3db4ea, 0x299253be, 0x26735fb8, 0x10927de8, 0x2593b5c9, 0x1bf0b94e, 0x2a790fd2, 0xdd91}}}, + {{{0x177e7775, 0x04545370, 0x1b657d8e, 0x02ab2711, 0x091aeb5e, 0x01dd67a9, 0x0f3b9615, 0x075ff2c6, 0x9d896a}}, + {{0x1a056691, 0x1e7b69d5, 0x06494efb, 0x139afdc5, 0x0927de89, 0x1276b928, 0x1c2e53a5, 0x1c87e937, 0xdd91a9}}}, /* 5*16^20*G: */ - {{{0x3c2a3293, 0x3f781378, 0x103476c5, 0x222e1bba, 0x02f4cd56, 0x2c295cca, 0x23792d0e, 0x2e3b9c45, 0x8327}}, - {{0x0e0df9bd, 0x2f215386, 0x2326a416, 0x2bf6ad3b, 0x39708496, 0x2cfa9989, 0x0a98e18b, 0x1f899bb8, 0x0499}}}, + {{{0x1c2a3293, 0x1ef026f1, 0x00d1db17, 0x1170ddd2, 0x0f4cd568, 0x052b9941, 0x1e4b43ac, 0x1dce22c6, 0x8327b8}}, + {{0x0e0df9bd, 0x1e42a70c, 0x0c9a905a, 0x1fb569dc, 0x1708496a, 0x1f53313c, 0x063862ec, 0x04cddc15, 0x4997e}}}, /* 7*16^20*G: */ - {{{0x0562c042, 0x1086c9b1, 0x38dfb1a2, 0x0b48c8d2, 0x1a8ed609, 0x1998763e, 0x1b16897d, 0x0aaa8a9b, 0x5ae4}}, - {{0x0f79269c, 0x2417337e, 0x07cd8dbf, 0x3836e544, 0x389d4a94, 0x30777180, 0x3051eab5, 0x0e9f017f, 0x99d9}}}, + {{{0x0562c042, 0x010d9362, 0x037ec689, 0x1a464697, 0x08ed6092, 0x130ec7cd, 0x05a25f59, 0x15454db6, 0x5ae42a}}, + {{0x0f79269c, 0x082e66fc, 0x1f3636fe, 0x01b72a20, 0x09d4a94e, 0x0eee301c, 0x147aad70, 0x0f80bfe0, 0x99d93a}}}, /* 9*16^20*G: */ - {{{0x1e85af61, 0x0d2204a1, 0x14ae766b, 0x23b5c8b7, 0x021b0f4e, 0x3ada3fdb, 0x1c8eb59a, 0x0eb909a8, 0x92c2}}, - {{0x036a2b09, 0x39c8d9a7, 0x2286fed4, 0x08eb60ad, 0x38d5792d, 0x085f571c, 0x11bb409f, 0x3e23c055, 0x414c}}}, + {{{0x1e85af61, 0x1a440942, 0x12b9d9ac, 0x1dae45ba, 0x01b0f4e8, 0x1b47fb61, 0x03ad66ba, 0x1c84d439, 0x92c23a}}, + {{0x036a2b09, 0x1391b34e, 0x0a1bfb53, 0x075b056c, 0x0d5792d2, 0x0beae39c, 0x0ed027c8, 0x11e02aa3, 0x414cf8}}}, /* 11*16^20*G: */ - {{{0x07b5eba8, 0x38abc6cb, 0x118ea36c, 0x2afb71fe, 0x38df422d, 0x03d05dab, 0x3df1088d, 0x18231dab, 0xfee5}}, - {{0x0d0b9b5c, 0x3d4574da, 0x39054793, 0x203fd0af, 0x07c14ee3, 0x100be64a, 0x258afb11, 0x16644d3f, 0x3807}}}, + {{{0x07b5eba8, 0x11578d96, 0x063a8db3, 0x17db8ff2, 0x0df422da, 0x1a0bb57c, 0x1c422343, 0x118ed5fb, 0xfee560}}, + {{0x0d0b9b5c, 0x1a8ae9b4, 0x04151e4f, 0x01fe857f, 0x1c14ee38, 0x017cc943, 0x02bec450, 0x12269fcb, 0x380759}}}, /* 13*16^20*G: */ - {{{0x3c63caf4, 0x078ee92c, 0x0f53d528, 0x23fceaca, 0x2a6afca2, 0x044ed318, 0x267e620a, 0x113ae4b9, 0x42e5}}, - {{0x169c29c8, 0x21ebb026, 0x3efc5f11, 0x29439eda, 0x015e7873, 0x3c88305d, 0x0c671f71, 0x15383e47, 0x9ff8}}}, + {{{0x1c63caf4, 0x0f1dd259, 0x1d4f54a0, 0x1fe75651, 0x06afca28, 0x09da6315, 0x1f988284, 0x1d725ccc, 0x42e544}}, + {{0x169c29c8, 0x03d7604c, 0x1bf17c46, 0x0a1cf6d7, 0x15e7873a, 0x11060ba0, 0x19c7dc7c, 0x1c1f2398, 0x9ff854}}}, /* 15*16^20*G: */ - {{{0x1e0f09a1, 0x028af661, 0x14032838, 0x28427c6e, 0x300efef0, 0x25bb4a91, 0x32ce3839, 0x20ed9954, 0x7aed}}, - {{0x05857d73, 0x1176337a, 0x33f4a540, 0x22cbcc03, 0x032d8ed8, 0x2bf42ac4, 0x1ef7c7dd, 0x1517e68c, 0xf5b8}}} + {{{0x1e0f09a1, 0x0515ecc2, 0x100ca0e0, 0x0213e372, 0x00efef0a, 0x17695238, 0x138e0e65, 0x16ccaa65, 0x7aed83}}, + {{0x05857d73, 0x02ec66f4, 0x0fd29501, 0x165e601e, 0x12d8ed88, 0x1e855881, 0x1df1f76b, 0x0bf3463d, 0xf5b854}}} }, { /* 1*16^21*G: */ - {{{0x24fce725, 0x1619a82b, 0x2a6c5b72, 0x3a36f471, 0x1771b4e7, 0x2a417a3c, 0x207adf5e, 0x1cac3d28, 0xe063}}, - {{0x0eee31dd, 0x09c0d3e5, 0x3104870b, 0x12129de1, 0x1a488cd7, 0x09eecab5, 0x18cfe12a, 0x225d2f38, 0x7a90}}}, + {{{0x04fce725, 0x0c335057, 0x09b16dc9, 0x11b7a38d, 0x171b4e7e, 0x082f478b, 0x1eb7d7aa, 0x161e9440, 0xe06372}}, + {{0x0eee31dd, 0x1381a7ca, 0x04121c2c, 0x1094ef0e, 0x0488cd74, 0x1dd956ad, 0x13f84a89, 0x0e979c31, 0x7a9089}}}, /* 3*16^21*G: */ - {{{0x1a328d6a, 0x2eaa0623, 0x1adc18bd, 0x135dcea5, 0x308fa7b2, 0x1a264616, 0x34e00a34, 0x3016e988, 0xc663}}, - {{0x3ec9b8c0, 0x0ec2edaa, 0x12bf9cc2, 0x21547a94, 0x171317dd, 0x2bf73c9d, 0x21c38d39, 0x3a6357dc, 0x3331}}}, + {{{0x1a328d6a, 0x1d540c46, 0x0b7062f6, 0x1aee752b, 0x08fa7b24, 0x04c8c2d8, 0x18028d1a, 0x0b74c469, 0xc663c0}}, + {{0x1ec9b8c0, 0x1d85db55, 0x0afe7308, 0x0aa3d4a2, 0x11317dd8, 0x1ee793ab, 0x10e34e6b, 0x11abee43, 0x3331e9}}}, /* 5*16^21*G: */ - {{{0x3996de2f, 0x32472120, 0x0b25114b, 0x33b7cbb8, 0x0fe4e977, 0x2cc37ba8, 0x06a459ce, 0x09a0b7ee, 0xd3fc}}, - {{0x14526f8c, 0x31248907, 0x37abf168, 0x166d2637, 0x3781da4e, 0x2d1d5353, 0x30a18f68, 0x37e66917, 0xc4f0}}}, + {{{0x1996de2f, 0x048e4241, 0x0c94452f, 0x1dbe5dc1, 0x1e4e977c, 0x186f7507, 0x091673ac, 0x105bf70d, 0xd3fc26}}, + {{0x14526f8c, 0x0249120e, 0x1eafc5a3, 0x136931be, 0x181da4e5, 0x03aa6a7b, 0x0863da2d, 0x13348be1, 0xc4f0df}}}, /* 7*16^21*G: */ - {{{0x03e697ea, 0x31b12344, 0x05f83e85, 0x399e3ee6, 0x3fabd19c, 0x287fb268, 0x2c0237dc, 0x12d0ffac, 0xc17a}}, - {{0x1edc6c87, 0x3b8ee1f7, 0x39f02ab0, 0x38686d5f, 0x201fae96, 0x05e3dc65, 0x35954cae, 0x170b556a, 0x3935}}}, + {{{0x03e697ea, 0x03624688, 0x17e0fa17, 0x0cf1f730, 0x1abd19ce, 0x0ff64d1f, 0x008df728, 0x087fd658, 0xc17a4b}}, + {{0x1edc6c87, 0x171dc3ee, 0x07c0aac3, 0x03436aff, 0x01fae96e, 0x1c7b8cb0, 0x05532b85, 0x05aab56b, 0x39355c}}}, /* 9*16^21*G: */ - {{{0x3163da1b, 0x0b4b0c08, 0x393a3118, 0x03b7b983, 0x011fde9a, 0x24d275ff, 0x390b468c, 0x22df2899, 0x8f61}}, - {{0x03bdd76e, 0x1fcc4844, 0x249b6e7c, 0x14319a8c, 0x2c5a4264, 0x2f69d35e, 0x3eb6eb5f, 0x0fc97c22, 0x7823}}}, + {{{0x1163da1b, 0x16961811, 0x04e8c460, 0x1dbdcc1f, 0x11fde9a0, 0x1a4ebfe0, 0x02d1a324, 0x0f944cf2, 0x8f618b}}, + {{0x03bdd76e, 0x1f989088, 0x126db9f1, 0x018cd464, 0x05a42645, 0x0d3a6bd6, 0x0dbad7ef, 0x04be117d, 0x78233f}}}, /* 11*16^21*G: */ - {{{0x0ec8ae90, 0x3a1643f8, 0x0bbc5dee, 0x2c9ae4ba, 0x03f1b8cf, 0x356e36b2, 0x21e6eb86, 0x303c56de, 0x9798}}, - {{0x252844d3, 0x2a6b0bab, 0x03188e27, 0x392596f4, 0x1c73bee2, 0x3b25253e, 0x02ed3dd2, 0x38aa9d69, 0xba40}}}, + {{{0x0ec8ae90, 0x142c87f0, 0x0ef177bb, 0x04d725d1, 0x1f1b8cfb, 0x0dc6d641, 0x19bae1b5, 0x1e2b6f43, 0x9798c0}}, + {{0x052844d3, 0x14d61757, 0x0c62389e, 0x092cb7a0, 0x073bee2e, 0x04a4a7ce, 0x1b4f74bb, 0x154eb485, 0xba40e2}}}, /* 13*16^21*G: */ - {{{0x11d66b7f, 0x16865e3c, 0x187dc810, 0x29a49414, 0x1284757a, 0x3c6e42e2, 0x22d6747c, 0x1bb8fed6, 0xfdfa}}, - {{0x38e5178b, 0x2aa3e019, 0x3d78de9d, 0x11be7744, 0x1a18c4d8, 0x0307268f, 0x198db93c, 0x3cc78892, 0x4d9c}}}, + {{{0x11d66b7f, 0x0d0cbc78, 0x01f72041, 0x0d24a0a3, 0x084757aa, 0x0dc85c49, 0x159d1f3c, 0x1c7f6b45, 0xfdfa6e}}, + {{0x18e5178b, 0x1547c033, 0x15e37a76, 0x0df3ba27, 0x018c4d84, 0x00e4d1ed, 0x036e4f03, 0x03c44933, 0x4d9cf3}}}, /* 15*16^21*G: */ - {{{0x1265bcf0, 0x201d5e12, 0x11c7d30b, 0x338ade10, 0x0f220e69, 0x3aa69187, 0x29e43add, 0x338e3788, 0xfd58}}, - {{0x2b996292, 0x0cf9ea73, 0x0f1cd1df, 0x0986ff8a, 0x05e4fb87, 0x20aae692, 0x3215bd53, 0x29794dd8, 0xffe0}}} + {{{0x1265bcf0, 0x003abc24, 0x071f4c2e, 0x1c56f082, 0x1220e69c, 0x14d230e7, 0x190eb77a, 0x071bc453, 0xfd58ce}}, + {{0x0b996292, 0x19f3d4e7, 0x1c73477c, 0x0c37fc51, 0x1e4fb872, 0x155cd242, 0x056f54e0, 0x1ca6ec64, 0xffe0a5}}} }, { /* 1*16^22*G: */ - {{{0x10559754, 0x02b5a423, 0x2a3f5854, 0x2c42f778, 0x0ce02204, 0x02efe770, 0x1d45358d, 0x1e9c5735, 0x213c}}, - {{0x34b458f2, 0x3fcb09d4, 0x36a7eedd, 0x12143d7c, 0x1ba190bb, 0x0eb41891, 0x06250701, 0x2b42d6b9, 0x4b6d}}}, + {{{0x10559754, 0x056b4846, 0x08fd6150, 0x0217bbc5, 0x0e02204b, 0x1dfcee06, 0x114d6342, 0x0e2b9aba, 0x213c7a}}, + {{0x14b458f2, 0x1f9613a9, 0x1a9fbb77, 0x10a1ebe6, 0x1a190bb4, 0x1683122d, 0x0941c04e, 0x016b5c8c, 0x4b6dad}}}, /* 3*16^22*G: */ - {{{0x1e05dccc, 0x0cb60046, 0x019a93e5, 0x0fe8fb53, 0x13d172ae, 0x1b825ae5, 0x1a030954, 0x3db85d4f, 0xb8ce}}, - {{0x0c6d5750, 0x0052833f, 0x26b68133, 0x1d5ff0da, 0x12bd99df, 0x3529d393, 0x09bbf6a4, 0x229829b3, 0x302b}}}, + {{{0x1e05dccc, 0x196c008c, 0x066a4f94, 0x1f47da98, 0x1d172ae3, 0x104b5ca9, 0x00c2551b, 0x1c2ea7b4, 0xb8cef6}}, + {{0x0c6d5750, 0x00a5067e, 0x1ada04cc, 0x0aff86d4, 0x0bd99df7, 0x053a7269, 0x0efda935, 0x0c14d993, 0x302b8a}}}, /* 5*16^22*G: */ - {{{0x373bb31a, 0x16f7fb84, 0x3db97b48, 0x07dedad7, 0x3b5f4970, 0x282f78ba, 0x07385e02, 0x0cf9de6d, 0x03fb}}, - {{0x3d215c9e, 0x0d32f9a5, 0x07640d4e, 0x169f1db1, 0x3b572bc6, 0x30586aae, 0x2fe281e0, 0x36549523, 0xf36a}}}, + {{{0x173bb31a, 0x0deff709, 0x16e5ed21, 0x1ef6d6bf, 0x15f49701, 0x05ef175d, 0x0e1780a8, 0x1cef368e, 0x3fb33}}, + {{0x1d215c9e, 0x1a65f34b, 0x1d903538, 0x14f8ed88, 0x1572bc65, 0x0b0d55dd, 0x18a07830, 0x0a4a91df, 0xf36ad9}}}, /* 7*16^22*G: */ - {{{0x1d9a4ab4, 0x16d457af, 0x15bb7c0a, 0x1f0db061, 0x0f7a3671, 0x05bded34, 0x03e1161f, 0x1f34427b, 0x4b17}}, - {{0x235ab6f7, 0x2ab77f91, 0x1741f558, 0x0df8957c, 0x226b486e, 0x23d9ca4d, 0x2fa65fda, 0x19ba6978, 0x3ec9}}}, + {{{0x1d9a4ab4, 0x0da8af5e, 0x16edf029, 0x186d830a, 0x17a36717, 0x17bda687, 0x184587c5, 0x1a213d87, 0x4b177c}}, + {{0x035ab6f7, 0x156eff23, 0x1d07d562, 0x0fc4abe2, 0x06b486e3, 0x1b3949b1, 0x0997f6a3, 0x1d34bc5f, 0x3ec966}}}, /* 9*16^22*G: */ - {{{0x301c23a4, 0x3d1beca6, 0x3a49cf56, 0x0a905611, 0x39cd75c2, 0x00e0a6e6, 0x27a06c2a, 0x00d481a8, 0x5e87}}, - {{0x10d986f9, 0x085e65ac, 0x24ccfda1, 0x05c761d2, 0x2c6e2da2, 0x1d5746b8, 0x09221e71, 0x1913bee7, 0x5b96}}}, + {{{0x101c23a4, 0x1a37d94d, 0x09273d5b, 0x1482b08f, 0x1cd75c22, 0x1c14dcdc, 0x081b0a80, 0x0a40d44f, 0x5e8703}}, + {{0x10d986f9, 0x10bccb58, 0x1333f684, 0x0e3b0e94, 0x06e2da21, 0x0ae8d716, 0x08879c5d, 0x09df7392, 0x5b9664}}}, /* 11*16^22*G: */ - {{{0x007b0c66, 0x3cfcd748, 0x16c86fb1, 0x29ffb919, 0x2ceb7434, 0x08913d82, 0x1680a447, 0x30c064c3, 0xe545}}, - {{0x31f2d470, 0x21fd5f49, 0x35a239dd, 0x3960a386, 0x19bcbf97, 0x31bf68e5, 0x2955e7e5, 0x0d03a318, 0xe06a}}}, + {{{0x007b0c66, 0x19f9ae90, 0x1b21bec7, 0x0ffdc8ca, 0x0eb7434a, 0x1227b056, 0x002911c8, 0x003261ad, 0xe545c3}}, + {{0x11f2d470, 0x03fabe93, 0x1688e776, 0x0b051c36, 0x1bcbf97e, 0x17ed1cac, 0x1579f971, 0x01d18c52, 0xe06a34}}}, /* 13*16^22*G: */ - {{{0x03648bba, 0x2960642e, 0x1c3c7444, 0x283c2c1a, 0x01b39882, 0x0fb8897c, 0x0f580a13, 0x10855e95, 0xb2a4}}, - {{0x00fb6452, 0x11bead28, 0x09c17bb2, 0x36154547, 0x3d7e31c0, 0x3ef25e3e, 0x366619e9, 0x17f0ada4, 0xfe4f}}}, + {{{0x03648bba, 0x12c0c85c, 0x10f1d112, 0x01e160d3, 0x1b39882a, 0x17112f80, 0x160284cf, 0x02af4a9e, 0xb2a442}}, + {{0x00fb6452, 0x037d5a50, 0x0705eec9, 0x10aa2a39, 0x17e31c0d, 0x1e4bc7de, 0x19867a7e, 0x1856d26c, 0xfe4f5f}}}, /* 15*16^22*G: */ - {{{0x2bab27d0, 0x3db748bb, 0x045103fc, 0x02d07e8b, 0x197007f7, 0x25c06463, 0x138651ba, 0x2383cf51, 0x1b90}}, - {{0x00d3d110, 0x07a19d79, 0x07e51b57, 0x2ef2a4d6, 0x3c4b9ab5, 0x15f24605, 0x26b5e6f3, 0x1897bb11, 0x9b6d}}} + {{{0x0bab27d0, 0x1b6e9177, 0x11440ff3, 0x1683f458, 0x17007f70, 0x180c8c6c, 0x01946ea5, 0x01e7a8a7, 0x1b908e}}, + {{0x00d3d110, 0x0f433af2, 0x1f946d5c, 0x179526b0, 0x04b9ab5b, 0x1e48c0be, 0x0d79bcd5, 0x0bdd88cd, 0x9b6d62}}} }, { /* 1*16^23*G: */ - {{{0x08fbd53c, 0x0330e8ec, 0x1c62cddf, 0x20e31c2b, 0x019a87e2, 0x2e4d4a95, 0x0b34e8db, 0x09ca9ebd, 0x4e7c}}, - {{0x17dcaae6, 0x02ce5060, 0x3f7dd33e, 0x02e5852f, 0x2f681b53, 0x3f427db7, 0x10b18e16, 0x271d9b27, 0x1774}}}, + {{{0x08fbd53c, 0x0661d1d8, 0x118b377c, 0x0718e15b, 0x19a87e28, 0x09a952a0, 0x0d3a36ee, 0x054f5e96, 0x4e7c27}}, + {{0x17dcaae6, 0x059ca0c0, 0x1df74cf8, 0x172c297f, 0x1681b530, 0x084fb6f7, 0x0c6385bf, 0x0ecd93a1, 0x17749c}}}, /* 3*16^23*G: */ - {{{0x2521b3ff, 0x38a61193, 0x1aa750ce, 0x0f01c5fa, 0x2e24a523, 0x1134afa6, 0x1455c75e, 0x138c0432, 0x0248}}, - {{0x0269da7e, 0x306b92e4, 0x23ac8bbc, 0x1c01b7a4, 0x2d0eebad, 0x30acf0ac, 0x3e30d07e, 0x34282a88, 0x9619}}}, + {{{0x0521b3ff, 0x114c2327, 0x0a9d433b, 0x180e2fd3, 0x024a5233, 0x0695f4d7, 0x1571d791, 0x06021928, 0x2484e}}, + {{0x0269da7e, 0x00d725c8, 0x0eb22ef3, 0x000dbd24, 0x10eebad7, 0x159e1596, 0x0c341fb0, 0x1415447c, 0x9619d0}}}, /* 5*16^23*G: */ - {{{0x004ba7b9, 0x25ade7ea, 0x0741751f, 0x35a91c0c, 0x2c954e20, 0x26dc359c, 0x2ce57ef7, 0x3149b3ed, 0x16c1}}, - {{0x1c5bd741, 0x1d6f8e94, 0x1c9a9cc4, 0x1d57006f, 0x0a94deec, 0x189d1672, 0x31439062, 0x1fdf0d00, 0xdb15}}}, + {{{0x004ba7b9, 0x0b5bcfd4, 0x1d05d47e, 0x0d48e060, 0x0954e20d, 0x1b86b396, 0x195fbde6, 0x04d9f6d9, 0x16c1c5}}, + {{0x1c5bd741, 0x1adf1d28, 0x126a7311, 0x0ab8037b, 0x094deec7, 0x13a2ce45, 0x10e41898, 0x0f868062, 0xdb157f}}}, /* 7*16^23*G: */ - {{{0x236683fa, 0x20d921ea, 0x0ec0825e, 0x2086d4e0, 0x127b6695, 0x22739dd1, 0x131af87a, 0x0f35d4fe, 0x0397}}, - {{0x3f4a577f, 0x3d7ecadd, 0x3e981ded, 0x1e213863, 0x35a26cd7, 0x384ad8ca, 0x0a3a3643, 0x168b30c3, 0x38cf}}}, + {{{0x036683fa, 0x01b243d5, 0x1b02097a, 0x0436a701, 0x07b66958, 0x0e73ba29, 0x06be1ea2, 0x1aea7f26, 0x3973c}}, + {{0x1f4a577f, 0x1afd95bb, 0x1a6077b7, 0x1109c31f, 0x1a26cd77, 0x095b195a, 0x0e8d90f8, 0x05986194, 0x38cf5a}}}, /* 9*16^23*G: */ - {{{0x00bf6f06, 0x202ce667, 0x1043b571, 0x0f04cc89, 0x20576571, 0x3013d2c0, 0x0f1511c2, 0x26ee9cbb, 0xba6a}}, - {{0x381db551, 0x0cafbdc1, 0x0697aafe, 0x17453deb, 0x18bd8e9e, 0x082fcb95, 0x211b0320, 0x078e2cd2, 0x1377}}}, + {{{0x00bf6f06, 0x0059ccce, 0x010ed5c6, 0x1826644a, 0x05765713, 0x027a5810, 0x054470b0, 0x174e5d9e, 0xba6a9b}}, + {{0x181db551, 0x195f7b83, 0x1a5eabf8, 0x1a29ef58, 0x0bd8e9e5, 0x05f972ac, 0x06c0c808, 0x07166942, 0x13771e}}}, /* 11*16^23*G: */ - {{{0x31231a43, 0x347be7c1, 0x1ad43b9f, 0x35453599, 0x1e442f44, 0x3b654193, 0x04dd2d8a, 0x2f3309f3, 0x35c5}}, - {{0x1620c8f6, 0x36dcb914, 0x23cf0ae7, 0x3de93301, 0x3a589d4c, 0x396082db, 0x346ce734, 0x1d5c8ee5, 0x0e36}}}, + {{{0x11231a43, 0x08f7cf83, 0x0b50ee7f, 0x0a29accb, 0x0442f44d, 0x0ca8326f, 0x174b62bb, 0x1984f989, 0x35c5bc}}, + {{0x1620c8f6, 0x0db97228, 0x0f3c2b9f, 0x0f49980c, 0x0589d4cf, 0x0c105b7d, 0x1b39cd39, 0x0e4772e8, 0xe3675}}}, /* 13*16^23*G: */ - {{{0x3dd40609, 0x3d02f15b, 0x181cd76b, 0x10642603, 0x08356ac7, 0x0bc4bf16, 0x186bca12, 0x27091715, 0xfd47}}, - {{0x2a64ca53, 0x378bc4d9, 0x21ca4739, 0x04ebb5c9, 0x1841fd91, 0x2b5e90f2, 0x0afeff2c, 0x33ed49a5, 0x3069}}}, + {{{0x1dd40609, 0x1a05e2b7, 0x00735daf, 0x0321301b, 0x0356ac74, 0x1897e2c4, 0x1af2848b, 0x048b8ab0, 0xfd479c}}, + {{0x0a64ca53, 0x0f1789b3, 0x07291ce7, 0x075dae4c, 0x041fd911, 0x0bd21e4c, 0x1fbfcb2b, 0x16a4d295, 0x3069cf}}}, /* 15*16^23*G: */ - {{{0x2b799a7f, 0x36dc0bd4, 0x3b8e8424, 0x062db354, 0x2c7d544f, 0x363ae6bc, 0x0d864bde, 0x000a8eb3, 0x6c40}}, - {{0x13c81e32, 0x2d7320b3, 0x20483f68, 0x1eaf5320, 0x1ddcbdc0, 0x2e0da838, 0x235be690, 0x37054c2d, 0x95c2}}} + {{{0x0b799a7f, 0x0db817a9, 0x0e3a1093, 0x116d9aa7, 0x07d544f1, 0x075cd796, 0x0192f7b6, 0x0547599b, 0x6c4000}}, + {{0x13c81e32, 0x1ae64166, 0x0120fda2, 0x157a9904, 0x1dcbdc07, 0x01b5070e, 0x16f9a42e, 0x02a616c6, 0x95c2dc}}} }, { /* 1*16^24*G: */ - {{{0x00fb27b6, 0x0909f8a1, 0x24305763, 0x1b8f6caf, 0x286aa5c7, 0x08e2b585, 0x38b1b10f, 0x138f6f9d, 0xfea7}}, - {{0x323cb96f, 0x0074f6df, 0x33f7b777, 0x1ad65ae5, 0x36af9312, 0x19d37b32, 0x313297cf, 0x1a36e6c2, 0x6e05}}}, + {{{0x00fb27b6, 0x1213f142, 0x10c15d8c, 0x1c7b657c, 0x06aa5c76, 0x1c56b0b4, 0x0c6c43c8, 0x07b7cef1, 0xfea74e}}, + {{0x123cb96f, 0x00e9edbf, 0x0fdedddc, 0x16b2d72e, 0x0af93126, 0x1a6f665b, 0x0ca5f3d9, 0x1b736162, 0x6e0568}}}, /* 3*16^24*G: */ - {{{0x3e889756, 0x37606ba6, 0x3004bb25, 0x1ed9265e, 0x1899f3f2, 0x3365ec9c, 0x1fea8226, 0x22f0cc84, 0x762e}}, - {{0x3ca6b774, 0x17896781, 0x084fa5e2, 0x1cb6cc52, 0x02e34719, 0x3313c526, 0x3e97c3c7, 0x250982bc, 0xc028}}}, + {{{0x1e889756, 0x0ec0d74d, 0x0012ec97, 0x16c932f6, 0x099f3f27, 0x0cbd938c, 0x1aa089b3, 0x1866423f, 0x762e8b}}, + {{0x1ca6b774, 0x0f12cf03, 0x013e9789, 0x05b66291, 0x0e347197, 0x0278a4c1, 0x05f0f1f3, 0x04c15e7d, 0xc02894}}}, /* 5*16^24*G: */ - {{{0x0975d2ea, 0x1bdd7a5c, 0x014e8ea2, 0x14ab3e84, 0x08f4a91e, 0x26f6ec8c, 0x095348e1, 0x1f51f7d8, 0xdf07}}, - {{0x31936f95, 0x28f0b678, 0x3bdd277a, 0x07b16e13, 0x22527c8a, 0x21097262, 0x37f4424c, 0x1ea2003b, 0xf861}}}, + {{{0x0975d2ea, 0x17baf4b8, 0x053a3a89, 0x0559f420, 0x0f4a91e5, 0x1edd9184, 0x14d23866, 0x08fbec12, 0xdf077d}}, + {{0x11936f95, 0x11e16cf1, 0x0f749dea, 0x1d8b709f, 0x0527c8a1, 0x012e4c51, 0x1d109321, 0x11001def, 0xf8617a}}}, /* 7*16^24*G: */ - {{{0x3c4c92d7, 0x2e1247ee, 0x14391b45, 0x36d35bb9, 0x0b142935, 0x1f7aa0cd, 0x3da032e1, 0x1f5d62f4, 0x9f3e}}, - {{0x314906dd, 0x32eeff3e, 0x294e1186, 0x0a88c0f5, 0x2b150245, 0x18ac872e, 0x1466b588, 0x2107a9df, 0xecd2}}}, + {{{0x1c4c92d7, 0x1c248fdd, 0x10e46d16, 0x169addca, 0x1142935d, 0x0f5419a5, 0x080cb85f, 0x0eb17a7b, 0x9f3e7d}}, + {{0x114906dd, 0x05ddfe7d, 0x0538461b, 0x144607ad, 0x11502452, 0x1590e5d5, 0x19ad6218, 0x03d4efa8, 0xecd284}}}, /* 9*16^24*G: */ - {{{0x32a8c483, 0x2b835cca, 0x1040ac35, 0x12c32231, 0x39528117, 0x230f48bb, 0x0cf9edc3, 0x1e575ed7, 0xa0cc}}, - {{0x12cc6ba9, 0x0259d156, 0x36936055, 0x0d23c6f7, 0x31df786b, 0x1d3f25c8, 0x3873ee23, 0x0048be2c, 0xabc3}}}, + {{{0x12a8c483, 0x1706b995, 0x0102b0d6, 0x1619118a, 0x15281174, 0x01e9177c, 0x1e7b70e3, 0x0baf6b99, 0xa0cc79}}, + {{0x12cc6ba9, 0x04b3a2ac, 0x1a4d8154, 0x091e37be, 0x1df786b3, 0x07e4b918, 0x1cfb88dd, 0x045f1670, 0xabc301}}}, /* 11*16^24*G: */ - {{{0x05dd3aee, 0x1c3c6daf, 0x396d2f21, 0x054ea2a3, 0x2976ca13, 0x08aa6b1a, 0x3c7cce0e, 0x14294554, 0x6d1c}}, - {{0x3df597f7, 0x3b8d5393, 0x0ed53adf, 0x078c42aa, 0x07d47485, 0x09c8008a, 0x3dfdc977, 0x052381aa, 0xafff}}}, + {{{0x05dd3aee, 0x1878db5e, 0x05b4bc85, 0x0a75151f, 0x176ca131, 0x154d6354, 0x1f338388, 0x14a2aa78, 0x6d1c50}}, + {{0x1df597f7, 0x171aa727, 0x1b54eb7f, 0x1c621551, 0x1d474851, 0x19001143, 0x1f725dc9, 0x11c0d57b, 0xafff14}}}, /* 13*16^24*G: */ - {{{0x24a6d0bb, 0x1e32a6df, 0x1a1afdc6, 0x274c48bd, 0x26418f65, 0x069b62a2, 0x3f9f3f31, 0x075862e5, 0x5e5f}}, - {{0x1033eaf9, 0x1a0e11e4, 0x06f653a1, 0x1557cb94, 0x2721da72, 0x3daf3413, 0x3e6f7358, 0x140ac1a9, 0xd7b1}}}, + {{{0x04a6d0bb, 0x1c654dbf, 0x086bf719, 0x1a6245eb, 0x0418f659, 0x136c5453, 0x07cfcc46, 0x0c3172ff, 0x5e5f1d}}, + {{0x1033eaf9, 0x141c23c8, 0x1bd94e85, 0x0abe5ca0, 0x121da725, 0x15e68273, 0x1bdcd63d, 0x0560d4fc, 0xd7b150}}}, /* 15*16^24*G: */ - {{{0x0f005e3f, 0x36a6d791, 0x2c39bd2d, 0x3da38c6f, 0x01a1495a, 0x0f2e6b38, 0x2427fffd, 0x229acf05, 0xf813}}, - {{0x2f357eb7, 0x0b5f8080, 0x14be2134, 0x3b106f55, 0x25cb51f4, 0x005795ea, 0x0ebd9f9d, 0x23cefbed, 0xca75}}} + {{{0x0f005e3f, 0x0d4daf22, 0x10e6f4b7, 0x0d1c637d, 0x1a1495af, 0x05cd6700, 0x09ffff4f, 0x0d6782c8, 0xf8138a}}, + {{0x0f357eb7, 0x16bf0101, 0x12f884d0, 0x18837aaa, 0x1cb51f4e, 0x0af2bd52, 0x0f67e740, 0x077df69d, 0xca758f}}} }, { /* 1*16^25*G: */ - {{{0x17bdde39, 0x0b00a910, 0x36043295, 0x11385e6d, 0x1968d315, 0x095c3566, 0x3cf0e10a, 0x1044fd9d, 0x76e6}}, - {{0x1901ac01, 0x12c5d4b4, 0x16d2032b, 0x0a8cf4ad, 0x01f0d35e, 0x019b5c1a, 0x295cf577, 0x37e37b93, 0xc90d}}}, + {{{0x17bdde39, 0x16015220, 0x1810ca54, 0x09c2f36e, 0x168d3154, 0x0b86accc, 0x1c384289, 0x027ecef9, 0x76e641}}, + {{0x1901ac01, 0x058ba968, 0x1b480cad, 0x1467a56a, 0x1f0d35e2, 0x136b8340, 0x173d5dc1, 0x11bdc9d2, 0xc90ddf}}}, /* 3*16^25*G: */ - {{{0x0078ee8d, 0x3c142473, 0x06919442, 0x2fc83394, 0x1b4ff64e, 0x3dc98eaa, 0x1a9be25f, 0x15eb6167, 0xd08e}}, - {{0x2da63e86, 0x265fd370, 0x022ed9de, 0x0fbdf3e5, 0x3e6df412, 0x05cbb9d5, 0x088d72d6, 0x25e612ad, 0x852e}}}, + {{{0x0078ee8d, 0x182848e6, 0x1a46510b, 0x1e419ca0, 0x14ff64eb, 0x1931d54d, 0x06f897fd, 0x15b0b3b5, 0xd08e57}}, + {{0x0da63e86, 0x0cbfa6e1, 0x08bb677a, 0x1def9f28, 0x06df4123, 0x19773abf, 0x035cb585, 0x13095691, 0x852e97}}}, /* 5*16^25*G: */ - {{{0x029129ec, 0x164519c1, 0x24825481, 0x2b8eb3c7, 0x131d080c, 0x22fa03b3, 0x04d275f5, 0x30217935, 0x7da6}}, - {{0x2cd9ff0e, 0x2d42bb8a, 0x0ca586ae, 0x12302195, 0x1627bf04, 0x34081d24, 0x01857511, 0x051aee7d, 0xf498}}}, + {{{0x029129ec, 0x0c8a3382, 0x12095205, 0x1c759e3c, 0x11d080ca, 0x1f407669, 0x149d7d62, 0x10bc9a89, 0x7da6c0}}, + {{0x0cd9ff0e, 0x1a857715, 0x12961aba, 0x11810ca9, 0x027bf044, 0x0103a48b, 0x015d4474, 0x0d773e83, 0xf49814}}}, /* 7*16^25*G: */ - {{{0x11654f22, 0x3e0f5255, 0x31aaee94, 0x3dfce508, 0x29d94fb2, 0x3a4006f9, 0x1be6e21b, 0x2433fd70, 0x90d0}}, - {{0x201a43e1, 0x3d77815d, 0x1a3f8740, 0x358d594f, 0x3f70336d, 0x3c08781a, 0x0f61a953, 0x26874aeb, 0xcd56}}}, + {{{0x11654f22, 0x1c1ea4aa, 0x06abba53, 0x0fe72846, 0x1d94fb2f, 0x0800df34, 0x19b886fa, 0x19feb837, 0x90d090}}, + {{0x001a43e1, 0x1aef02bb, 0x08fe1d03, 0x0c6aca7b, 0x170336dd, 0x010f035f, 0x186a54fc, 0x03a5759e, 0xcd569a}}}, /* 9*16^25*G: */ - {{{0x076b19fa, 0x2dbbd947, 0x28819d71, 0x35b81b41, 0x21292ed9, 0x08b0c420, 0x1d1ecc73, 0x26161f3c, 0xda47}}, - {{0x326f5af7, 0x2a89bbac, 0x153fc206, 0x1ef44fa5, 0x16569ea6, 0x0da41df8, 0x0af01d17, 0x35de26f3, 0xebb1}}}, + {{{0x076b19fa, 0x1b77b28e, 0x020675c6, 0x0dc0da0d, 0x1292ed9d, 0x16188410, 0x07b31cc8, 0x0b0f9e3a, 0xda4798}}, + {{0x126f5af7, 0x15137759, 0x14ff081a, 0x17a27d2a, 0x0569ea67, 0x1483bf0b, 0x1c0745cd, 0x0f137995, 0xebb1d7}}}, /* 11*16^25*G: */ - {{{0x39135dbd, 0x364bed96, 0x1d8631ec, 0x3021ebce, 0x29897cf0, 0x1eabd60b, 0x1ee6ad81, 0x1d412a37, 0xe3e4}}, - {{0x0748045d, 0x241abcf9, 0x2c95da96, 0x2880bfd7, 0x383ffea5, 0x2320654a, 0x3c6c40b9, 0x16fe0272, 0x930a}}}, + {{{0x19135dbd, 0x0c97db2d, 0x1618c7b3, 0x010f5e73, 0x1897cf0c, 0x157ac174, 0x19ab605e, 0x00951bbd, 0xe3e475}}, + {{0x0748045d, 0x083579f2, 0x12576a5a, 0x0405febd, 0x03ffea5a, 0x040ca95c, 0x1b102e63, 0x1f013978, 0x930a5b}}}, /* 13*16^25*G: */ - {{{0x0dee455f, 0x2fc2e797, 0x0ce4075c, 0x19fff9ba, 0x0bdb4aff, 0x114ce3e0, 0x0a9b0a47, 0x195bfa1c, 0x7e8c}}, - {{0x171b9cba, 0x1cf7a660, 0x2f466271, 0x28b459d1, 0x03a53b4a, 0x3dd83d20, 0x0740f2a3, 0x318cb28c, 0xbddd}}}, + {{{0x0dee455f, 0x1f85cf2e, 0x13901d72, 0x0fffcdd1, 0x1db4aff6, 0x099c7c05, 0x06c291d1, 0x0dfd0e15, 0x7e8c65}}, + {{0x171b9cba, 0x19ef4cc0, 0x1d1989c5, 0x05a2ce8d, 0x1a53b4aa, 0x1b07a401, 0x103ca8fd, 0x0659460e, 0xbdddc6}}}, /* 15*16^25*G: */ - {{{0x2698b59e, 0x1de5ae6d, 0x13447a43, 0x0cd64962, 0x23c7260a, 0x2c0d6acf, 0x15eb15be, 0x107e246a, 0x3df8}}, - {{0x2b92baf5, 0x33e399e5, 0x14949f8b, 0x3f219ec8, 0x1cf3867b, 0x0aeba3c4, 0x090c1da0, 0x39b7e62c, 0xb38f}}} + {{{0x0698b59e, 0x1bcb5cdb, 0x0d11e90d, 0x06b24b12, 0x1c7260a3, 0x01ad59f1, 0x1ac56fac, 0x1f12352b, 0x3df841}}, + {{0x0b92baf5, 0x07c733cb, 0x12527e2f, 0x190cf642, 0x0f3867bf, 0x1d74788e, 0x0307680a, 0x1bf31612, 0xb38fe6}}} }, { /* 1*16^26*G: */ - {{{0x2bcbb891, 0x2ac54090, 0x326cbee3, 0x1f3190f7, 0x3f8f9a8f, 0x206ea9d0, 0x2abe1e82, 0x315ac0ec, 0xc738}}, - {{0x299a84c3, 0x1f9cd765, 0x080cfe91, 0x0c53bbde, 0x3fbbbb82, 0x063cbab2, 0x2d2537f7, 0x2d5e2546, 0x893f}}}, + {{{0x0bcbb891, 0x158a8121, 0x09b2fb8e, 0x198c87be, 0x18f9a8f7, 0x0dd53a1f, 0x0f87a0a0, 0x0d607655, 0xc738c5}}, + {{0x099a84c3, 0x1f39aecb, 0x0033fa45, 0x029ddef1, 0x1bbbb823, 0x0797565f, 0x094dfdc6, 0x0f12a35a, 0x893fb5}}}, /* 3*16^26*G: */ - {{{0x0761d58d, 0x12eabcce, 0x0d60e2f3, 0x1326f902, 0x20df7aca, 0x09028d5c, 0x3614610a, 0x1849e08f, 0xb8c4}}, - {{0x1d1051a4, 0x0e3a82ea, 0x2107c5b6, 0x1d411e17, 0x33c5053f, 0x1163da5f, 0x0e37d14a, 0x365b145c, 0x8f9e}}}, + {{{0x0761d58d, 0x05d5799c, 0x15838bcd, 0x1937c811, 0x0df7aca4, 0x0051ab90, 0x05184289, 0x04f047ec, 0xb8c461}}, + {{0x1d1051a4, 0x1c7505d4, 0x041f16d8, 0x0a08f0bc, 0x1c5053f7, 0x0c7b4bf9, 0x0df45291, 0x0d8a2e1c, 0x8f9ed9}}}, /* 5*16^26*G: */ - {{{0x050b0040, 0x36c2cc10, 0x0134adc2, 0x3d1f6e7c, 0x1a3671f3, 0x03264ffa, 0x271f7a35, 0x1ba7dc40, 0x08d5}}, - {{0x1b3fd0a1, 0x163899e9, 0x21782beb, 0x35f11c83, 0x39b285f6, 0x34542a35, 0x29aa21ff, 0x216baf42, 0xa121}}}, + {{{0x050b0040, 0x0d859820, 0x04d2b70b, 0x08fb73e0, 0x03671f3f, 0x04c9ff4d, 0x07de8d43, 0x13ee204e, 0x8d56e}}, + {{0x1b3fd0a1, 0x0c7133d2, 0x05e0afad, 0x0f88e41c, 0x1b285f6d, 0x0a8546bc, 0x0a887ff4, 0x15d7a153, 0xa12185}}}, /* 7*16^26*G: */ - {{{0x13573b7f, 0x15958f7c, 0x30b6270f, 0x268717b4, 0x265a3788, 0x083e5def, 0x3ce6341e, 0x3c8cb50b, 0xdc13}}, - {{0x0c1f2ba6, 0x0ab348a1, 0x3404b1c4, 0x11551c05, 0x290a7670, 0x10436a12, 0x2340c3c7, 0x2ea010a7, 0xc909}}}, + {{{0x13573b7f, 0x0b2b1ef8, 0x02d89c3d, 0x1438bda6, 0x05a37889, 0x07cbbdf3, 0x198d0788, 0x065a85f9, 0xdc13f2}}, + {{0x0c1f2ba6, 0x15669142, 0x1012c710, 0x0aa8e02e, 0x10a76704, 0x086d4254, 0x1030f1d0, 0x100853c6, 0xc909ba}}}, /* 9*16^26*G: */ - {{{0x07ae9ceb, 0x00bd642e, 0x0ef2d14b, 0x1b087a9c, 0x2119a822, 0x0655976c, 0x37f073af, 0x0b798077, 0x25c0}}, - {{0x0bc6e275, 0x1c24344d, 0x26587264, 0x319077c2, 0x2d11d537, 0x2138373e, 0x2383c0c8, 0x3ab4b204, 0x8a9f}}}, + {{{0x07ae9ceb, 0x017ac85c, 0x1bcb452c, 0x1843d4e1, 0x119a8226, 0x0ab2ed90, 0x1c1cebc6, 0x1cc03bef, 0x25c02d}}, + {{0x0bc6e275, 0x1848689a, 0x1961c991, 0x0c83be14, 0x111d537c, 0x0706e7d6, 0x00f03221, 0x1a590247, 0x8a9fea}}}, /* 11*16^26*G: */ - {{{0x2c5a3c34, 0x3e0263db, 0x15949fe1, 0x33a0b00a, 0x2e3e58ae, 0x2e7d329e, 0x0e49ce8a, 0x2746cb3e, 0xfedd}}, - {{0x213d7714, 0x0ad52fd3, 0x1bf82976, 0x2bad51a6, 0x0f4b00ad, 0x3a14c4b2, 0x3b8e0b0b, 0x0930c614, 0xa52e}}}, + {{{0x0c5a3c34, 0x1c04c7b7, 0x16527f87, 0x1d058052, 0x03e58aec, 0x0fa653d7, 0x1273a2ae, 0x03659f1c, 0xfedd9d}}, + {{0x013d7714, 0x15aa5fa7, 0x0fe0a5d8, 0x1d6a8d33, 0x14b00ada, 0x02989647, 0x0382c2fa, 0x18630a77, 0xa52e24}}}, /* 13*16^26*G: */ - {{{0x2ab6a396, 0x2d395346, 0x11360769, 0x0086e468, 0x0488b373, 0x38b5fd7a, 0x2a48c2de, 0x0ca1af1b, 0x3e0e}}, - {{0x1980e27e, 0x3acc7923, 0x3468f6a2, 0x2c04107c, 0x053fc66a, 0x07f877ad, 0x337964f3, 0x205cbe8e, 0xca44}}}, + {{{0x0ab6a396, 0x1a72a68d, 0x04d81da6, 0x04372342, 0x088b3730, 0x16bfaf42, 0x1230b7b8, 0x10d78dd4, 0x3e0e32}}, + {{0x1980e27e, 0x1598f246, 0x11a3da8b, 0x002083e6, 0x13fc66ab, 0x1f0ef5a2, 0x1e593cc7, 0x0e5f4766, 0xca4481}}}, /* 15*16^26*G: */ - {{{0x341023ec, 0x2bcd6188, 0x3ecf570a, 0x11763ddb, 0x02b9af56, 0x0b808026, 0x32d28498, 0x2e4c2030, 0x344a}}, - {{0x1e1eeb87, 0x13e260a4, 0x03995d70, 0x13a5dabf, 0x114c5ffc, 0x23cb47a9, 0x0462a73f, 0x0ac10ac9, 0x6e1c}}} + {{{0x141023ec, 0x179ac311, 0x1b3d5c2a, 0x0bb1eedf, 0x0b9af564, 0x101004c1, 0x14a1260b, 0x06101865, 0x344ab9}}, + {{0x1e1eeb87, 0x07c4c148, 0x0e6575c1, 0x1d2ed5f8, 0x14c5ffc4, 0x1968f528, 0x18a9cfe3, 0x00856488, 0x6e1c2b}}} }, { /* 1*16^27*G: */ - {{{0x08f6c14b, 0x1cba7d96, 0x29250143, 0x35cb97ce, 0x172877d1, 0x131d8df2, 0x25b81e26, 0x1899522d, 0xd895}}, - {{0x1d7d991f, 0x24d8fb5d, 0x3b067e17, 0x10a358ca, 0x0340eb03, 0x3b182063, 0x07eae728, 0x2a8e3caf, 0xfebf}}}, + {{{0x08f6c14b, 0x1974fb2c, 0x0494050d, 0x0e5cbe75, 0x12877d1d, 0x03b1be4b, 0x0e078993, 0x0ca916cb, 0xd89562}}, + {{0x1d7d991f, 0x09b1f6ba, 0x0c19f85e, 0x051ac657, 0x140eb034, 0x03040c61, 0x1ab9ca3b, 0x071e578f, 0xfebfaa}}}, /* 3*16^27*G: */ - {{{0x2127b756, 0x02ea1ffd, 0x3a097048, 0x10a2f92a, 0x20b41603, 0x0d8b6941, 0x1f12672d, 0x1e0bdc5b, 0x6d8c}}, - {{0x3f172571, 0x1547dd2a, 0x17cdcca6, 0x0ea9b68b, 0x134daf4e, 0x26a0b4db, 0x1b911145, 0x37c225bf, 0x99ae}}}, + {{{0x0127b756, 0x05d43ffb, 0x0825c120, 0x0517c957, 0x0b416034, 0x116d2830, 0x0499cb4d, 0x05ee2dbe, 0x6d8c78}}, + {{0x1f172571, 0x0a8fba55, 0x1f373299, 0x154db45a, 0x14daf4e3, 0x14169b69, 0x04445166, 0x0112dfb7, 0x99aedf}}}, /* 5*16^27*G: */ - {{{0x358cf17a, 0x37b869cd, 0x18823524, 0x3e1772e9, 0x0097f8f1, 0x166bbc6d, 0x37aca8d0, 0x2fb7656f, 0xebca}}, - {{0x1caa0ccd, 0x11b3717d, 0x0ace95c4, 0x3eb484b4, 0x032e6b10, 0x00286d9f, 0x2b9cb02c, 0x3383e3c8, 0x47d3}}}, + {{{0x158cf17a, 0x0f70d39b, 0x0208d493, 0x10bb974b, 0x097f8f1f, 0x0d778da0, 0x0b2a3416, 0x1bb2b7ef, 0xebcabe}}, + {{0x1caa0ccd, 0x0366e2fa, 0x0b3a5711, 0x15a425a1, 0x12e6b10f, 0x050db3e1, 0x072c0b00, 0x01f1e457, 0x47d3ce}}}, /* 7*16^27*G: */ - {{{0x2c855c5b, 0x33bb9456, 0x17c8afbb, 0x21588680, 0x17fc2811, 0x0c68da78, 0x0ce24453, 0x134b92f5, 0xe8df}}, - {{0x2e465650, 0x27579cb0, 0x21e4d7d5, 0x18ed57c7, 0x2f32c596, 0x136d3d67, 0x39b26444, 0x3f5c311f, 0x6c57}}}, + {{{0x0c855c5b, 0x077728ad, 0x1f22beef, 0x0ac43402, 0x1fc28118, 0x0d1b4f0b, 0x189114cc, 0x05c97a99, 0xe8df4d}}, + {{0x0e465650, 0x0eaf3961, 0x07935f56, 0x076abe3c, 0x132c5966, 0x0da7acf7, 0x0c991113, 0x0e188ff3, 0x6c57fd}}}, /* 9*16^27*G: */ - {{{0x12e7e454, 0x023d6f69, 0x30e6150d, 0x0cbbfbc3, 0x181662fe, 0x121808ea, 0x0a832912, 0x34f5c63b, 0x4068}}, - {{0x18ef191e, 0x1e6b3797, 0x3c373327, 0x23487b44, 0x1d38d198, 0x305165f6, 0x247aab9e, 0x14edc952, 0x8cd8}}}, + {{{0x12e7e454, 0x047aded2, 0x03985434, 0x05dfde1e, 0x01662fe3, 0x03011d4c, 0x00ca4492, 0x1ae31d95, 0x4068d3}}, + {{0x18ef191e, 0x1cd66f2e, 0x10dccc9d, 0x1a43da27, 0x138d1988, 0x0a2cbece, 0x1eaae7b0, 0x16e4a948, 0x8cd853}}}, /* 11*16^27*G: */ - {{{0x06c5d939, 0x215eb7e1, 0x3a933de0, 0x1d68a1de, 0x0a027ea4, 0x2fccb983, 0x025e0b55, 0x03b36c76, 0x1255}}, - {{0x19e757c9, 0x0a9d3f15, 0x0d8d4319, 0x22dd07fb, 0x324a7283, 0x2390f05d, 0x2d7a7544, 0x20cd3e1c, 0x7b8f}}}, + {{{0x06c5d939, 0x02bd6fc2, 0x0a4cf782, 0x0b450ef7, 0x0027ea47, 0x19973065, 0x1782d56f, 0x19b63b04, 0x12550e}}, + {{0x19e757c9, 0x153a7e2a, 0x16350c64, 0x16e83fd9, 0x04a72838, 0x121e0bb9, 0x1e9d5123, 0x069f0e5a, 0x7b8f83}}}, /* 13*16^27*G: */ - {{{0x16c8a56f, 0x2342ab19, 0x0f374213, 0x024f150d, 0x3ad08f85, 0x2eded4eb, 0x185d4c69, 0x19c6b0ed, 0x944d}}, - {{0x1a7be289, 0x27d37197, 0x106517eb, 0x35305d37, 0x3ac61967, 0x10e4d84c, 0x01fff4c1, 0x1965ded4, 0xa710}}}, + {{{0x16c8a56f, 0x06855632, 0x1cdd084e, 0x1278a869, 0x0d08f850, 0x1bda9d7d, 0x17531a6e, 0x035876b0, 0x944d67}}, + {{0x1a7be289, 0x0fa6e32e, 0x01945fae, 0x0982e9ba, 0x0c61967d, 0x1c9b099d, 0x1ffd3050, 0x12ef6a03, 0xa71065}}}, /* 15*16^27*G: */ - {{{0x2e08f15a, 0x3bae2862, 0x012900ba, 0x1a795b72, 0x13c305fd, 0x2c0d956b, 0x19a0cfe6, 0x13a47342, 0x86a5}}, - {{0x01388308, 0x1493479f, 0x335254d3, 0x04a74496, 0x35686777, 0x0aa341b5, 0x384603a7, 0x18520de9, 0xcfee}}} + {{{0x0e08f15a, 0x175c50c5, 0x04a402eb, 0x13cadb90, 0x1c305fd6, 0x01b2ad69, 0x0833f9ac, 0x1239a133, 0x86a54e}}, + {{0x01388308, 0x09268f3e, 0x0d49534d, 0x053a24b6, 0x16867771, 0x146836ba, 0x1180e9ca, 0x0906f4f0, 0xcfee61}}} }, { /* 1*16^28*G: */ - {{{0x0f676e03, 0x24542959, 0x3e84edd4, 0x3ff1cda4, 0x1e8761ce, 0x3d90cd5c, 0x17518eb0, 0x2500caa5, 0xb8da}}, - {{0x0efdf6e7, 0x1223939d, 0x1ff3b511, 0x33161365, 0x2808b092, 0x267325d8, 0x1a1e4d7c, 0x37e91201, 0x2804}}}, + {{{0x0f676e03, 0x08a852b2, 0x1a13b752, 0x1f8e6d27, 0x08761cef, 0x1219ab8f, 0x1463ac3d, 0x006552ae, 0xb8da94}}, + {{0x0efdf6e7, 0x0447273a, 0x1fced445, 0x18b09b2b, 0x008b092c, 0x0e64bb14, 0x07935f26, 0x148900b4, 0x2804df}}}, /* 3*16^28*G: */ - {{{0x06e1346b, 0x28661277, 0x05af1c5e, 0x2f9ec40e, 0x1152c05a, 0x31d87c53, 0x2d10be54, 0x1a3fc260, 0x0690}}, - {{0x17226c13, 0x2ed62953, 0x0c6026e7, 0x3da24e65, 0x06442aa4, 0x176caf42, 0x3de26da8, 0x38f8242f, 0xb863}}}, + {{{0x06e1346b, 0x10cc24ee, 0x16bc717a, 0x1cf62070, 0x152c05ab, 0x1b0f8a68, 0x042f9531, 0x1fe1305a, 0x69068}}, + {{0x17226c13, 0x1dac52a6, 0x11809b9e, 0x0d127329, 0x0442aa4f, 0x0d95e843, 0x189b6a17, 0x1c1217fb, 0xb863e3}}}, /* 5*16^28*G: */ - {{{0x1ca1f6a1, 0x039a47f3, 0x08cff1a3, 0x232f450d, 0x286ce106, 0x1b7172c7, 0x19761528, 0x0d24f2c9, 0x898c}}, - {{0x164f647c, 0x12b7083c, 0x32bd79ca, 0x29f3e5e7, 0x2c6e93b2, 0x1150914a, 0x2a5549d8, 0x1661aad5, 0x75f7}}}, + {{{0x1ca1f6a1, 0x07348fe6, 0x033fc68c, 0x197a2869, 0x06ce1068, 0x0e2e58f4, 0x1d854a1b, 0x127964b2, 0x898c34}}, + {{0x164f647c, 0x056e1078, 0x0af5e729, 0x0f9f2f3e, 0x06e93b2a, 0x0a122956, 0x15527611, 0x10d56ad4, 0x75f759}}}, /* 7*16^28*G: */ - {{{0x3d1e3998, 0x29a780f0, 0x3a04328a, 0x15b22e45, 0x2a274e5e, 0x0a675c08, 0x18bf01a5, 0x38bfb4a4, 0xb213}}, - {{0x325fb81e, 0x30b2f718, 0x3ded175e, 0x0d0596fa, 0x243bc3d5, 0x187afe0e, 0x13c12c3d, 0x23b083cb, 0x229f}}}, + {{{0x1d1e3998, 0x134f01e1, 0x0810ca2a, 0x0d91722f, 0x0274e5e5, 0x0ceb8115, 0x0fc0694a, 0x1fda5231, 0xb213e2}}, + {{0x125fb81e, 0x0165ee31, 0x17b45d7b, 0x082cb7d7, 0x03bc3d53, 0x0f5fc1d2, 0x104b0f58, 0x1841e5a7, 0x229f8e}}}, /* 9*16^28*G: */ - {{{0x225be234, 0x02f87fb2, 0x1df35070, 0x20f8f9c3, 0x206e060e, 0x342e9a45, 0x3f93e5d1, 0x0eb605b1, 0x4b3b}}, - {{0x120e8362, 0x18edf80e, 0x3211b840, 0x39ff64b3, 0x0cc04c41, 0x17a5b7f6, 0x2bc9c787, 0x008ee176, 0x5eec}}}, + {{{0x025be234, 0x05f0ff65, 0x17cd41c0, 0x07c7ce1b, 0x06e060e8, 0x05d348b0, 0x04f97474, 0x1b02d8ff, 0x4b3b3a}}, + {{0x120e8362, 0x11dbf01c, 0x0846e101, 0x0ffb259e, 0x0c04c41e, 0x14b6fec6, 0x1271e1d7, 0x0770bb57, 0x5eec02}}}, /* 11*16^28*G: */ - {{{0x2289f55e, 0x2598d29f, 0x2c76707b, 0x1dac3c38, 0x0965be29, 0x0946c09e, 0x04f96020, 0x222db76c, 0x9f7b}}, - {{0x3e1e4bde, 0x0f34ed97, 0x310a2b1b, 0x394db83a, 0x0fc71fc0, 0x051ad0a6, 0x010f7be3, 0x3de131c1, 0x32f9}}}, + {{{0x0289f55e, 0x0b31a53f, 0x11d9c1ee, 0x0d61e1c5, 0x165be297, 0x08d813c4, 0x1e580809, 0x16dbb609, 0x9f7b88}}, + {{0x1e1e4bde, 0x1e69db2f, 0x0428ac6c, 0x0a6dc1d6, 0x1c71fc0e, 0x035a14c7, 0x03def8c5, 0x1098e082, 0x32f9f7}}}, /* 13*16^28*G: */ - {{{0x1dfe1d2b, 0x19527230, 0x16878e51, 0x24fd4279, 0x3b73a4c4, 0x332b7f4f, 0x048e3e76, 0x10fa72dd, 0xd58a}}, - {{0x0cd50922, 0x33c9e56e, 0x0bd6fbff, 0x366e8857, 0x28276b54, 0x1ca44ca0, 0x083cf10a, 0x219ae816, 0xfc17}}}, + {{{0x1dfe1d2b, 0x12a4e460, 0x1a1e3945, 0x07ea13ca, 0x173a4c49, 0x056fe9fd, 0x038f9db3, 0x1d396e89, 0xd58a43}}, + {{0x0cd50922, 0x0793cadc, 0x0f5befff, 0x137442b9, 0x0276b54d, 0x14899414, 0x0f3c429c, 0x0d740b10, 0xfc1786}}}, /* 15*16^28*G: */ - {{{0x249c795e, 0x090546f8, 0x1ce805e1, 0x1101aaa6, 0x27ea4eed, 0x365a70f0, 0x18310cd6, 0x1c4e5c44, 0x21d2}}, - {{0x19208ece, 0x0004bb0e, 0x2dfb761b, 0x1c651292, 0x2bb4c3d6, 0x0d6e1548, 0x1acea177, 0x3e6d2c1d, 0x94c5}}} + {{{0x049c795e, 0x120a8df1, 0x13a01784, 0x080d5533, 0x1ea4eed4, 0x0b4e1e13, 0x0c4335b6, 0x072e2230, 0x21d271}}, + {{0x19208ece, 0x0009761c, 0x17edd86c, 0x03289495, 0x1b4c3d67, 0x0dc2a915, 0x13a85dcd, 0x16960eb5, 0x94c5f9}}} }, { /* 1*16^29*G: */ - {{{0x23c0df5d, 0x06845de3, 0x156a792f, 0x067bfed4, 0x1d7fab20, 0x2b6ae51d, 0x3b33a7d8, 0x3a851107, 0xe80f}}, - {{0x2ac9ec78, 0x32d0a46d, 0x3322ea9f, 0x0557a02b, 0x0a94472d, 0x25da328f, 0x200771e8, 0x379fd8e3, 0xeed1}}}, + {{{0x03c0df5d, 0x0d08bbc7, 0x15a9e4bc, 0x13dff6a2, 0x17fab201, 0x0d5ca3ae, 0x0ce9f62b, 0x028883f6, 0xe80fea}}, + {{0x0ac9ec78, 0x05a148db, 0x0c8baa7f, 0x0abd015e, 0x094472d1, 0x1b4651e5, 0x01dc7a25, 0x0fec71c0, 0xeed1de}}}, /* 3*16^29*G: */ - {{{0x17592d55, 0x300d67b3, 0x0e350192, 0x356e51d0, 0x3ce3b106, 0x3fbda58c, 0x1052608a, 0x31b6f128, 0x5d2e}}, - {{0x2f5183a7, 0x19b9743a, 0x11151742, 0x0a9ef36b, 0x0cd6950e, 0x1c43e89a, 0x245eb58f, 0x337e271b, 0x0a92}}}, + {{{0x17592d55, 0x001acf66, 0x18d4064b, 0x0b728e81, 0x0e3b106d, 0x17b4b19e, 0x149822bf, 0x1b789420, 0x5d2ec6}}, + {{0x0f5183a7, 0x1372e875, 0x04545d09, 0x14f79b5a, 0x0d6950e2, 0x087d1346, 0x17ad63dc, 0x1f138dc8, 0xa92cd}}}, /* 5*16^29*G: */ - {{{0x3e8f9f5c, 0x247d2d27, 0x1880a519, 0x187c7856, 0x1f404d73, 0x32b8d085, 0x3f742fe2, 0x0770ec46, 0xac37}}, - {{0x325a503c, 0x1ea0ffcc, 0x2751e1d1, 0x254d163b, 0x14e73522, 0x04079cc9, 0x1a477ff2, 0x05b061c2, 0xc516}}}, + {{{0x1e8f9f5c, 0x08fa5a4f, 0x02029466, 0x03e3c2b3, 0x1404d736, 0x171a10af, 0x1d0bf8b2, 0x1876237e, 0xac371d}}, + {{0x125a503c, 0x1d41ff99, 0x1d478745, 0x0a68b1dc, 0x0e735229, 0x00f3992a, 0x11dffc84, 0x1830e134, 0xc51616}}}, /* 7*16^29*G: */ - {{{0x19e33446, 0x12872354, 0x2af385df, 0x224ef114, 0x22a17a40, 0x2302f408, 0x1840c934, 0x000e853c, 0x8942}}, - {{0x26387689, 0x034e2803, 0x1e74f984, 0x3f5dcd9e, 0x3de4e06b, 0x2cb5b43b, 0x1077a4d8, 0x00e56569, 0xa9fd}}}, + {{{0x19e33446, 0x050e46a8, 0x0bce177d, 0x127788a5, 0x0a17a408, 0x005e8111, 0x10324d23, 0x07429e30, 0x894200}}, + {{0x06387689, 0x069c5007, 0x19d3e610, 0x1aee6cf3, 0x1e4e06bf, 0x16b6877e, 0x1de9362c, 0x12b2b4a0, 0xa9fd03}}}, /* 9*16^29*G: */ - {{{0x3913cb26, 0x35ca3256, 0x13bd6d03, 0x3ad06700, 0x105c9899, 0x36913fd5, 0x342a8a2c, 0x099acc28, 0x2770}}, - {{0x3348a7a2, 0x3f9c5ccf, 0x0815bebb, 0x103246f3, 0x32b324e9, 0x0b49341f, 0x0db1a555, 0x2f179e6c, 0xf649}}}, + {{{0x1913cb26, 0x0b9464ad, 0x0ef5b40f, 0x16833802, 0x05c9899e, 0x1227faa8, 0x0aa28b36, 0x0d661468, 0x277026}}, + {{0x1348a7a2, 0x1f38b99f, 0x0056faef, 0x01923799, 0x0b324e94, 0x092683f9, 0x0c69554b, 0x0bcf361b, 0xf649bc}}}, /* 11*16^29*G: */ - {{{0x195e8247, 0x02aa8085, 0x286cd1af, 0x2ff71155, 0x38ba9097, 0x179b8073, 0x3ed2178e, 0x3434e0f2, 0x75e4}}, - {{0x19982d22, 0x288ff675, 0x29ad893c, 0x36ad6dba, 0x3726d47d, 0x3e5c3b1e, 0x10990741, 0x10a85d50, 0x1fce}}}, + {{{0x195e8247, 0x0555010a, 0x01b346bc, 0x1fb88aad, 0x0ba9097b, 0x13700e7c, 0x1485e397, 0x1a70797d, 0x75e4d0}}, + {{0x19982d22, 0x111fecea, 0x06b624f2, 0x156b6dd5, 0x126d47dd, 0x0b8763db, 0x0641d07e, 0x142ea821, 0x1fce42}}}, /* 13*16^29*G: */ - {{{0x26333323, 0x11e7d136, 0x0f4abf47, 0x2eef071a, 0x04da849c, 0x08358166, 0x1bbf03f0, 0x2d8e0cd8, 0x3ed1}}, - {{0x35d61ba3, 0x2c4ff122, 0x378f7294, 0x2dca2842, 0x0f929ea9, 0x1f2625a2, 0x34ee75d9, 0x0b6922d6, 0xd84f}}}, + {{{0x06333323, 0x03cfa26d, 0x1d2afd1d, 0x177838d1, 0x0da849cb, 0x06b02cc2, 0x0fc0fc08, 0x07066c37, 0x3ed1b6}}, + {{0x15d61ba3, 0x189fe245, 0x1e3dca52, 0x0e514216, 0x1929ea9b, 0x04c4b447, 0x1b9d765f, 0x14916b69, 0xd84f2d}}}, /* 15*16^29*G: */ - {{{0x333980bf, 0x09415f52, 0x0dd00baf, 0x28dc0b94, 0x08dd4368, 0x1bf5dc8d, 0x18181b84, 0x34bc1a9d, 0x70fd}}, - {{0x20b75785, 0x0bbaa33a, 0x1d74a561, 0x040d60e1, 0x2e596b0a, 0x29043447, 0x18696957, 0x32b03435, 0x5edf}}} + {{{0x133980bf, 0x1282bea5, 0x17402ebc, 0x06e05ca1, 0x0dd4368a, 0x1ebb91a4, 0x0606e11b, 0x1e0d4eb0, 0x70fdd2}}, + {{0x00b75785, 0x17754675, 0x15d29584, 0x006b070b, 0x0596b0a1, 0x008688f7, 0x1a5a55e9, 0x181a1ab0, 0x5edfca}}} }, { /* 1*16^30*G: */ - {{{0x04e16070, 0x3701eef3, 0x2fd6915d, 0x286080c7, 0x167543f2, 0x29239475, 0x1704313b, 0x1a5ef7f3, 0xa301}}, - {{0x1e177ea1, 0x30346810, 0x0a11a130, 0x0d76fdf0, 0x140f9b17, 0x2027e897, 0x3e4f5081, 0x3e473ed9, 0x7370}}}, + {{{0x04e16070, 0x0e03dde6, 0x1f5a4577, 0x0304063d, 0x07543f2a, 0x04728eab, 0x010c4ee9, 0x0f7bf9ae, 0xa30169}}, + {{0x1e177ea1, 0x0068d020, 0x084684c3, 0x0bb7ef81, 0x00f9b173, 0x04fd12ea, 0x13d42060, 0x039f6cfc, 0x7370f9}}}, /* 3*16^30*G: */ - {{{0x138011fc, 0x1c049c00, 0x17285626, 0x165a99eb, 0x200a4d83, 0x2c4cc208, 0x1eb11156, 0x04e8c205, 0x6e83}}, - {{0x3f15ab7d, 0x2b2da7e8, 0x1c51f9a6, 0x2be456ba, 0x1ac30426, 0x04b6c807, 0x0f204c1a, 0x2062f709, 0xc147}}}, + {{{0x138011fc, 0x18093800, 0x1ca15899, 0x12d4cf5a, 0x00a4d835, 0x09984110, 0x0c4455ac, 0x146102bd, 0x6e8313}}, + {{0x1f15ab7d, 0x165b4fd1, 0x1147e69a, 0x1f22b5d3, 0x0c30426a, 0x16d900ed, 0x08130684, 0x117b849e, 0xc14781}}}, /* 5*16^30*G: */ - {{{0x100e6ba7, 0x0e9d26e3, 0x0916f7f5, 0x0dbb16d1, 0x19e1b43d, 0x0780e293, 0x0851f2bd, 0x2a4265e1, 0xf952}}, - {{0x0175e4c1, 0x36ebbb94, 0x062a2b98, 0x15c59ed3, 0x3fa0f655, 0x0dda8b89, 0x3cebf861, 0x0e96c22a, 0xd8a9}}}, + {{{0x100e6ba7, 0x1d3a4dc6, 0x045bdfd4, 0x0dd8b689, 0x1e1b43d3, 0x101c526c, 0x147caf47, 0x0132f090, 0xf952a9}}, + {{0x0175e4c1, 0x0dd77728, 0x18a8ae63, 0x0e2cf698, 0x1a0f6555, 0x1b51713f, 0x1afe184d, 0x0b611579, 0xd8a93a}}}, /* 7*16^30*G: */ - {{{0x03aa0e93, 0x2401968a, 0x2fb1f626, 0x0b8e50eb, 0x1e893a8f, 0x00c68676, 0x3fee7504, 0x1b578c74, 0x9401}}, - {{0x07addac2, 0x23bb49a2, 0x257b07a3, 0x210dceea, 0x2e6fd7f4, 0x1574d53b, 0x14d96403, 0x0cbb9711, 0x6750}}}, + {{{0x03aa0e93, 0x08032d14, 0x1ec7d89a, 0x1c72875d, 0x0893a8f2, 0x18d0cecf, 0x1b9d4100, 0x0bc63a7f, 0x94016d}}, + {{0x07addac2, 0x07769344, 0x15ec1e8e, 0x086e7754, 0x06fd7f48, 0x0e9aa777, 0x165900d5, 0x1dcb88a9, 0x675032}}}, /* 9*16^30*G: */ - {{{0x0266b17b, 0x03d218b8, 0x262bb32b, 0x0d5a2880, 0x1f09c202, 0x25e211aa, 0x3b2891bb, 0x345d3567, 0xef22}}, - {{0x39dac83e, 0x0a9b810d, 0x1c341b73, 0x39c9dbdc, 0x34a1073e, 0x27330eb8, 0x24c7568f, 0x21325eac, 0xbc57}}}, + {{{0x0266b17b, 0x07a43170, 0x18aeccac, 0x0ad14404, 0x109c2023, 0x1c42354f, 0x0a246ee5, 0x0e9ab3f6, 0xef22d1}}, + {{0x19dac83e, 0x1537021b, 0x10d06dcc, 0x0e4edee3, 0x0a1073ee, 0x0661d71a, 0x11d5a3e7, 0x192f5649, 0xbc5784}}}, /* 11*16^30*G: */ - {{{0x12d382a0, 0x0c4c056a, 0x2ecd9ae2, 0x2372ef38, 0x2df927f2, 0x2b31e02c, 0x3892d39c, 0x3bf3933a, 0xb5f7}}, - {{0x25b4b532, 0x28bc2aee, 0x1acf8c5b, 0x3ec25b4a, 0x0bddd371, 0x255f1b83, 0x3f2353c0, 0x1516d470, 0x6843}}}, + {{{0x12d382a0, 0x18980ad4, 0x1b366b88, 0x1b9779c5, 0x1f927f28, 0x063c0596, 0x04b4e72b, 0x19c99d71, 0xb5f7ef}}, + {{0x05b4b532, 0x117855dd, 0x0b3e316e, 0x1612da53, 0x1ddd371f, 0x0be37065, 0x08d4f025, 0x0b6a387e, 0x684354}}}, /* 13*16^30*G: */ - {{{0x012cffa5, 0x39a49191, 0x28cc5c47, 0x3b508219, 0x14624389, 0x1d5363ef, 0x31076408, 0x30f4acb9, 0x1cdd}}, - {{0x1521954e, 0x379b6273, 0x336b528a, 0x0726109a, 0x02b08ac4, 0x2c49afe5, 0x1f8a63fd, 0x1a832cbc, 0x1e47}}}, + {{{0x012cffa5, 0x13492322, 0x0331711f, 0x1a8410cd, 0x0624389e, 0x0a6c7dea, 0x01d9021d, 0x1a565ce2, 0x1cddc3}}, + {{0x1521954e, 0x0f36c4e6, 0x0dad4a2b, 0x193084d6, 0x0b08ac41, 0x0935fca1, 0x0298ff6c, 0x01965e3f, 0x1e476a}}}, /* 15*16^30*G: */ - {{{0x34a9f22f, 0x0d7f90e4, 0x17a8e2ad, 0x02067148, 0x0835b0cc, 0x3e2e2e52, 0x0e939f21, 0x2cd67c97, 0x2acc}}, - {{0x375c4927, 0x2dd772ce, 0x1ba550b7, 0x12f5efb1, 0x30edf115, 0x04e8dfb7, 0x2d2e5192, 0x293a5622, 0xd518}}} + {{{0x14a9f22f, 0x1aff21c9, 0x1ea38ab4, 0x10338a42, 0x035b0cc0, 0x05c5ca44, 0x04e7c87e, 0x0b3e4b9d, 0x2accb3}}, + {{0x175c4927, 0x1baee59d, 0x0e9542de, 0x17af7d8b, 0x0edf1154, 0x1d1bf6f8, 0x0b946484, 0x1d2b115a, 0xd518a4}}} }, { /* 1*16^31*G: */ - {{{0x3fb04ed4, 0x2deb18f8, 0x1307fffa, 0x330cc2c4, 0x278de208, 0x3e741449, 0x2b936463, 0x216ce275, 0x90ad}}, - {{0x0b6ef150, 0x24753523, 0x182894d9, 0x2bbeaf85, 0x3222b839, 0x372f6509, 0x38261aff, 0x1e8d8828, 0x0e50}}}, + {{{0x1fb04ed4, 0x1bd631f1, 0x0c1fffea, 0x18661622, 0x18de208c, 0x0e828933, 0x04d918fe, 0x16713ad7, 0x90ad85}}, + {{0x0b6ef150, 0x08ea6a46, 0x00a25366, 0x1df57c2b, 0x022b839a, 0x05eca139, 0x0986bff7, 0x06c41470, 0xe507a}}}, /* 3*16^31*G: */ - {{{0x30b7b678, 0x09d76cce, 0x0f638166, 0x0f10c46f, 0x2b6c76f1, 0x21af2909, 0x0231ba19, 0x125ccd39, 0x186e}}, - {{0x38d91fc1, 0x1e81dbcb, 0x09535dca, 0x01dc8951, 0x37e67e11, 0x3f209702, 0x3bd84aa7, 0x18392601, 0xc0d4}}}, + {{{0x10b7b678, 0x13aed99d, 0x1d8e0598, 0x18862379, 0x16c76f13, 0x15e52135, 0x0c6e8661, 0x0e669c84, 0x186e49}}, + {{0x18d91fc1, 0x1d03b797, 0x054d7729, 0x0ee44a89, 0x1e67e110, 0x0412e05b, 0x1612a9ff, 0x1c9300f7, 0xc0d460}}}, /* 5*16^31*G: */ - {{{0x33421fb8, 0x3c1b972e, 0x35a55d0c, 0x125c7cbb, 0x37241298, 0x01acd30e, 0x1bf62e7e, 0x2360d3db, 0x061c}}, - {{0x0e3ccd80, 0x257bd9a1, 0x26fcdd29, 0x19c4d2ce, 0x05eb5c80, 0x0e496438, 0x3b4b7ba9, 0x1ab66400, 0x6dfc}}}, + {{{0x13421fb8, 0x18372e5d, 0x16957433, 0x12e3e5de, 0x12412984, 0x159a61db, 0x1d8b9f81, 0x1069edb7, 0x61c8d}}, + {{0x0e3ccd80, 0x0af7b342, 0x1bf374a6, 0x0e269674, 0x1eb5c806, 0x092c8702, 0x12deea4e, 0x1b320076, 0x6dfc6a}}}, /* 7*16^31*G: */ - {{{0x2f6b35a4, 0x0492f862, 0x327fb487, 0x27cde9aa, 0x3a68ad88, 0x18c901cc, 0x2e513b73, 0x2d8e8823, 0xf6a6}}, - {{0x01f422a6, 0x2badbfb2, 0x1ee1862c, 0x355d5b9d, 0x20186f19, 0x34dc13d5, 0x1138b1ca, 0x322a000b, 0x3df7}}}, + {{{0x0f6b35a4, 0x0925f0c5, 0x09fed21c, 0x1e6f4d56, 0x068ad889, 0x1920399d, 0x144edcd8, 0x074411dc, 0xf6a6b6}}, + {{0x01f422a6, 0x175b7f64, 0x1b8618b2, 0x0aeadceb, 0x0186f19d, 0x1b827ab0, 0x0e2c72b4, 0x150005a2, 0x3df7c8}}}, /* 9*16^31*G: */ - {{{0x26954c11, 0x25a08fa2, 0x160d018b, 0x2a290f05, 0x0778ff7f, 0x346c3c54, 0x2c376220, 0x3f0a30a1, 0x87a2}}, - {{0x272a8b45, 0x15b8ccb8, 0x278124b7, 0x1224cfca, 0x127532cc, 0x06523683, 0x2ecef97b, 0x1462d16a, 0x33ad}}}, + {{{0x06954c11, 0x0b411f45, 0x1834062e, 0x1148782a, 0x178ff7fa, 0x0d878a83, 0x0dd88834, 0x051850d8, 0x87a2fc}}, + {{0x072a8b45, 0x0b719971, 0x1e0492dd, 0x11267e54, 0x07532cc4, 0x0a46d069, 0x13be5ec6, 0x1168b55d, 0x33ad51}}}, /* 11*16^31*G: */ - {{{0x22706ab6, 0x391d1cab, 0x2e53c0da, 0x02cd0774, 0x384cfe3c, 0x15bbf2f0, 0x081a6845, 0x0b811b9e, 0xe147}}, - {{0x1d58de05, 0x1ba1a85a, 0x13cd2753, 0x16275551, 0x0621f8aa, 0x1a465e32, 0x18fc683f, 0x24aa91f1, 0x82cd}}}, + {{{0x02706ab6, 0x123a3957, 0x194f036b, 0x16683ba5, 0x04cfe3c0, 0x177e5e1c, 0x069a1155, 0x008dcf10, 0xe1472e}}, + {{0x1d58de05, 0x174350b4, 0x0f349d4d, 0x113aaa8a, 0x021f8aa5, 0x08cbc643, 0x1f1a0fda, 0x1548f8b1, 0x82cd92}}}, /* 13*16^31*G: */ - {{{0x07a84fb6, 0x2feb9508, 0x3a15021e, 0x08da1d43, 0x08b9ebc4, 0x2d358079, 0x0aef5de8, 0x24b2013e, 0x1caf}}, - {{0x27149109, 0x1ac60640, 0x22ce6761, 0x07305a5a, 0x101622ec, 0x2993e3fc, 0x2e53a481, 0x2e16b25d, 0xbc24}}}, + {{{0x07a84fb6, 0x1fd72a10, 0x0854087a, 0x06d0ea1f, 0x0b9ebc42, 0x06b00f24, 0x1bd77a2d, 0x19009f15, 0x1caf92}}, + {{0x07149109, 0x158c0c81, 0x0b399d85, 0x1982d2d4, 0x01622ec1, 0x127c7f88, 0x14e92069, 0x0b592edc, 0xbc24b8}}}, /* 15*16^31*G: */ - {{{0x0a955911, 0x1da33f85, 0x0ded52db, 0x1f85a898, 0x17839710, 0x27bfa6cf, 0x1650d258, 0x3f5a6bc2, 0x705b}}, - {{0x3fd200e4, 0x2edf1a4f, 0x242e72d8, 0x1fced48a, 0x0051fa29, 0x18f607d5, 0x3f990a7e, 0x2904c2dc, 0xe14a}}} + {{{0x0a955911, 0x1b467f0a, 0x17b54b6d, 0x1c2d44c1, 0x18397107, 0x17f4d9eb, 0x14349627, 0x0d35e12c, 0x705bfd}}, + {{0x1fd200e4, 0x1dbe349f, 0x10b9cb62, 0x1e76a454, 0x051fa297, 0x1ec0faa0, 0x06429f98, 0x02616e7f, 0xe14aa4}}} }, { /* 1*16^32*G: */ - {{{0x1ec4c0da, 0x2ded1132, 0x23ea3351, 0x23159e1c, 0x1f162ee8, 0x2706b660, 0x35f33923, 0x2e74bd8e, 0x8f68}}, - {{0x101fff82, 0x08f2fde5, 0x1510bfdf, 0x3a8b3fa5, 0x3e215dbb, 0x36430ada, 0x23986de1, 0x27cb6e81, 0x662a}}}, + {{{0x1ec4c0da, 0x1bda2264, 0x0fa8cd46, 0x18acf0e4, 0x1162ee88, 0x00d6cc0f, 0x1cce48e7, 0x1a5ec76b, 0x8f68b9}}, + {{0x101fff82, 0x11e5fbca, 0x1442ff7c, 0x1459fd2a, 0x0215dbbe, 0x08615b5f, 0x061b7876, 0x05b740c7, 0x662a9f}}}, /* 3*16^32*G: */ - {{{0x123809fa, 0x238ae3b7, 0x1d954be1, 0x21172cd4, 0x051f08fd, 0x24cd8fc9, 0x09f228ba, 0x076f8b94, 0x3838}}, - {{0x331fed52, 0x35c1d460, 0x2d8f24db, 0x207f32cc, 0x0eb1cc36, 0x10169548, 0x117dcb09, 0x0b4283ee, 0xe4a3}}}, + {{{0x123809fa, 0x0715c76e, 0x16552f86, 0x08b966a3, 0x11f08fd8, 0x19b1f922, 0x1c8a2ea4, 0x17c5ca13, 0x38381d}}, + {{0x131fed52, 0x0b83a8c1, 0x163c936f, 0x03f99665, 0x0b1cc368, 0x02d2a907, 0x1f72c250, 0x0141f722, 0xe4a32d}}}, /* 5*16^32*G: */ - {{{0x17c2a310, 0x3a909922, 0x01226303, 0x21aba950, 0x0699a1f1, 0x086e0aa9, 0x32ae6f69, 0x09c9390d, 0x4926}}, - {{0x1e27ded0, 0x3106da05, 0x35ff8ce0, 0x058d84a9, 0x14303b6d, 0x33e95a5c, 0x3abf95a2, 0x39dcef29, 0x1337}}}, + {{{0x17c2a310, 0x15213244, 0x04898c0f, 0x0d5d4a80, 0x099a1f18, 0x0dc15523, 0x0b9bda48, 0x049c86e5, 0x492627}}, + {{0x1e27ded0, 0x020db40a, 0x17fe3383, 0x0c6c254e, 0x0303b6d1, 0x1d2b4b8a, 0x0fe568b3, 0x0e7794f5, 0x1337e7}}}, /* 7*16^32*G: */ - {{{0x0ebd2d31, 0x0e12c1e7, 0x306db8d1, 0x330695bf, 0x37e2f84d, 0x094ecf91, 0x00c90d5e, 0x15a30689, 0xe306}}, - {{0x12546e44, 0x24ad020e, 0x23738266, 0x2f2010af, 0x3d0db6ff, 0x3cac41fd, 0x34260888, 0x1bf8de24, 0x0eac}}}, + {{{0x0ebd2d31, 0x1c2583ce, 0x01b6e344, 0x1834adfe, 0x1e2f84dc, 0x09d9f23b, 0x12435789, 0x11834481, 0xe30656}}, + {{0x12546e44, 0x095a041c, 0x0dce099a, 0x1900857c, 0x10db6ffb, 0x15883fbe, 0x0982223c, 0x1c6f1268, 0xeac6f}}}, /* 9*16^32*G: */ - {{{0x363136b0, 0x14c30e78, 0x2b41dd9c, 0x3afe366a, 0x3bd63374, 0x2c39d88f, 0x0cefc271, 0x0403890a, 0x3b9e}}, - {{0x2cdbbc8a, 0x14fb05bd, 0x2d31f819, 0x2b8a28ce, 0x075b26a2, 0x14cfae3d, 0x2bb71df1, 0x26054b45, 0xfafb}}}, + {{{0x163136b0, 0x09861cf1, 0x0d077671, 0x17f1b355, 0x1d63374e, 0x073b11fd, 0x1bf09c6c, 0x01c48519, 0x3b9e10}}, + {{0x0cdbbc8a, 0x09f60b7b, 0x14c7e065, 0x1c514675, 0x15b26a2a, 0x19f5c7a3, 0x0dc77c54, 0x02a5a2d7, 0xfafb98}}}, /* 11*16^32*G: */ - {{{0x2f485d3f, 0x1823c11c, 0x107beee9, 0x3281da20, 0x1edef717, 0x1b2a03d7, 0x2c9a92b7, 0x2b525c4a, 0xbb0a}}, - {{0x3ca2f975, 0x1e4e4940, 0x1670bffe, 0x1696be8c, 0x17da3489, 0x34807dca, 0x354798ec, 0x2714f160, 0xea69}}}, + {{{0x0f485d3f, 0x10478239, 0x01efbba5, 0x140ed102, 0x0def717c, 0x05407aef, 0x06a4addb, 0x092e2559, 0xbb0aad}}, + {{0x1ca2f975, 0x1c9c9281, 0x19c2fff9, 0x14b5f462, 0x1da34895, 0x100fb94b, 0x11e63b34, 0x0a78b06a, 0xea699c}}}, /* 13*16^32*G: */ - {{{0x36718dc9, 0x2bbb4ce8, 0x01123de4, 0x3962d36c, 0x3e0113e1, 0x23ac65eb, 0x2fcc0d4e, 0x02b2393b, 0x7909}}, - {{0x1cfae7c5, 0x18cc8ac4, 0x3a9008b9, 0x0dabedc2, 0x1aaa56dd, 0x205b2f36, 0x05b8f13d, 0x1c8ae464, 0xeaab}}}, + {{{0x16718dc9, 0x177699d1, 0x0448f792, 0x0b169b60, 0x00113e1e, 0x158cbd7f, 0x130353a3, 0x191c9ddf, 0x79090a}}, + {{0x1cfae7c5, 0x11991588, 0x0a4022e5, 0x0d5f6e17, 0x0aa56dd3, 0x0b65e6cd, 0x0e3c4f60, 0x0572320b, 0xeaab72}}}, /* 15*16^32*G: */ - {{{0x3f60c7d1, 0x09a5a531, 0x1775ad2a, 0x35c779f3, 0x09ba668d, 0x0f6ef395, 0x17b551c0, 0x206b7a7e, 0xe77c}}, - {{0x02d72449, 0x3b1607ca, 0x02986d34, 0x051c3dc7, 0x28154363, 0x30ecc8fa, 0x01321c5f, 0x051e3bbe, 0x3acf}}} + {{{0x1f60c7d1, 0x134b4a63, 0x1dd6b4a8, 0x0e3bcf9a, 0x1ba668dd, 0x0dde72a4, 0x0d54700f, 0x15bd3f2f, 0xe77c81}}, + {{0x02d72449, 0x162c0f94, 0x0a61b4d3, 0x08e1ee38, 0x01543631, 0x1d991f54, 0x0c8717f0, 0x0f1ddf02, 0x3acf14}}} }, { /* 1*16^33*G: */ - {{{0x13231e11, 0x1a1bf541, 0x3681e3e6, 0x123a1940, 0x0c36091f, 0x267fe466, 0x385d65ff, 0x3ec05dab, 0xe4f3}}, - {{0x2feb73bc, 0x08b0e15d, 0x151d1c98, 0x31f9d3b2, 0x02b7286c, 0x069b43a8, 0x34f1c166, 0x18ceb43b, 0x1e63}}}, + {{{0x13231e11, 0x1437ea82, 0x1a078f99, 0x11d0ca06, 0x036091f4, 0x0ffc8cc6, 0x17597fe6, 0x002ed5f0, 0xe4f3fb}}, + {{0x0feb73bc, 0x1161c2bb, 0x14747260, 0x0fce9d92, 0x0b7286cc, 0x13687501, 0x1c705986, 0x075a1de9, 0x1e6363}}}, /* 3*16^33*G: */ - {{{0x2bf05bd6, 0x0e67c139, 0x12a99465, 0x3d5b80c8, 0x070deca2, 0x0bd47fad, 0x04fe9083, 0x0c906fb9, 0x900c}}, - {{0x300d358b, 0x394ab4ef, 0x04efb15d, 0x2614d60f, 0x0b2439d6, 0x31c8115c, 0x1f0f5f95, 0x3e7a3a2c, 0x6c31}}}, + {{{0x0bf05bd6, 0x1ccf8273, 0x0aa65194, 0x0adc0642, 0x10deca2f, 0x1a8ff5a3, 0x1fa420cb, 0x0837dc89, 0x900c32}}, + {{0x100d358b, 0x129569df, 0x13bec577, 0x10a6b078, 0x12439d69, 0x19022b85, 0x03d7e571, 0x1d1d163e, 0x6c31f9}}}, /* 5*16^33*G: */ - {{{0x1f105c50, 0x29f0a332, 0x31385257, 0x3837bbde, 0x0233cd82, 0x2330d00f, 0x190aad62, 0x00d8aac1, 0x5a8d}}, - {{0x38a4cde9, 0x326c8060, 0x2d013c35, 0x017da299, 0x03ff74a6, 0x29adc905, 0x0e536936, 0x3aac44f5, 0xc059}}}, + {{{0x1f105c50, 0x13e14664, 0x04e1495e, 0x01bddef6, 0x033cd82e, 0x061a01e1, 0x02ab58a3, 0x0c5560b2, 0x5a8d03}}, + {{0x18a4cde9, 0x04d900c1, 0x1404f0d7, 0x0bed14cd, 0x1ff74a60, 0x15b920a1, 0x14da4da9, 0x16227a9c, 0xc059ea}}}, /* 7*16^33*G: */ - {{{0x32d64feb, 0x11f862e6, 0x292292c6, 0x1cbe2964, 0x0ba4e837, 0x3ce95ddb, 0x2f60a48e, 0x1340c48c, 0xd93f}}, - {{0x34698359, 0x2c3ef564, 0x2c90da37, 0x3810c2fb, 0x1c8c4d93, 0x1cc47153, 0x32733a23, 0x15575172, 0x7925}}}, + {{{0x12d64feb, 0x03f0c5cd, 0x048a4b19, 0x05f14b25, 0x1a4e8377, 0x1d2bbb65, 0x182923bc, 0x0062465e, 0xd93f4d}}, + {{0x14698359, 0x187deac9, 0x124368de, 0x008617dd, 0x08c4d93e, 0x188e2a6e, 0x1cce88dc, 0x0ba8b964, 0x792555}}}, /* 9*16^33*G: */ - {{{0x039fbc84, 0x08881335, 0x057a0167, 0x1c18a458, 0x2ac65b7e, 0x138af198, 0x328441b1, 0x1a71b8db, 0x2f07}}, - {{0x1c201bec, 0x3ee40b78, 0x04dd5d73, 0x29e6da93, 0x0e2149cc, 0x37c01e64, 0x3bdddfa5, 0x3cdc935c, 0xb434}}}, + {{{0x039fbc84, 0x1110266a, 0x15e8059c, 0x00c522c0, 0x0c65b7e7, 0x115e3315, 0x01106c53, 0x18dc6de5, 0x2f0769}}, + {{0x1c201bec, 0x1dc816f0, 0x137575cf, 0x0f36d498, 0x02149cca, 0x1803cc87, 0x1777e977, 0x0e49ae77, 0xb434f3}}}, /* 11*16^33*G: */ - {{{0x06a758ea, 0x14dfab32, 0x27f19c4d, 0x0620c624, 0x016e3991, 0x1a256855, 0x20309958, 0x19e01567, 0xfe7e}}, - {{0x1b7ab649, 0x13c8b657, 0x03120d1e, 0x2005c1d1, 0x09251f3b, 0x02385a61, 0x1dcb988c, 0x1a59e8a0, 0x38aa}}}, + {{{0x06a758ea, 0x09bf5664, 0x1fc67135, 0x11063124, 0x16e39911, 0x04ad0aa0, 0x0c26561a, 0x100ab3c0, 0xfe7e67}}, + {{0x1b7ab649, 0x07916cae, 0x0c483479, 0x002e0e88, 0x1251f3b8, 0x070b4c24, 0x12e62302, 0x0cf4503b, 0x38aa69}}}, /* 13*16^33*G: */ - {{{0x0cfffefa, 0x39c5589a, 0x0651afad, 0x060113dc, 0x03af8510, 0x3dbe4543, 0x03127d6d, 0x3d729d4e, 0x91ba}}, - {{0x1f7f6faf, 0x1f4dbcd3, 0x2fd303dc, 0x2fbcc439, 0x1d3d92f4, 0x25a7c49f, 0x3bcebe5d, 0x33c464d1, 0x04e5}}}, + {{{0x0cfffefa, 0x138ab134, 0x1946beb7, 0x10089ee0, 0x1af85101, 0x17c8a861, 0x049f5b7d, 0x194ea706, 0x91baf5}}, + {{0x1f7f6faf, 0x1e9b79a6, 0x1f4c0f71, 0x1de621cd, 0x13d92f4b, 0x14f893ee, 0x13af9765, 0x023268f7, 0x4e5cf}}}, /* 15*16^33*G: */ - {{{0x0d33c546, 0x3f0245fa, 0x05edaf32, 0x15d7ecca, 0x35ddd782, 0x314dcf83, 0x378a7cb2, 0x104872cf, 0x4458}}, - {{0x000b4fd4, 0x029b461c, 0x32ca7366, 0x0bc28f3e, 0x1ada2085, 0x097ab8e4, 0x0753a772, 0x24ddfcfe, 0x308d}}} + {{{0x0d33c546, 0x1e048bf4, 0x17b6bccb, 0x0ebf6650, 0x1ddd7825, 0x09b9f07a, 0x029f2cb1, 0x043967ef, 0x445841}}, + {{0x000b4fd4, 0x05368c38, 0x0b29cd98, 0x1e1479f6, 0x0da20852, 0x0f571c8d, 0x14e9dc89, 0x0efe7f0e, 0x308d93}}} }, { /* 1*16^34*G: */ - {{{0x20eae29e, 0x1bedbab8, 0x14e1d071, 0x00d3cbc3, 0x1a4266c7, 0x1854de91, 0x3f331eb9, 0x3ea6c63a, 0x8c00}}, - {{0x2702414b, 0x1f4a9319, 0x1e36c54e, 0x3eb6bea0, 0x36c974c2, 0x30d0e8dc, 0x121a1a9d, 0x1c99ffa9, 0xefa4}}}, + {{{0x00eae29e, 0x17db7571, 0x138741c5, 0x069e5e1a, 0x04266c70, 0x0a9bd22d, 0x0cc7ae58, 0x13631d7e, 0x8c00fa}}, + {{0x0702414b, 0x1e952633, 0x18db1539, 0x15b5f503, 0x0c974c2f, 0x1a1d1b9b, 0x0686a770, 0x0cffd4a4, 0xefa472}}}, /* 3*16^34*G: */ - {{{0x2bfd913d, 0x0fe5580f, 0x254c9eac, 0x29a039bb, 0x2a8d2050, 0x01e82130, 0x3ddf874d, 0x0aa9fa41, 0x3636}}, - {{0x052e243d, 0x113e6bab, 0x2b2faafc, 0x0c2ec435, 0x1a2a82d8, 0x18910dc3, 0x0afd5341, 0x1e19db2e, 0x48f2}}}, + {{{0x0bfd913d, 0x1fcab01f, 0x15327ab0, 0x0d01cddc, 0x08d2050a, 0x1d042615, 0x17e1d341, 0x14fd20fb, 0x36362a}}, + {{0x052e243d, 0x027cd756, 0x0cbeabf1, 0x017621ad, 0x02a82d83, 0x1221b86d, 0x1f54d058, 0x0ced9715, 0x48f278}}}, /* 5*16^34*G: */ - {{{0x2d132896, 0x32aeafe6, 0x3bc6c967, 0x2c78eead, 0x19200dfc, 0x16b658b7, 0x21e02f29, 0x25db7cca, 0x4487}}, - {{0x2f685248, 0x23006c4a, 0x276aa7a4, 0x2d035698, 0x161a3306, 0x26a41dd1, 0x1afe1efc, 0x16183445, 0x27bd}}}, + {{{0x0d132896, 0x055d5fcd, 0x0f1b259f, 0x03c7756f, 0x1200dfcb, 0x16cb16ec, 0x180bca56, 0x0dbe6543, 0x448797}}, + {{0x0f685248, 0x0600d895, 0x1daa9e92, 0x081ab4c4, 0x01a3306b, 0x1483ba2b, 0x1f87bf26, 0x0c1a22b5, 0x27bd58}}}, /* 7*16^34*G: */ - {{{0x3fa2670c, 0x02055bda, 0x06273e6e, 0x003e0ae8, 0x35032474, 0x2a72aa0c, 0x383788b6, 0x0eb0a2f2, 0x4a4d}}, - {{0x16c1764d, 0x022e7ff7, 0x329beed8, 0x0c16532f, 0x302b9d49, 0x1dc4777b, 0x05a4f17e, 0x2e470061, 0x70ab}}}, + {{{0x1fa2670c, 0x040ab7b5, 0x189cf9b8, 0x01f05740, 0x10324740, 0x0e55419a, 0x0de22daa, 0x18517970, 0x4a4d3a}}, + {{0x16c1764d, 0x045cffee, 0x0a6fbb60, 0x00b2997e, 0x02b9d493, 0x188eef78, 0x093c5f9d, 0x0380308b, 0x70abb9}}}, /* 9*16^34*G: */ - {{{0x0cb24aa7, 0x365abf89, 0x1345c530, 0x0c42318e, 0x38fe1890, 0x39bf627f, 0x11802c3a, 0x0b4642ba, 0x5f7b}}, - {{0x0a693d7d, 0x35e01d0d, 0x3c81d0c6, 0x237adc24, 0x267c47ce, 0x0fe028f3, 0x1f2b330a, 0x0d80313f, 0x0770}}}, + {{{0x0cb24aa7, 0x0cb57f12, 0x0d1714c3, 0x02118c72, 0x0fe18903, 0x17ec4ffc, 0x000b0eb9, 0x03215d23, 0x5f7b2d}}, + {{0x0a693d7d, 0x0bc03a1a, 0x1207431b, 0x1bd6e127, 0x07c47ce8, 0x1c051e73, 0x0accc28f, 0x00189fbe, 0x77036}}}, /* 11*16^34*G: */ - {{{0x2f7fb8bd, 0x0646f17c, 0x3e4090a4, 0x31192857, 0x0886d87b, 0x30939b65, 0x190d02ae, 0x1d144ce7, 0x5139}}, - {{0x03908c0f, 0x0252b0b6, 0x3f98d5a8, 0x3f0cb4f8, 0x015c47fa, 0x23fbf6ba, 0x03bf34b8, 0x050f91d9, 0xfcd7}}}, + {{{0x0f7fb8bd, 0x0c8de2f9, 0x19024290, 0x08c942bf, 0x086d87bc, 0x12736ca4, 0x0340abb0, 0x0a2673b2, 0x513974}}, + {{0x03908c0f, 0x04a5616c, 0x1e6356a0, 0x1865a7c7, 0x15c47faf, 0x1f7ed740, 0x0fcd2e23, 0x07c8ec87, 0xfcd714}}}, /* 13*16^34*G: */ - {{{0x2e36ca73, 0x0add2457, 0x3bbf3ede, 0x321934da, 0x014887ea, 0x0a444afc, 0x3dfb8aa4, 0x05b58afe, 0xcf83}}, - {{0x2ec25534, 0x2d248650, 0x08d710f5, 0x25856636, 0x1cca681c, 0x11142243, 0x19d73e38, 0x2d637ad7, 0x09fe}}}, + {{{0x0e36ca73, 0x15ba48af, 0x0efcfb78, 0x10c9a6d7, 0x14887eac, 0x08895f80, 0x1ee2a90a, 0x1ac57f7b, 0xcf8316}}, + {{0x0ec25534, 0x1a490ca1, 0x035c43d6, 0x0c2b31b1, 0x0ca681c9, 0x0284486e, 0x15cf8e11, 0x11bd6bb3, 0x9feb5}}}, /* 15*16^34*G: */ - {{{0x3752f97d, 0x3224df5a, 0x33476613, 0x0bbef1d7, 0x0fa6165a, 0x274a19a3, 0x3b49de53, 0x37a69312, 0x8610}}, - {{0x1f1b1af2, 0x015f7350, 0x05543e08, 0x2ad367d5, 0x33f99e57, 0x33666c94, 0x30bbc937, 0x25e80ad8, 0xd319}}} + {{{0x1752f97d, 0x0449beb5, 0x0d1d984f, 0x1df78ebe, 0x1a6165a2, 0x09433467, 0x127794e7, 0x13498976, 0x8610de}}, + {{0x1f1b1af2, 0x02bee6a0, 0x1550f820, 0x169b3ea8, 0x1f99e57a, 0x0ccd9299, 0x0ef24df3, 0x14056c61, 0xd31997}}} }, { /* 1*16^35*G: */ - {{{0x20cb3e41, 0x25ff77f1, 0x08b92c09, 0x0f4213cc, 0x298ed314, 0x033b02a7, 0x0829f3e1, 0x1b39a775, 0xe7a2}}, - {{0x0f2cfd51, 0x3a2a5087, 0x20e83e20, 0x29acb010, 0x2fbb18d0, 0x2c01a86a, 0x3984b471, 0x238c03e9, 0x2a75}}}, + {{{0x00cb3e41, 0x0bfeefe3, 0x02e4b026, 0x1a109e61, 0x18ed3143, 0x076054f4, 0x0a7cf843, 0x1cd3ba90, 0xe7a26c}}, + {{0x0f2cfd51, 0x1454a10e, 0x03a0f883, 0x0d658084, 0x1bb18d0a, 0x00350d57, 0x012d1c6c, 0x0601f4f3, 0x2a758e}}}, /* 3*16^35*G: */ - {{{0x3aee42db, 0x03e7f4af, 0x330714a7, 0x2eef16d1, 0x2cbfc1d9, 0x2dbb6e47, 0x19150fc7, 0x09f9f66d, 0xcc34}}, - {{0x15d87bdb, 0x188a7004, 0x272422dc, 0x3972eb63, 0x21520010, 0x38ff4fec, 0x1c6a1885, 0x26106948, 0xea24}}}, + {{{0x1aee42db, 0x07cfe95f, 0x0c1c529c, 0x1778b68e, 0x0bfc1d9b, 0x176dc8f6, 0x0543f1ed, 0x1cfb36b2, 0xcc3427}}, + {{0x15d87bdb, 0x1114e008, 0x1c908b71, 0x0b975b1c, 0x1520010e, 0x1fe9fd90, 0x1a862178, 0x0834a438, 0xea2498}}}, /* 5*16^35*G: */ - {{{0x3ed4a086, 0x3d0d9b19, 0x29c410ef, 0x35d70563, 0x0b5cf4b1, 0x0f1617ef, 0x0445dec8, 0x016eb366, 0x948f}}, - {{0x1e2bca4b, 0x0a86003e, 0x03fa2d1a, 0x08ca29c7, 0x1139411c, 0x11429980, 0x22a3382f, 0x2a27fed6, 0x864c}}}, + {{{0x1ed4a086, 0x1a1b3633, 0x071043bf, 0x0eb82b1d, 0x15cf4b1d, 0x02c2fde5, 0x1177b20f, 0x1759b308, 0x948f05}}, + {{0x1e2bca4b, 0x150c007c, 0x0fe8b468, 0x06514e38, 0x139411c2, 0x08533008, 0x08ce0bd1, 0x13ff6b45, 0x864ca8}}}, /* 7*16^35*G: */ - {{{0x37542c21, 0x032fa9b2, 0x2a64c15c, 0x067d34a3, 0x1d6d43ae, 0x1bf11514, 0x19ac9065, 0x0658a4a4, 0x2584}}, - {{0x272bfabf, 0x2faf8c65, 0x0c2ad7b3, 0x38e861b9, 0x3513d5f3, 0x176a9331, 0x3244801e, 0x16c7c736, 0xfcb3}}}, + {{{0x17542c21, 0x065f5365, 0x09930570, 0x13e9a51d, 0x16d43ae1, 0x1e22a28e, 0x0b24195b, 0x0c525233, 0x258419}}, + {{0x072bfabf, 0x1f5f18cb, 0x10ab5ece, 0x07430dc9, 0x113d5f3e, 0x0d52663a, 0x11200797, 0x03e39b64, 0xfcb35b}}}, /* 9*16^35*G: */ - {{{0x0c1ecbf8, 0x0f1187d0, 0x2eed7ca4, 0x227c37a6, 0x28421f64, 0x25d53307, 0x3c52522a, 0x337104dc, 0x7e12}}, - {{0x30bed615, 0x3516e336, 0x3e1d9f59, 0x1a7d8763, 0x0d1259c9, 0x3e536af9, 0x1c837143, 0x13e22223, 0x7128}}}, + {{{0x0c1ecbf8, 0x1e230fa0, 0x1bb5f290, 0x13e1bd35, 0x0421f648, 0x1aa660f4, 0x14948aa5, 0x18826e78, 0x7e12cd}}, + {{0x10bed615, 0x0a2dc66d, 0x18767d67, 0x13ec3b1f, 0x11259c96, 0x0a6d5f26, 0x00dc50fe, 0x111111b9, 0x71284f}}}, /* 11*16^35*G: */ - {{{0x14557d86, 0x1f999470, 0x2667ff41, 0x3fbb11e3, 0x05a6cf1c, 0x2e4729e8, 0x342a6772, 0x30bfca8d, 0x4b8e}}, - {{0x35167eb9, 0x3766c646, 0x3c3f692b, 0x357cbbc3, 0x27ac5f28, 0x101cb794, 0x157ab14a, 0x30ffc130, 0xfde6}}}, + {{{0x14557d86, 0x1f3328e0, 0x199ffd05, 0x1dd88f1c, 0x1a6cf1cf, 0x08e53d02, 0x0a99dcae, 0x1fe546e8, 0x4b8ec2}}, + {{0x15167eb9, 0x0ecd8c8d, 0x10fda4af, 0x0be5de1f, 0x1ac5f28d, 0x0396f293, 0x1eac5290, 0x1fe0982a, 0xfde6c3}}}, /* 13*16^35*G: */ - {{{0x0780763c, 0x0ae0b4ed, 0x265691d5, 0x229b57a4, 0x3ac07e5f, 0x10db71a5, 0x23a42532, 0x3041cce5, 0xfcd5}}, - {{0x38e851cb, 0x1539d080, 0x16463a4b, 0x066c8b9c, 0x32e38cb1, 0x0836cd7d, 0x22c463b7, 0x2af8b954, 0x18dd}}}, + {{{0x0780763c, 0x15c169da, 0x195a4754, 0x14dabd24, 0x0c07e5f8, 0x1b6e34bd, 0x09094c90, 0x00e672c7, 0xfcd5c1}}, + {{0x18e851cb, 0x0a73a101, 0x1918e92d, 0x13645ce2, 0x0e38cb11, 0x06d9afb9, 0x1118edc8, 0x1c5caa45, 0x18ddab}}}, /* 15*16^35*G: */ - {{{0x1d8ef686, 0x338ef8c1, 0x2272e66b, 0x23923d00, 0x266e53f6, 0x22976be0, 0x3cbe5223, 0x0b3b9610, 0x900f}}, - {{0x2121a8cf, 0x1ce9259f, 0x09156d50, 0x1b37fd0f, 0x09d11059, 0x31546c4d, 0x0425ad61, 0x30557b18, 0x732a}}} + {{{0x1d8ef686, 0x071df182, 0x09cb99af, 0x1c91e804, 0x06e53f68, 0x12ed7c13, 0x0f9488e2, 0x1dcb0879, 0x900f2c}}, + {{0x0121a8cf, 0x19d24b3f, 0x0455b541, 0x19bfe879, 0x1d110596, 0x0a8d89a4, 0x096b5871, 0x0abd8c08, 0x732ac1}}} }, { /* 1*16^36*G: */ - {{{0x1e6b80ef, 0x33ca7acf, 0x179424f3, 0x32f2e59f, 0x3cbdc571, 0x1503088e, 0x22ec8d23, 0x2783b8d9, 0xb645}}, - {{0x1a71ba45, 0x0c2fc2d8, 0x0e35b2ff, 0x2ceb9b52, 0x261db3c4, 0x2b7c5b95, 0x3e06de1d, 0x21db41bc, 0x067c}}}, + {{{0x1e6b80ef, 0x0794f59e, 0x1e5093cf, 0x17972cfa, 0x0bdc571c, 0x006111de, 0x1b2348d5, 0x01dc6cc5, 0xb6459e}}, + {{0x1a71ba45, 0x185f85b0, 0x18d6cbfc, 0x075cda91, 0x01db3c4b, 0x0f8b72b3, 0x01b7876b, 0x0da0de7c, 0x67c87}}}, /* 3*16^36*G: */ - {{{0x319888e9, 0x0e73c9e4, 0x2448a8b4, 0x04ae9afc, 0x2681673d, 0x1834c0a5, 0x3a6e2dde, 0x3a9dceb0, 0x1f90}}, - {{0x2f113b79, 0x1bf7f25f, 0x19522e65, 0x0dd47fb9, 0x2b96a821, 0x054f49c7, 0x2a10e958, 0x0d9f0576, 0x89be}}}, + {{{0x119888e9, 0x1ce793c9, 0x1122a2d0, 0x0574d7e4, 0x081673d1, 0x069814b3, 0x1b8b7798, 0x0ee75874, 0x1f90ea}}, + {{0x0f113b79, 0x17efe4bf, 0x0548b995, 0x0ea3fdcb, 0x196a8213, 0x09e938f5, 0x043a5605, 0x0f82bb54, 0x89be36}}}, /* 5*16^36*G: */ - {{{0x3562222c, 0x217bedbc, 0x1e6f2c60, 0x00d11e64, 0x0b52bade, 0x00aeb4cd, 0x3e0ad6e7, 0x39537b7f, 0x13a4}}, - {{0x28200145, 0x32c59a32, 0x1c904c08, 0x3e715deb, 0x209a52d4, 0x2b0be075, 0x2e813b2c, 0x1f539605, 0xc9d6}}}, + {{{0x1562222c, 0x02f7db79, 0x19bcb182, 0x0688f323, 0x152bade0, 0x15d699a5, 0x02b5b9c0, 0x09bdbffc, 0x13a4e5}}, + {{0x08200145, 0x058b3465, 0x12413023, 0x138aef5b, 0x09a52d4f, 0x017c0eb0, 0x004ecb2b, 0x09cb02dd, 0xc9d67d}}}, /* 7*16^36*G: */ - {{{0x343b46bb, 0x0df93703, 0x2c925254, 0x3b4e98fe, 0x055dbd12, 0x01f01761, 0x0aadd1d4, 0x07afc8cf, 0x6199}}, - {{0x0c20a848, 0x123d6407, 0x12ecd8ef, 0x2a1ca729, 0x3badf11c, 0x3ce1c59b, 0x1e492952, 0x38c23cff, 0x01c5}}}, + {{{0x143b46bb, 0x1bf26e07, 0x12494950, 0x1a74c7f5, 0x15dbd12e, 0x1e02ec22, 0x0b747501, 0x17e46795, 0x61991e}}, + {{0x0c20a848, 0x047ac80e, 0x0bb363bd, 0x10e5394a, 0x1adf11ca, 0x1c38b37d, 0x124a54bc, 0x011e7fbc, 0x1c5e3}}}, /* 9*16^36*G: */ - {{{0x121add3b, 0x396f8f77, 0x1727d8f7, 0x26a513d1, 0x1626118b, 0x0e736c34, 0x3d387490, 0x2ba92de1, 0xea27}}, - {{0x368ce7dd, 0x2d78a476, 0x24e1be71, 0x2c84b5a3, 0x1c2f6278, 0x0f3ac8c9, 0x217de572, 0x3c79b90a, 0xc70f}}}, + {{{0x121add3b, 0x12df1eee, 0x1c9f63df, 0x15289e8a, 0x026118b9, 0x0e6d868b, 0x0e1d240e, 0x1496f0fa, 0xea27ae}}, + {{0x168ce7dd, 0x1af148ed, 0x1386f9c6, 0x0425ad1c, 0x02f6278b, 0x0759192e, 0x1f795c8f, 0x1cdc8542, 0xc70ff1}}}, /* 11*16^36*G: */ - {{{0x211ff757, 0x3a2be2ed, 0x04c226e6, 0x133a5d07, 0x22b6da9b, 0x0043e2db, 0x3fd54ba9, 0x144d5adf, 0x5946}}, - {{0x094d031a, 0x2299bb2a, 0x3bffe3b2, 0x06ef1edf, 0x0406f996, 0x00e34057, 0x32750042, 0x0d833977, 0x3611}}}, + {{{0x011ff757, 0x1457c5db, 0x13089b9b, 0x19d2e838, 0x0b6da9b4, 0x087c5b71, 0x1552ea40, 0x06ad6fff, 0x594651}}, + {{0x094d031a, 0x05337654, 0x0fff8eca, 0x1778f6ff, 0x006f9961, 0x1c680ae2, 0x1d401080, 0x019cbbe4, 0x361136}}}, /* 13*16^36*G: */ - {{{0x236160b5, 0x1d89628d, 0x0e7ebc06, 0x314fc91c, 0x091ec0cc, 0x0ebde5c0, 0x33290e84, 0x1b8e457d, 0x16b2}}, - {{0x18a1dc0e, 0x11897efd, 0x0ba3ef81, 0x0d8eab1c, 0x3654d4e1, 0x190d4918, 0x2ef8bb63, 0x159698c0, 0x060f}}}, + {{{0x036160b5, 0x1b12c51b, 0x19faf019, 0x0a7e48e1, 0x11ec0ccc, 0x17bcb804, 0x0a43a10e, 0x0722bee6, 0x16b26e}}, + {{0x18a1dc0e, 0x0312fdfa, 0x0e8fbe05, 0x0c7558e1, 0x054d4e13, 0x01a9231b, 0x1e2ed8d9, 0x0b4c605d, 0x60f56}}}, /* 15*16^36*G: */ - {{{0x37b32db8, 0x25934a24, 0x247791f3, 0x07b5d27d, 0x2cea85c9, 0x2850f210, 0x19f931be, 0x14a57115, 0x024b}}, - {{0x2a64f760, 0x25153eaa, 0x05b81a95, 0x2ada0448, 0x1e5be862, 0x38a08731, 0x3309c7b6, 0x3be3d6ff, 0x609f}}} + {{{0x17b32db8, 0x0b269449, 0x11de47ce, 0x1dae93ec, 0x0ea85c91, 0x0a1e4216, 0x1e4c6fa8, 0x12b88ab3, 0x24b52}}, + {{0x0a64f760, 0x0a2a7d55, 0x16e06a56, 0x16d02240, 0x05be862a, 0x1410e62f, 0x0271edb8, 0x11eb7fe6, 0x609fef}}} }, { /* 1*16^37*G: */ - {{{0x096943e8, 0x3b683d6d, 0x273c5a5d, 0x1bc7f19f, 0x0f06231d, 0x08d2a846, 0x3b840793, 0x20320a02, 0xd68a}}, - {{0x2b133120, 0x25321099, 0x045295a2, 0x039ee3de, 0x30e28b5b, 0x2c7e45de, 0x186d00c4, 0x2a7ffd2d, 0xdb8b}}}, + {{{0x096943e8, 0x16d07ada, 0x1cf16977, 0x1e3f8cfc, 0x106231d6, 0x1a5508c7, 0x0101e4c8, 0x19050177, 0xd68a80}}, + {{0x0b133120, 0x0a642133, 0x114a568a, 0x1cf71ef0, 0x0e28b5b0, 0x0fc8bbd8, 0x1b40312c, 0x1ffe96b0, 0xdb8ba9}}}, /* 3*16^37*G: */ - {{{0x0ca1c4f9, 0x16d0aa86, 0x2b7e2823, 0x13bf8d32, 0x1f16f44f, 0x02e0f698, 0x1728c4c4, 0x3de3c8af, 0x7815}}, - {{0x3778bc15, 0x2ac7a8da, 0x177d1e19, 0x2d0b7985, 0x18c35d5c, 0x24f3cc51, 0x1af6a7dd, 0x007a334e, 0xc1c6}}}, + {{{0x0ca1c4f9, 0x0da1550c, 0x0df8a08d, 0x1dfc6995, 0x116f44f4, 0x1c1ed30f, 0x0a313102, 0x11e457ae, 0x7815f7}}, + {{0x1778bc15, 0x158f51b5, 0x1df47866, 0x085bcc2a, 0x0c35d5cb, 0x1e798a2c, 0x1da9f764, 0x1d19a735, 0xc1c601}}}, /* 5*16^37*G: */ - {{{0x2e8c8530, 0x349b870f, 0x38f4d8e6, 0x0b7da07b, 0x2a6c6d51, 0x1df19005, 0x040176e3, 0x1cf3683b, 0xc392}}, - {{0x398446c7, 0x100c3c3d, 0x2eed715c, 0x3b7f2f68, 0x03199850, 0x074e5107, 0x33c8e9d0, 0x2f9095d0, 0x8c41}}}, + {{{0x0e8c8530, 0x09370e1f, 0x03d3639b, 0x1bed03df, 0x06c6d512, 0x1e3200b5, 0x005db8dd, 0x19b41d88, 0xc39273}}, + {{0x198446c7, 0x0018787b, 0x1bb5c571, 0x1bf97b45, 0x1199850e, 0x09ca20e1, 0x123a7407, 0x084ae867, 0x8c41be}}}, /* 7*16^37*G: */ - {{{0x237a26c1, 0x07c902ec, 0x0dbf6a53, 0x1b1b9630, 0x103b2516, 0x0890c707, 0x011b0275, 0x1d11fd61, 0xda31}}, - {{0x2cf74d6f, 0x1460dbb3, 0x3a81525f, 0x1a0db175, 0x19d8b7d3, 0x21059f09, 0x18c69d23, 0x25ee1fd7, 0x753b}}}, + {{{0x037a26c1, 0x0f9205d9, 0x16fda94c, 0x18dcb181, 0x03b25166, 0x1218e0e8, 0x06c09d48, 0x08feb082, 0xda3174}}, + {{0x0cf74d6f, 0x08c1b767, 0x0a05497d, 0x106d8baf, 0x1d8b7d36, 0x00b3e12c, 0x11a748e1, 0x170febb1, 0x753b97}}}, /* 9*16^37*G: */ - {{{0x3739dc49, 0x0ad8a2a4, 0x2f55603d, 0x24e4b699, 0x3f231a23, 0x12b1422f, 0x30e6c106, 0x39b2c0ab, 0x6a4b}}, - {{0x32edd5cf, 0x39a8ae77, 0x14a4a4d3, 0x1f8ad32c, 0x3a8058ab, 0x059b8d83, 0x107597dc, 0x23ea8aa2, 0xf15d}}}, + {{{0x1739dc49, 0x15b14549, 0x1d5580f4, 0x0725b4cd, 0x1231a239, 0x162845ff, 0x19b04192, 0x196055e1, 0x6a4be6}}, + {{0x12edd5cf, 0x13515cef, 0x1292934f, 0x1c569962, 0x08058ab7, 0x1371b07d, 0x1d65f705, 0x15455120, 0xf15d8f}}}, /* 11*16^37*G: */ - {{{0x06987fac, 0x22fa2831, 0x0a86f679, 0x3243e190, 0x098a3c8b, 0x260980fb, 0x27f1344e, 0x31a7c4eb, 0x01f7}}, - {{0x19174c68, 0x3e479ce0, 0x1f6bc263, 0x1fd77886, 0x1ab6f9cb, 0x040db8ca, 0x1a22de5b, 0x330fcdbf, 0x9d4e}}}, + {{{0x06987fac, 0x05f45062, 0x0a1bd9e6, 0x121f0c81, 0x18a3c8bc, 0x01301f64, 0x1c4d13a6, 0x13e275cf, 0x1f7c6}}, + {{0x19174c68, 0x1c8f39c0, 0x1daf098f, 0x1ebbc433, 0x0b6f9cb7, 0x01b7194d, 0x08b796c4, 0x07e6dfb4, 0x9d4ecc}}}, /* 13*16^37*G: */ - {{{0x36daba4d, 0x34ce86f5, 0x03196261, 0x197ec388, 0x3a2bcb9c, 0x018bb763, 0x3d381cb7, 0x25005d87, 0x557e}}, - {{0x37a52316, 0x04dd286e, 0x243590a5, 0x3a6e3d7e, 0x0cbc86c5, 0x0d73e857, 0x3a7e046d, 0x23ce9807, 0x7a7e}}}, + {{{0x16daba4d, 0x099d0deb, 0x0c658987, 0x0bf61c40, 0x02bcb9c6, 0x1176ec7d, 0x0e072dc1, 0x002ec3fa, 0x557e94}}, + {{0x17a52316, 0x09ba50dd, 0x10d64294, 0x1371ebf4, 0x0bc86c5e, 0x0e7d0ae6, 0x1f811b4d, 0x074c03f4, 0x7a7e8f}}}, /* 15*16^37*G: */ - {{{0x29f5341a, 0x0e3d4bfc, 0x29636b80, 0x31e8cb19, 0x3101419c, 0x27503a9e, 0x085a93b2, 0x36a08666, 0x3ada}}, - {{0x2586c6cc, 0x1456024d, 0x05e8fbcb, 0x35b4b96d, 0x2b1017e9, 0x38d6fcda, 0x1369f552, 0x0788a266, 0xbfea}}} + {{{0x09f5341a, 0x1c7a97f9, 0x058dae00, 0x0f4658cd, 0x101419cc, 0x0a0753d8, 0x16a4eca7, 0x10433310, 0x3adada}}, + {{0x0586c6cc, 0x08ac049b, 0x17a3ef2d, 0x0da5cb68, 0x11017e9d, 0x1adf9b55, 0x1a7d54b8, 0x04513326, 0xbfea1e}}} }, { /* 1*16^38*G: */ - {{{0x028d3d5d, 0x0256603f, 0x3449cea4, 0x04abae5c, 0x3a30b096, 0x3009c241, 0x0804252d, 0x3b5f7d97, 0x324a}}, - {{0x16ab7c84, 0x19c892be, 0x23328439, 0x084ec31f, 0x2c1f4f19, 0x03030d6b, 0x21f2ff13, 0x0d95dd2d, 0x648a}}}, + {{{0x028d3d5d, 0x04acc07e, 0x11273a90, 0x055d72e6, 0x030b0961, 0x0138483d, 0x01094b70, 0x0fbecb90, 0x324aed}}, + {{0x16ab7c84, 0x1391257c, 0x0cca10e5, 0x027618fc, 0x01f4f192, 0x0061ad76, 0x1cbfc4c3, 0x0aee96c3, 0x648a36}}}, /* 3*16^38*G: */ - {{{0x2fd53ed3, 0x17245d60, 0x1a56ccef, 0x0fdd3ee7, 0x1f7c4916, 0x3d82e4c7, 0x372ad5b8, 0x02f56659, 0x2084}}, - {{0x1a7a7132, 0x1c50ff94, 0x0e708998, 0x21f11ce5, 0x3afac254, 0x2f51da9a, 0x18243487, 0x0d25f3b0, 0xf299}}}, + {{{0x0fd53ed3, 0x0e48bac1, 0x095b33bd, 0x1ee9f73b, 0x17c49163, 0x105c98ef, 0x0ab56e3d, 0x1ab32cee, 0x20840b}}, + {{0x1a7a7132, 0x18a1ff28, 0x19c22661, 0x0f88e729, 0x0fac2548, 0x0a3b535d, 0x090d21ef, 0x12f9d830, 0xf29934}}}, /* 5*16^38*G: */ - {{{0x08a35b35, 0x2f4b2ed6, 0x00a121ed, 0x2d762297, 0x08ebfd1a, 0x0f40a796, 0x339bbbd1, 0x2ffd83ac, 0xe6b6}}, - {{0x1c1007bd, 0x15ca4f6e, 0x3e999c7c, 0x0edb274e, 0x1961ddfe, 0x3d0f8e0d, 0x0d2f3266, 0x3caf4cc0, 0x1a5f}}}, + {{{0x08a35b35, 0x1e965dac, 0x028487b6, 0x0bb114b8, 0x0ebfd1ab, 0x0814f2c4, 0x06eef44f, 0x1ec1d667, 0xe6b6bf}}, + {{0x1c1007bd, 0x0b949edc, 0x1a6671f1, 0x16d93a77, 0x161ddfe3, 0x01f1c1ac, 0x0bcc99bd, 0x17a6601a, 0x1a5ff2}}}, /* 7*16^38*G: */ - {{{0x00360dd3, 0x353be34b, 0x050e2090, 0x2a2a0db6, 0x0ce3bb47, 0x02e021b8, 0x099b288b, 0x05dd16f9, 0xe053}}, - {{0x3c24f87b, 0x0abb3644, 0x0103dc2b, 0x2e61f7a6, 0x36a01461, 0x02560ad6, 0x12f39cd8, 0x0edc6976, 0xdc1c}}}, + {{{0x00360dd3, 0x0a77c696, 0x14388243, 0x11506db0, 0x0e3bb47a, 0x1c043706, 0x06ca22c2, 0x0e8b7c93, 0xe05317}}, + {{0x1c24f87b, 0x15766c89, 0x040f70ac, 0x130fbd30, 0x0a01461b, 0x0ac15adb, 0x1ce73602, 0x0e34bb25, 0xdc1c3b}}}, /* 9*16^38*G: */ - {{{0x1098dfea, 0x3051998b, 0x2a678797, 0x372cf24b, 0x3a5e57fa, 0x23974aa0, 0x06c59e01, 0x0ece9de2, 0xa815}}, - {{0x2e6d892f, 0x2926a77d, 0x2daf4158, 0x2d783dd0, 0x053e03b1, 0x236e715e, 0x060fc53d, 0x0e591874, 0x2a47}}}, + {{{0x1098dfea, 0x00a33316, 0x099e1e5f, 0x1967925d, 0x05e57fad, 0x12e9541d, 0x11678063, 0x074ef10d, 0xa8153b}}, + {{0x0e6d892f, 0x124d4efb, 0x16bd0562, 0x0bc1ee85, 0x13e03b1b, 0x0dce2bc2, 0x03f14f63, 0x0c8c3a0c, 0x2a4739}}}, /* 11*16^38*G: */ - {{{0x0bcecfa5, 0x29f9de92, 0x316bb020, 0x0358b686, 0x0eda3b2a, 0x11a5718e, 0x0addadeb, 0x30ecc3fb, 0x4f05}}, - {{0x15d37b53, 0x3b34092a, 0x01b48cd2, 0x1fb90c7c, 0x1534b944, 0x18c8d856, 0x1426fadd, 0x267a980f, 0x53a4}}}, + {{{0x0bcecfa5, 0x13f3bd24, 0x05aec082, 0x1ac5b436, 0x0da3b2a0, 0x14ae31c7, 0x176b7ad1, 0x1661fd95, 0x4f05c3}}, + {{0x15d37b53, 0x16681254, 0x06d2334b, 0x1dc863e0, 0x134b9447, 0x191b0aca, 0x09beb758, 0x1d4c07a8, 0x53a499}}}, /* 13*16^38*G: */ - {{{0x084b96aa, 0x1879d964, 0x22abcce4, 0x0a618d54, 0x3b980ed0, 0x101786a8, 0x3a91be26, 0x26ae67d9, 0xd930}}, - {{0x02b28a86, 0x09b13cdf, 0x3cfe978f, 0x2db27eeb, 0x34cb5fd3, 0x043c1989, 0x2c557d7e, 0x26caa6d3, 0x6ef9}}}, + {{{0x084b96aa, 0x10f3b2c8, 0x0aaf3391, 0x130c6aa4, 0x1980ed02, 0x02f0d51d, 0x046f8990, 0x1733ecf5, 0xd9309a}}, + {{0x02b28a86, 0x136279be, 0x13fa5e3c, 0x0d93f75f, 0x0cb5fd3b, 0x0783313a, 0x155f5f84, 0x055369d8, 0x6ef99b}}}, /* 15*16^38*G: */ - {{{0x1f8fcf0e, 0x3dee3416, 0x3c4a6fac, 0x16dbff79, 0x2a3411d6, 0x30d11b7a, 0x22d35ba9, 0x1f284e15, 0x7d58}}, - {{0x18bc9459, 0x00706827, 0x323780a5, 0x18e402b4, 0x3d6ad0c4, 0x0d002db3, 0x04c61272, 0x1700e20c, 0xa729}}} + {{{0x1f8fcf0e, 0x1bdc682c, 0x1129beb3, 0x16dffbcf, 0x03411d65, 0x1a236f55, 0x14d6ea70, 0x14270ac5, 0x7d587c}}, + {{0x18bc9459, 0x00e0d04e, 0x08de0294, 0x072015a6, 0x16ad0c46, 0x0005b67e, 0x11849c8d, 0x00710609, 0xa7295c}}} }, { /* 1*16^39*G: */ - {{{0x3d054c96, 0x3a2f4dcf, 0x0d1ca888, 0x31050eea, 0x3ee5dcee, 0x077f6f97, 0x1e61f6d5, 0x30524673, 0x4df9}}, - {{0x0ad10d5d, 0x0baeb01b, 0x28849019, 0x3541b370, 0x1d85d4b5, 0x25d308e8, 0x18728050, 0x3b14424b, 0x0035}}}, + {{{0x1d054c96, 0x145e9b9f, 0x1472a223, 0x08287751, 0x0e5dceec, 0x0fedf2ff, 0x187db547, 0x092339bc, 0x4df9c1}}, + {{0x0ad10d5d, 0x175d6036, 0x02124064, 0x0a0d9b85, 0x185d4b5d, 0x1a611d0e, 0x1ca01425, 0x0a2125b0, 0x35ec}}}, /* 3*16^39*G: */ - {{{0x1def001d, 0x13c89769, 0x09ba27ef, 0x3e6ef5a6, 0x23b64b21, 0x02f47027, 0x22caf20e, 0x28cb6c9f, 0xa549}}, - {{0x30624783, 0x3576c69f, 0x2c9705ad, 0x05078a98, 0x259456eb, 0x330c3b62, 0x166cbdf4, 0x1e9e41b6, 0x799b}}}, + {{{0x1def001d, 0x07912ed2, 0x06e89fbd, 0x1377ad31, 0x1b64b21f, 0x1e8e04f1, 0x12bc8382, 0x05b64fc5, 0xa549a3}}, + {{0x10624783, 0x0aed8d3f, 0x125c16b7, 0x083c54c5, 0x19456eb1, 0x01876c52, 0x1b2f7d33, 0x0f20db2c, 0x799b7a}}}, /* 5*16^39*G: */ - {{{0x052ed4cb, 0x16bbc797, 0x009ec5a0, 0x1537becf, 0x132e6ec9, 0x022f660d, 0x3ecd123f, 0x23cc3681, 0x7e79}}, - {{0x14bb9462, 0x15c5981e, 0x39f37a12, 0x1cd5c6ff, 0x32f057b1, 0x2a55277b, 0x1ac83041, 0x33312893, 0xd23d}}}, + {{{0x052ed4cb, 0x0d778f2e, 0x027b1681, 0x09bdf678, 0x12e6ec95, 0x05ecc1a9, 0x13448fc2, 0x061b40fd, 0x7e798f}}, + {{0x14bb9462, 0x0b8b303c, 0x07cde849, 0x06ae37ff, 0x0f057b17, 0x0aa4ef79, 0x120c106a, 0x189449b5, 0xd23dcc}}}, /* 7*16^39*G: */ - {{{0x13630834, 0x37ce83ef, 0x3dac067f, 0x18fc4a18, 0x0c810884, 0x2e7a5aea, 0x14783ad5, 0x28800c54, 0x224f}}, - {{0x047a2272, 0x34f11cdf, 0x0a50f75c, 0x18a493b0, 0x1d09f53d, 0x2dc3e8e4, 0x2da5c3c4, 0x138caecf, 0xbbe5}}}, + {{{0x13630834, 0x0f9d07de, 0x16b019ff, 0x07e250c7, 0x08108846, 0x0f4b5d46, 0x1e0eb56e, 0x00062a28, 0x224fa2}}, + {{0x047a2272, 0x09e239be, 0x0943dd73, 0x05249d81, 0x109f53d6, 0x187d1c8e, 0x0970f12d, 0x065767db, 0xbbe54e}}}, /* 9*16^39*G: */ - {{{0x183c19d7, 0x19d92745, 0x02cf57bb, 0x2ed7916b, 0x228ef2bb, 0x28973390, 0x239e4129, 0x28331802, 0xc2d4}}, - {{0x0507928d, 0x0bca2e0b, 0x3345c977, 0x2012a0c5, 0x01260d26, 0x20ed7dfd, 0x06294d41, 0x283e7020, 0x65ad}}}, + {{{0x183c19d7, 0x13b24e8a, 0x0b3d5eed, 0x16bc8b58, 0x08ef2bbb, 0x12e67211, 0x07904a68, 0x198c0147, 0xc2d4a0}}, + {{0x0507928d, 0x17945c16, 0x0d1725dc, 0x0095062e, 0x1260d268, 0x1dafbfa0, 0x0a535060, 0x1f38100c, 0x65ada0}}}, /* 11*16^39*G: */ - {{{0x3c940c9a, 0x13202b52, 0x2f423308, 0x33cf384e, 0x0ddc2113, 0x161789d1, 0x1f3190e5, 0x0a9fb0c1, 0x2ec2}}, - {{0x051e7a4d, 0x34653f66, 0x1a35bdac, 0x101460f6, 0x1c7feb12, 0x3893d40a, 0x379684c2, 0x291a378c, 0x8b1d}}}, + {{{0x1c940c9a, 0x064056a5, 0x1d08cc21, 0x1e79c275, 0x1dc2113c, 0x02f13a26, 0x0c643956, 0x0fd860be, 0x2ec22a}}, + {{0x051e7a4d, 0x08ca7ecc, 0x08d6f6b3, 0x00a307b3, 0x07feb124, 0x127a814e, 0x05a130b8, 0x0d1bc66f, 0x8b1da4}}}, /* 13*16^39*G: */ - {{{0x1d683eeb, 0x29c3b97f, 0x08d3133a, 0x0dbace28, 0x04b8f33e, 0x2bd94942, 0x28cecab1, 0x1a5ce3e6, 0xafc6}}, - {{0x30cd4509, 0x078a72ac, 0x1eddfdc9, 0x02ead549, 0x239c1657, 0x1671ff28, 0x22752bc3, 0x0865db74, 0x002c}}}, + {{{0x1d683eeb, 0x138772fe, 0x034c4cea, 0x0dd67141, 0x0b8f33e3, 0x1b292842, 0x13b2ac6b, 0x0e71f351, 0xafc669}}, + {{0x10cd4509, 0x0f14e559, 0x1b77f724, 0x1756aa4b, 0x19c16570, 0x0e3fe511, 0x1d4af0d6, 0x12edba44, 0x2c21}}}, /* 15*16^39*G: */ - {{{0x376f4293, 0x28807e1e, 0x13c5139e, 0x3a5e2d59, 0x0b282e10, 0x2f233cdc, 0x03309121, 0x1ed6a7cd, 0xd255}}, - {{0x1282740a, 0x36c61e89, 0x2405a5f1, 0x12da0e37, 0x0ad21fe3, 0x20bc1bad, 0x027f0126, 0x2cd0d579, 0xa787}}} + {{{0x176f4293, 0x1100fc3d, 0x0f144e7a, 0x12f16aca, 0x1282e10e, 0x04679b85, 0x0c24486f, 0x0b53e686, 0xd2557b}}, + {{0x1282740a, 0x0d8c3d12, 0x101697c7, 0x16d071bc, 0x0d21fe34, 0x178375a5, 0x1fc049a0, 0x086abc84, 0xa787b3}}} }, { /* 1*16^40*G: */ - {{{0x2c1f98cd, 0x2ff26722, 0x17f0308c, 0x0d224153, 0x06602152, 0x362a7073, 0x34870fae, 0x066a1291, 0x9c39}}, - {{0x14fc599d, 0x39f9780f, 0x064c8e6b, 0x14c9bddb, 0x20e64190, 0x3c112fc9, 0x1dd57584, 0x13c3d293, 0xddb8}}}, + {{{0x0c1f98cd, 0x1fe4ce45, 0x1fc0c232, 0x09120a9a, 0x06021523, 0x054e0e63, 0x01c3ebb6, 0x150948e9, 0x9c3919}}, + {{0x14fc599d, 0x13f2f01e, 0x193239af, 0x064deed8, 0x0e641905, 0x0225f930, 0x155d613c, 0x01e949bb, 0xddb84f}}}, /* 3*16^40*G: */ - {{{0x0fb64db3, 0x1ee6354e, 0x1dd53841, 0x3b79328e, 0x13b8d6a7, 0x2ee0fef9, 0x1ccb740b, 0x08e48a6f, 0xc114}}, - {{0x3c0259be, 0x08c33a7f, 0x14567d1e, 0x1d602413, 0x178bd1a8, 0x3b3793fa, 0x06fc2a5c, 0x3db716d2, 0x1237}}}, + {{{0x0fb64db3, 0x1dcc6a9c, 0x1754e105, 0x1bc99473, 0x1b8d6a7e, 0x1c1fdf29, 0x12dd02ee, 0x124537b9, 0xc11423}}, + {{0x1c0259be, 0x118674ff, 0x1159f478, 0x0b01209a, 0x18bd1a87, 0x06f27f4b, 0x1f0a973b, 0x1b8b690d, 0x1237f6}}}, /* 5*16^40*G: */ - {{{0x03081e46, 0x3b7b60d0, 0x14559ea1, 0x14886315, 0x2634713a, 0x3670b064, 0x37224082, 0x12fe0c69, 0x6c5b}}, - {{0x0bfbcd70, 0x347e72e0, 0x2c22a62e, 0x3433e09a, 0x2be47841, 0x11e18f38, 0x2d42fb23, 0x04dc5249, 0xcb05}}}, + {{{0x03081e46, 0x16f6c1a0, 0x11567a87, 0x044318aa, 0x034713a5, 0x0e160c93, 0x089020b6, 0x1f0634ee, 0x6c5b4b}}, + {{0x0bfbcd70, 0x08fce5c0, 0x108a98bb, 0x019f04d5, 0x1e47841d, 0x1c31e715, 0x10bec8d1, 0x0e2924da, 0xcb0513}}}, /* 7*16^40*G: */ - {{{0x064dcd4b, 0x32b96bb1, 0x111c124d, 0x0c31f566, 0x310a450c, 0x1c19972a, 0x0ade4b56, 0x2a1599c3, 0xe1e9}}, - {{0x3b041f2c, 0x342d897a, 0x0a16b292, 0x113466ab, 0x2577927f, 0x310d666c, 0x1c531b7a, 0x02a55115, 0x562b}}}, + {{{0x064dcd4b, 0x0572d762, 0x04704937, 0x018fab32, 0x10a450c3, 0x0332e558, 0x1792d59c, 0x0acce195, 0xe1e9a8}}, + {{0x1b041f2c, 0x085b12f5, 0x085aca4b, 0x09a33559, 0x177927f4, 0x01accd92, 0x14c6deb1, 0x12a88ab8, 0x562b0a}}}, /* 9*16^40*G: */ - {{{0x2badd73c, 0x0161dbf8, 0x2a64b7d0, 0x36737640, 0x1c14208f, 0x29d390bb, 0x1b099778, 0x0695eb44, 0x51b2}}, - {{0x2b36d8d1, 0x3df52b87, 0x0c734ba6, 0x0804c3ca, 0x2c1cfa6c, 0x281fc074, 0x3d3e5d54, 0x0c040007, 0x0079}}}, + {{{0x0badd73c, 0x02c3b7f1, 0x0992df40, 0x139bb205, 0x014208fd, 0x1a72176e, 0x0265de29, 0x0af5a236, 0x51b21a}}, + {{0x0b36d8d1, 0x1bea570f, 0x11cd2e9b, 0x00261e51, 0x01cfa6c2, 0x03f80e96, 0x0f975528, 0x020003fa, 0x7930}}}, /* 11*16^40*G: */ - {{{0x3b09f34b, 0x35d742dc, 0x0cc66ce6, 0x221cf982, 0x339d61e5, 0x2d8a5bcf, 0x0b79861a, 0x3ce98ec7, 0x9701}}, - {{0x00df5793, 0x33721433, 0x3dcc794a, 0x012f0e5f, 0x16833771, 0x00c6d4c5, 0x30ed15d7, 0x12eee32b, 0x3dd4}}}, + {{{0x1b09f34b, 0x0bae85b9, 0x1319b39b, 0x10e7cc11, 0x19d61e58, 0x114b79f9, 0x1e6186ad, 0x14c76396, 0x9701f3}}, + {{0x00df5793, 0x06e42866, 0x1731e52b, 0x097872ff, 0x08337710, 0x18da98ab, 0x1b4575c0, 0x177195e1, 0x3dd44b}}}, /* 13*16^40*G: */ - {{{0x3f1e2f46, 0x1739888e, 0x32778301, 0x1c3dc7a1, 0x163c5752, 0x164b8103, 0x266cc445, 0x2d074b27, 0xa036}}, - {{0x1effb349, 0x1cc789a5, 0x3f0b1f4f, 0x2038a0b3, 0x1eb08d06, 0x07daa91e, 0x16b3d7df, 0x246800fa, 0xc3bf}}}, + {{{0x1f1e2f46, 0x0e73111d, 0x09de0c05, 0x01ee3d0e, 0x03c57527, 0x0970206b, 0x1b311156, 0x03a593cc, 0xa036b4}}, + {{0x1effb349, 0x198f134a, 0x1c2c7d3d, 0x01c5059f, 0x0b08d068, 0x1b5523cf, 0x0cf5f7c7, 0x14007d2d, 0xc3bf91}}}, /* 15*16^40*G: */ - {{{0x0c4cea08, 0x3362e40e, 0x20ea21db, 0x12d62e83, 0x00465265, 0x298454d0, 0x28c506f4, 0x3eb6ea93, 0x6a85}}, - {{0x1862f4f3, 0x0677b396, 0x3d721b6a, 0x09c692d0, 0x3e6230b4, 0x24cf0523, 0x0659d531, 0x11812eb9, 0x00b6}}} + {{{0x0c4cea08, 0x06c5c81c, 0x03a8876f, 0x16b1741c, 0x04652654, 0x108a9a00, 0x1141bd29, 0x1b7549d1, 0x6a85fa}}, + {{0x1862f4f3, 0x0cef672c, 0x15c86da8, 0x0e349687, 0x06230b42, 0x19e0a47f, 0x16754c64, 0x00975c8c, 0xb646}}} }, { /* 1*16^41*G: */ - {{{0x20a959e5, 0x2884e084, 0x391d4cc5, 0x38524ea2, 0x0e06bb91, 0x017ca076, 0x12fdf8de, 0x05c2c774, 0x6057}}, - {{0x2385a2a8, 0x2266fa4c, 0x2e24c65e, 0x1454af0f, 0x1df26246, 0x268b6bdc, 0x24807add, 0x3c2c9a9a, 0x9a1a}}}, + {{{0x00a959e5, 0x1109c109, 0x04753316, 0x02927517, 0x006bb91e, 0x0f940ec7, 0x1f7e3781, 0x0163ba25, 0x605717}}, + {{0x0385a2a8, 0x04cdf499, 0x1893197a, 0x02a5787d, 0x1f262465, 0x116d7b8e, 0x001eb766, 0x164d4d49, 0x9a1af0}}}, /* 3*16^41*G: */ - {{{0x171c032b, 0x3536858a, 0x3afdc980, 0x1ad9a285, 0x0766c5ff, 0x046d7f7f, 0x002603dd, 0x2a3f35b8, 0x71eb}}, - {{0x1668359f, 0x1ead6a38, 0x34b4755e, 0x24c6b45d, 0x0cbb7f71, 0x18145bd5, 0x1d39def6, 0x049892d8, 0xd2ff}}}, + {{{0x171c032b, 0x0a6d0b14, 0x0bf72603, 0x16cd142f, 0x166c5ff6, 0x0dafefe3, 0x0980f744, 0x1f9adc00, 0x71eba8}}, + {{0x1668359f, 0x1d5ad470, 0x12d1d579, 0x0635a2ee, 0x0bb7f719, 0x028b7aa6, 0x0e77bd98, 0x0c496c3a, 0xd2ff12}}}, /* 5*16^41*G: */ - {{{0x2a03a61c, 0x01b91d14, 0x1070574d, 0x1e1a3d1a, 0x2a9dd050, 0x05d10aea, 0x09d232ca, 0x30c16cc9, 0x855e}}, - {{0x065dfc07, 0x37f1baab, 0x17e44965, 0x0cbdd3a8, 0x02fb4ed3, 0x0f2ffe6d, 0x01c17f54, 0x174bb17c, 0x0dd8}}}, + {{{0x0a03a61c, 0x03723a29, 0x01c15d34, 0x10d1e8d2, 0x09dd0507, 0x1a215d55, 0x148cb285, 0x00b66493, 0x855ec3}}, + {{0x065dfc07, 0x0fe37556, 0x1f912597, 0x05ee9d42, 0x0fb4ed33, 0x05ffcda1, 0x105fd50f, 0x05d8be03, 0xdd85d}}}, /* 7*16^41*G: */ - {{{0x1f32d706, 0x00302920, 0x06a0678b, 0x0633291d, 0x15bfa206, 0x034a68c2, 0x3fbf1f15, 0x121aaeac, 0x3ce4}}, - {{0x3c7fd9e4, 0x02dcd8df, 0x161e89f4, 0x345590f3, 0x094906ed, 0x3f411ac4, 0x3785288e, 0x10236ab8, 0xe775}}}, + {{{0x1f32d706, 0x00605240, 0x1a819e2c, 0x119948e8, 0x1bfa2061, 0x094d184a, 0x0fc7c543, 0x0d57567f, 0x3ce448}}, + {{0x1c7fd9e4, 0x05b9b1bf, 0x187a27d0, 0x02ac879a, 0x14906edd, 0x08235884, 0x014a23bf, 0x11b55c6f, 0xe77540}}}, /* 9*16^41*G: */ - {{{0x391cd3fb, 0x36d032ed, 0x329be686, 0x0a8cff65, 0x0844eb4a, 0x380c863e, 0x237faf02, 0x31450fd3, 0x11cc}}, - {{0x15160d86, 0x24dc5ae9, 0x0dd3472a, 0x02c7bf4b, 0x0cc239fa, 0x2389124e, 0x311deb52, 0x1acaa40a, 0x4aa5}}}, + {{{0x191cd3fb, 0x0da065db, 0x0a6f9a1b, 0x1467fb2e, 0x044eb4a2, 0x0190c7c4, 0x1febc0b8, 0x0287e9c6, 0x11ccc5}}, + {{0x15160d86, 0x09b8b5d2, 0x174d1caa, 0x163dfa59, 0x0c239fa0, 0x112249c6, 0x077ad4a3, 0x05520562, 0x4aa56b}}}, /* 11*16^41*G: */ - {{{0x218f7552, 0x21ee4465, 0x0054fac3, 0x1044e2e6, 0x2382ddbd, 0x25ddd3e0, 0x09c6f43b, 0x2ec5f945, 0x0250}}, - {{0x3510b14d, 0x3c212588, 0x33d6f1e3, 0x001bcf0c, 0x29d817da, 0x35f7dd7f, 0x28082342, 0x0c3f26ef, 0x7319}}}, + {{{0x018f7552, 0x03dc88cb, 0x0153eb0e, 0x02271730, 0x182ddbd4, 0x1bba7c11, 0x11bd0ee5, 0x02fca293, 0x250bb}}, + {{0x1510b14d, 0x18424b11, 0x0f5bc78f, 0x00de7866, 0x1d817da0, 0x1efbaff4, 0x0208d0b5, 0x1f9377d0, 0x731930}}}, /* 13*16^41*G: */ - {{{0x1f725d12, 0x1744fa4e, 0x0b5f4750, 0x1190aef7, 0x022fbfd9, 0x28e73828, 0x27fd3ab4, 0x27222cd1, 0x1a74}}, - {{0x23ac56e4, 0x04d94534, 0x190daa70, 0x1c821a62, 0x2f3d8f60, 0x22f9d70a, 0x00e2cf45, 0x34655cfb, 0x7e91}}}, + {{{0x1f725d12, 0x0e89f49c, 0x0d7d1d41, 0x0c8577b9, 0x02fbfd94, 0x1ce70501, 0x1f4ead28, 0x111668cf, 0x1a749c}}, + {{0x03ac56e4, 0x09b28a69, 0x0436a9c0, 0x0410d313, 0x13d8f607, 0x1f3ae157, 0x18b3d162, 0x12ae7d81, 0x7e91d1}}}, /* 15*16^41*G: */ - {{{0x29fae458, 0x18412394, 0x26ec97fd, 0x0297109d, 0x3b7b328b, 0x3455a977, 0x0218c109, 0x1a16f83e, 0xc750}}, - {{0x1757b598, 0x005a1065, 0x35951a2b, 0x1772940c, 0x32c7b40a, 0x0bd05319, 0x21e05fb5, 0x257e33e4, 0xead7}}} + {{{0x09fae458, 0x10824729, 0x1bb25ff5, 0x14b884ec, 0x17b328b0, 0x0ab52efd, 0x06304274, 0x0b7c1f04, 0xc75068}}, + {{0x1757b598, 0x00b420ca, 0x165468ac, 0x1b94a066, 0x0c7b40a5, 0x1a0a6339, 0x1817ed4b, 0x1f19f243, 0xead795}}} }, { /* 1*16^42*G: */ - {{{0x2cb94266, 0x069a5cfb, 0x3d4df12b, 0x33bc3ee9, 0x0da31880, 0x10e69146, 0x08411421, 0x37e388e8, 0xa576}}, - {{0x21b28ec8, 0x3a2f846b, 0x114d9f3e, 0x0b8429fd, 0x0cd82c43, 0x2e5ebf96, 0x240b2c92, 0x2fc839d9, 0x40a6}}}, + {{{0x0cb94266, 0x0d34b9f7, 0x1537c4ac, 0x1de1f74f, 0x1a31880c, 0x1cd228c6, 0x10450850, 0x11c47410, 0xa576df}}, + {{0x01b28ec8, 0x145f08d7, 0x05367cfb, 0x1c214fea, 0x0d82c432, 0x0bd7f2c6, 0x02cb24ae, 0x041cecc8, 0x40a6bf}}}, /* 3*16^42*G: */ - {{{0x0d9ed6c1, 0x1a2bad63, 0x3d593d6b, 0x139d16f0, 0x1edd0ec2, 0x3f061dc1, 0x0f53e80b, 0x0cdb72dd, 0x0328}}, - {{0x38fafeee, 0x3b1baf9b, 0x1cb494ad, 0x16fd37c9, 0x0d7c8c26, 0x35650e88, 0x19f28c46, 0x260e04bf, 0x71a8}}}, + {{{0x0d9ed6c1, 0x14575ac6, 0x1564f5ad, 0x1ce8b787, 0x0dd0ec24, 0x00c3b82f, 0x14fa02ff, 0x0db96e9e, 0x32833}}, + {{0x18fafeee, 0x16375f37, 0x12d252b7, 0x17e9be4b, 0x17c8c265, 0x0ca1d106, 0x1ca311b5, 0x07025fb3, 0x71a898}}}, /* 5*16^42*G: */ - {{{0x3235983a, 0x066a6a34, 0x13bceb29, 0x22840dc0, 0x3e1531e3, 0x0e49b5c3, 0x11c54dc6, 0x13aba2e4, 0xce4f}}, - {{0x0d3cdecf, 0x33f5ac64, 0x2bf740ae, 0x1b1948a3, 0x30754352, 0x37809279, 0x0fbbb3ea, 0x3e5cf0e4, 0xf3c9}}}, + {{{0x1235983a, 0x0cd4d469, 0x0ef3aca4, 0x14206e02, 0x01531e38, 0x0936b87f, 0x1153718e, 0x15d17223, 0xce4f4e}}, + {{0x0d3cdecf, 0x07eb58c8, 0x0fdd02bb, 0x18ca451d, 0x07543526, 0x10124f38, 0x0eecfab7, 0x0e78721f, 0xf3c9f9}}}, /* 7*16^42*G: */ - {{{0x15b0e6c9, 0x1b6aad99, 0x06e4c89a, 0x17fe73de, 0x38bcbddb, 0x0a3ecdb7, 0x0622278e, 0x2fe952e6, 0x4dbe}}, - {{0x1eb2cc25, 0x2529e155, 0x0504efae, 0x24c46caf, 0x2229f358, 0x2989b9b8, 0x13aedf45, 0x39ec0f24, 0x10fe}}}, + {{{0x15b0e6c9, 0x16d55b32, 0x1b932269, 0x1ff39ef0, 0x0bcbddb5, 0x07d9b6fc, 0x0889e38a, 0x14a9730c, 0x4dbebf}}, + {{0x1eb2cc25, 0x0a53c2aa, 0x1413beba, 0x06236578, 0x029f3589, 0x11373711, 0x0bb7d169, 0x16079227, 0x10fee7}}}, /* 9*16^42*G: */ - {{{0x25857295, 0x13806846, 0x3433f016, 0x32391fc0, 0x1ca12069, 0x38463f28, 0x05c218b2, 0x0902ffbd, 0xa42a}}, - {{0x0a7eb9c1, 0x1acddffb, 0x15193955, 0x28708b34, 0x1da4c427, 0x1ac8ac93, 0x05d4567a, 0x2cfc9840, 0x3aa0}}}, + {{{0x05857295, 0x0700d08d, 0x10cfc059, 0x11c8fe06, 0x0a12069c, 0x08c7e50e, 0x10862cb8, 0x017fde8b, 0xa42a24}}, + {{0x0a7eb9c1, 0x159bbff6, 0x1464e555, 0x038459a2, 0x1a4c427a, 0x1915926e, 0x15159e9a, 0x1e4c200b, 0x3aa0b3}}}, /* 11*16^42*G: */ - {{{0x2fcdc098, 0x0883fd55, 0x2e468032, 0x02b803da, 0x0499c155, 0x3c7e1b03, 0x322267a7, 0x0acbe5be, 0x34e1}}, - {{0x2a7474e2, 0x132c6b79, 0x19883f66, 0x37d44c3c, 0x3972db04, 0x132f2105, 0x1d322d97, 0x30b775ed, 0xa64a}}}, + {{{0x0fcdc098, 0x1107faab, 0x191a00c8, 0x15c01ed5, 0x099c1550, 0x0fc36062, 0x0899e9fc, 0x05f2df64, 0x34e12b}}, + {{0x0a7474e2, 0x0658d6f3, 0x0620fd99, 0x1ea261e3, 0x172db04d, 0x05e420bc, 0x0c8b65d3, 0x1bbaf6ba, 0xa64ac2}}}, /* 13*16^42*G: */ - {{{0x0f173b92, 0x335bad7a, 0x29fb7611, 0x1f9cbd05, 0x0d65683b, 0x0c68863d, 0x391f29be, 0x3490366e, 0x10f4}}, - {{0x233146c2, 0x240801b5, 0x086adb7c, 0x2edda745, 0x3908ba90, 0x2c96968c, 0x353ad211, 0x0b654245, 0x850e}}}, + {{{0x0f173b92, 0x06b75af4, 0x07edd847, 0x1ce5e82d, 0x165683b7, 0x0d10c7a6, 0x07ca6f8c, 0x081b3772, 0x10f4d2}}, + {{0x033146c2, 0x0810036b, 0x01ab6df2, 0x16ed3a29, 0x108ba90b, 0x12d2d19c, 0x0eb4846c, 0x12a122ea, 0x850e2d}}}, /* 15*16^42*G: */ - {{{0x28d84958, 0x39bf4766, 0x0acc5cae, 0x0477ac5b, 0x00cc866a, 0x066e5db5, 0x277e749f, 0x3a02da6d, 0xe846}}, - {{0x3882cf9f, 0x031191ed, 0x1e0c1a64, 0x1468cd9c, 0x18b76fad, 0x2f64411e, 0x07e2541d, 0x2e3f2253, 0xa29c}}} + {{{0x08d84958, 0x137e8ecd, 0x0b3172bb, 0x03bd62d9, 0x0cc866a1, 0x0dcbb6a0, 0x1f9d27c6, 0x016d36ce, 0xe846e8}}, + {{0x1882cf9f, 0x062323db, 0x18306990, 0x03466ce3, 0x0b76fad5, 0x0c8823cc, 0x1895076f, 0x1f91298f, 0xa29cb8}}} }, { /* 1*16^43*G: */ - {{{0x3e58ad71, 0x3dd8e226, 0x39a3a208, 0x0c347d73, 0x1e8c38bb, 0x17fa58a7, 0x2c3e30a0, 0x29e30a37, 0x7778}}, - {{0x3d9f43ac, 0x2d44ff07, 0x324ac563, 0x2ce1047f, 0x3f580087, 0x26384bcb, 0x1b22ff70, 0x1b66ad69, 0x3462}}}, + {{{0x1e58ad71, 0x1bb1c44d, 0x068e8823, 0x01a3eb9f, 0x08c38bb3, 0x1f4b14ef, 0x0f8c2817, 0x11851bd8, 0x7778a7}}, + {{0x1d9f43ac, 0x1a89fe0f, 0x092b158e, 0x070823fe, 0x1580087b, 0x0709797f, 0x08bfdc26, 0x1356b4b6, 0x34626d}}}, /* 3*16^43*G: */ - {{{0x3319c869, 0x3df1bab8, 0x21eb2702, 0x2a7e575d, 0x0cacdc18, 0x20e408bf, 0x33fc8d01, 0x01176605, 0x3018}}, - {{0x12b856f0, 0x3031db27, 0x23d9a7bf, 0x0aa13292, 0x222e3bca, 0x1890c835, 0x3b7b6f86, 0x315e0940, 0xac5f}}}, + {{{0x1319c869, 0x1be37571, 0x07ac9c0b, 0x13f2baec, 0x0acdc18a, 0x1c8117e6, 0x1f234060, 0x0bb302e7, 0x301804}}, + {{0x12b856f0, 0x0063b64e, 0x0f669eff, 0x15099494, 0x02e3bca2, 0x121906b1, 0x1edbe198, 0x0f04a076, 0xac5fc5}}}, /* 5*16^43*G: */ - {{{0x25ed29b5, 0x319a61be, 0x12add1b4, 0x20c2d81c, 0x23c885f5, 0x2d9f6e69, 0x17ef343a, 0x206d87b9, 0x3228}}, - {{0x3cd15ad2, 0x3d3c49b9, 0x0ee7604e, 0x20ebaae5, 0x1531e1ca, 0x02c677d0, 0x0344eb11, 0x00a105e8, 0x1677}}}, + {{{0x05ed29b5, 0x0334c37d, 0x0ab746d3, 0x0616c0e2, 0x1c885f58, 0x13edcd31, 0x1bcd0ead, 0x16c3dcaf, 0x322881}}, + {{0x1cd15ad2, 0x1a789373, 0x1b9d813b, 0x075d5729, 0x131e1ca8, 0x18cefa0a, 0x113ac442, 0x1082f406, 0x167702}}}, /* 7*16^43*G: */ - {{{0x06c96100, 0x2fea101e, 0x2e9c8e63, 0x18c046a9, 0x33dbcca1, 0x0f766cb7, 0x31b9ffb4, 0x11ceb03e, 0x3f38}}, - {{0x32624707, 0x078ab06f, 0x375f1bcf, 0x15c71f02, 0x079ce566, 0x131118bc, 0x00395253, 0x27157d75, 0x70c6}}}, + {{{0x06c96100, 0x1fd4203c, 0x1a72398e, 0x0602354d, 0x1dbcca16, 0x0ecd96f9, 0x0e7fed0f, 0x07581f63, 0x3f3847}}, + {{0x12624707, 0x0f1560df, 0x1d7c6f3c, 0x0e38f816, 0x19ce5665, 0x02231783, 0x0e5494d3, 0x0abeba80, 0x70c69c}}}, /* 9*16^43*G: */ - {{{0x3d22d2ac, 0x0d31bb1b, 0x1caace02, 0x377f849b, 0x05df2f10, 0x0f03825e, 0x3a76dcb4, 0x04f17f49, 0x2881}}, - {{0x0f42a268, 0x207ad57e, 0x148c8fd0, 0x30f51285, 0x176137dd, 0x1ddc9832, 0x3c5c8f20, 0x3ac0563e, 0xa1a7}}}, + {{{0x1d22d2ac, 0x1a637637, 0x12ab3808, 0x1bfc24db, 0x1df2f10d, 0x00704bc2, 0x1db72d0f, 0x18bfa4f4, 0x288113}}, + {{0x0f42a268, 0x00f5aafc, 0x12323f42, 0x07a8942a, 0x16137ddc, 0x1b93064b, 0x1723c81d, 0x002b1f78, 0xa1a7eb}}}, /* 11*16^43*G: */ - {{{0x245f8ea8, 0x12ea0374, 0x24d2900d, 0x1c9238e5, 0x119fe5d1, 0x3d36575c, 0x23a2a553, 0x28803211, 0xf963}}, - {{0x19bc99eb, 0x2f157ec1, 0x18b60824, 0x2e3c8d67, 0x3427208b, 0x1c88c07f, 0x383c0a3b, 0x2509a31f, 0x9c85}}}, + {{{0x045f8ea8, 0x05d406e9, 0x134a4035, 0x0491c72c, 0x19fe5d17, 0x06caeb88, 0x08a954fd, 0x001908c7, 0xf963a2}}, + {{0x19bc99eb, 0x1e2afd82, 0x02d82092, 0x11e46b3b, 0x027208bb, 0x11180ffa, 0x0f028edc, 0x04d18ff0, 0x9c8594}}}, /* 13*16^43*G: */ - {{{0x2606a315, 0x386a20c4, 0x26963ad9, 0x1c981cbc, 0x0e097e40, 0x362ca964, 0x0d9a7f98, 0x08933fdc, 0xa5d9}}, - {{0x1e3b68d1, 0x0d584cd6, 0x111a7c9d, 0x13434d1f, 0x180de9ed, 0x0c1aaf5e, 0x0da5b343, 0x22c00ec8, 0x8732}}}, + {{{0x0606a315, 0x10d44189, 0x1a58eb67, 0x04c0e5e4, 0x0097e407, 0x05952c87, 0x069fe636, 0x099fee1b, 0xa5d922}}, + {{0x1e3b68d1, 0x1ab099ac, 0x0469f274, 0x1a1a68fa, 0x00de9ed4, 0x0355ebcc, 0x096cd0cc, 0x0007641b, 0x87328b}}}, /* 15*16^43*G: */ - {{{0x06231493, 0x336ded50, 0x0cc4d469, 0x1046a0c3, 0x25e6a496, 0x13907403, 0x3c3604eb, 0x260b86dc, 0xf1fe}}, - {{0x358848c1, 0x25aa6699, 0x25ff0d01, 0x1cfecd1b, 0x3d99d3f1, 0x34f0817d, 0x24ddc216, 0x067abb66, 0x2e20}}} + {{{0x06231493, 0x06dbdaa0, 0x131351a7, 0x02350619, 0x1e6a4964, 0x120e8072, 0x0d813ad3, 0x05c36e78, 0xf1fe98}}, + {{0x158848c1, 0x0b54cd33, 0x17fc3406, 0x07f668dc, 0x199d3f17, 0x1e102fbe, 0x177085b4, 0x1d5db349, 0x2e2019}}} }, { /* 1*16^44*G: */ - {{{0x06d903ac, 0x027b6a70, 0x1ad7e5cb, 0x3e589d39, 0x3afd2ed5, 0x0a7f4c39, 0x3a844637, 0x2557b98d, 0x0928}}, - {{0x1bcd091f, 0x14603a4d, 0x0a8d83fc, 0x0f49bbea, 0x3a95eeac, 0x1e284c24, 0x342a827b, 0x08400f4f, 0xc256}}}, + {{{0x06d903ac, 0x04f6d4e0, 0x0b5f972c, 0x12c4e9cb, 0x0fd2ed5f, 0x0fe9873d, 0x01118dca, 0x0bdcc6f5, 0x92895}}, + {{0x1bcd091f, 0x08c0749a, 0x0a360ff1, 0x1a4ddf51, 0x095eeac3, 0x0509849d, 0x0aa09ede, 0x0007a7e8, 0xc25621}}}, /* 3*16^44*G: */ - {{{0x3874b839, 0x0444a1d5, 0x13d2b418, 0x10456ce5, 0x30b6aebe, 0x37c37ec8, 0x1e5a8053, 0x2e07f038, 0x3e03}}, - {{0x3c0594ba, 0x03073959, 0x1ab5b8da, 0x39717c3f, 0x198f667d, 0x3d981d5c, 0x07f42c44, 0x3858f7fc, 0xd13a}}}, + {{{0x1874b839, 0x088943ab, 0x0f4ad060, 0x022b672a, 0x0b6aebe4, 0x186fd918, 0x16a014f7, 0x03f81c3c, 0x3e03b8}}, + {{0x1c0594ba, 0x060e72b3, 0x0ad6e368, 0x0b8be1fb, 0x18f667de, 0x1303ab8c, 0x1d0b113d, 0x0c7bfe0f, 0xd13ae1}}}, /* 5*16^44*G: */ - {{{0x0357a513, 0x28fde39a, 0x1b3023f3, 0x146f44d1, 0x2922c5f1, 0x3e8a0ea8, 0x0492cd62, 0x302de8bd, 0xe662}}, - {{0x2017d07e, 0x24a88072, 0x1538d891, 0x00d73589, 0x21a419d8, 0x2b882284, 0x2452305d, 0x064f3984, 0xab0b}}}, + {{{0x0357a513, 0x11fbc734, 0x0cc08fce, 0x037a268b, 0x122c5f15, 0x1141d514, 0x04b358be, 0x16f45e89, 0xe662c0}}, + {{0x0017d07e, 0x095100e5, 0x14e36246, 0x06b9ac4a, 0x1a419d80, 0x11045090, 0x148c176b, 0x079cc248, 0xab0b19}}}, /* 7*16^44*G: */ - {{{0x1f37d242, 0x2657dfbf, 0x39c14b04, 0x27fb2981, 0x23587dc2, 0x218b1f2f, 0x0f6cb843, 0x202c7253, 0x40bf}}, - {{0x26405088, 0x347609e6, 0x2bd35583, 0x0c87ae90, 0x26fe1274, 0x0ffa6c6c, 0x2aaf04f5, 0x374d7615, 0xb579}}}, + {{{0x1f37d242, 0x0cafbf7e, 0x07052c12, 0x1fd94c0f, 0x1587dc29, 0x1163e5f1, 0x1b2e10e1, 0x1639299e, 0x40bf80}}, + {{0x06405088, 0x08ec13cd, 0x0f4d560f, 0x043d7485, 0x0fe12743, 0x1f4d8d93, 0x0bc13d4f, 0x06bb0ad5, 0xb579dd}}}, /* 9*16^44*G: */ - {{{0x195a3558, 0x2bcacd91, 0x234a7f2b, 0x01c7e178, 0x1b59f6ac, 0x3e5e04e3, 0x1ca70806, 0x3fa5d807, 0x3d14}}, - {{0x2443df4c, 0x1ab6ceb1, 0x3c1d727c, 0x3828b851, 0x356e1482, 0x26a4c76f, 0x281ef8f2, 0x2f75ba11, 0x16c6}}}, + {{{0x195a3558, 0x17959b22, 0x0d29fcae, 0x0e3f0bc4, 0x159f6ac0, 0x0bc09c6d, 0x09c201be, 0x12ec03b9, 0x3d14fe}}, + {{0x0443df4c, 0x156d9d63, 0x1075c9f1, 0x0145c28f, 0x16e1482e, 0x1498edfa, 0x07be3ca6, 0x1add08d0, 0x16c6bd}}}, /* 11*16^44*G: */ - {{{0x02b1fc24, 0x37a7d6b6, 0x23f7570e, 0x0a36071f, 0x12486525, 0x06b134b2, 0x265251cc, 0x29503a0b, 0xdd6f}}, - {{0x0e9b74ca, 0x290c7118, 0x17322304, 0x04379afb, 0x257e77ec, 0x1bc7afc5, 0x3186fe36, 0x0adfac74, 0x67e6}}}, + {{{0x02b1fc24, 0x0f4fad6c, 0x0fdd5c3b, 0x11b038fc, 0x04865252, 0x16269649, 0x14947306, 0x081d05cc, 0xdd6fa5}}, + {{0x0e9b74ca, 0x1218e230, 0x1cc88c12, 0x01bcd7da, 0x17e77ec1, 0x18f5f8b2, 0x01bf8d9b, 0x0fd63a63, 0x67e62b}}}, /* 13*16^44*G: */ - {{{0x3dd08e02, 0x07aa4564, 0x1adf0288, 0x2151edff, 0x3d1e8010, 0x1a5266a8, 0x15d780f8, 0x0b6a0b79, 0x13fa}}, - {{0x3cb03410, 0x29550770, 0x1a42b97d, 0x112beec6, 0x3432c7e6, 0x0d5881ae, 0x1da72313, 0x0e2c1155, 0x1363}}}, + {{{0x1dd08e02, 0x0f548ac9, 0x0b7c0a20, 0x0a8f6ffb, 0x11e80108, 0x0a4cd51e, 0x15e03e1a, 0x1505bcab, 0x13fa2d}}, + {{0x1cb03410, 0x12aa0ee1, 0x090ae5f6, 0x095f7633, 0x032c7e64, 0x0b1035da, 0x09c8c4cd, 0x1608aabb, 0x136338}}}, /* 15*16^44*G: */ - {{{0x144ee41a, 0x308ceae6, 0x37d69a6a, 0x26d5b74e, 0x06828287, 0x3042d9cb, 0x30a443f7, 0x121474f1, 0xd06c}}, - {{0x0b295e6f, 0x3c7e13a6, 0x162ee252, 0x1ee10d18, 0x3630919b, 0x02b353d3, 0x0d0adbbb, 0x3f530161, 0x5815}}} + {{{0x144ee41a, 0x0119d5cc, 0x1f5a69ab, 0x16adba76, 0x08282879, 0x085b3963, 0x0910fdf0, 0x0a3a78e1, 0xd06c48}}, + {{0x0b295e6f, 0x18fc274c, 0x18bb894b, 0x170868c2, 0x030919b7, 0x166a7a7b, 0x02b6eec2, 0x0980b09a, 0x5815fd}}} }, { /* 1*16^45*G: */ - {{{0x23d82751, 0x1eab9d45, 0x3ad35452, 0x116d2a41, 0x23b28556, 0x0193ce83, 0x1b109399, 0x3fbcfb1b, 0x85d0}}, - {{0x0eb1f962, 0x0b08de89, 0x07733158, 0x21d47a5a, 0x2cf5663e, 0x3525b960, 0x38c0be29, 0x192104e8, 0x1f03}}}, + {{{0x03d82751, 0x1d573a8b, 0x0b4d5149, 0x0b69520f, 0x1b285564, 0x1279d071, 0x0424e641, 0x1e7d8db6, 0x85d0fe}}, + {{0x0eb1f962, 0x1611bd12, 0x1dccc560, 0x0ea3d2d0, 0x0f5663e8, 0x04b72c16, 0x102f8a75, 0x10827471, 0x1f0364}}}, /* 3*16^45*G: */ - {{{0x2cde4cf3, 0x26554187, 0x38a066ab, 0x10394d51, 0x1d9ae793, 0x30b49b45, 0x022c3be7, 0x2ad2b045, 0x384d}}, - {{0x252d0566, 0x1f1e5ac8, 0x351ba73b, 0x10c28ce5, 0x34c6f01f, 0x13b5b68a, 0x1ca43bfb, 0x316f346e, 0xd6e3}}}, + {{{0x0cde4cf3, 0x0caa830f, 0x02819aae, 0x01ca6a8f, 0x19ae7934, 0x169368ae, 0x0b0ef9f0, 0x09582284, 0x384dab}}, + {{0x052d0566, 0x1e3cb591, 0x146e9ced, 0x0614672e, 0x0c6f01f4, 0x16b6d15a, 0x090efed3, 0x179a3739, 0xd6e3c5}}}, /* 5*16^45*G: */ - {{{0x1e5238c2, 0x22bcfa48, 0x00ecb8b9, 0x0d57d70e, 0x02ed4840, 0x05842d3a, 0x015aa41b, 0x3b03adf5, 0x14f0}}, - {{0x12f07922, 0x3a1a8d1e, 0x304939d6, 0x17003600, 0x02747fd2, 0x3f1cf8e1, 0x35d80921, 0x354f7520, 0xab12}}}, + {{{0x1e5238c2, 0x0579f490, 0x03b2e2e6, 0x0abeb870, 0x0ed48403, 0x1085a741, 0x16a906c5, 0x01d6fa82, 0x14f0ec}}, + {{0x12f07922, 0x14351a3c, 0x0124e75b, 0x1801b006, 0x0747fd25, 0x039f1c21, 0x1602487f, 0x07ba906b, 0xab12d5}}}, /* 7*16^45*G: */ - {{{0x1543e94d, 0x3d8d4bbf, 0x2f98e188, 0x04c0a9d5, 0x1a0ddadd, 0x30d19e29, 0x0287ec41, 0x3ceede0b, 0xeb42}}, - {{0x05924d89, 0x01567791, 0x20d6d424, 0x3611a379, 0x0dfb774c, 0x03755cbf, 0x1d92dc9a, 0x1b41d3c9, 0x234a}}}, + {{{0x1543e94d, 0x1b1a977e, 0x1e638623, 0x06054ead, 0x00ddadd1, 0x1a33c52d, 0x01fb1070, 0x176f0585, 0xeb42f3}}, + {{0x05924d89, 0x02acef22, 0x035b5090, 0x108d1bcc, 0x1fb774cd, 0x0eab97e6, 0x04b72683, 0x00e9e4bb, 0x234a6d}}}, /* 9*16^45*G: */ - {{{0x3e19aaed, 0x0c9396d5, 0x06673270, 0x26eb37a3, 0x06a92045, 0x3b00bdb8, 0x020d9a9e, 0x0e32945a, 0x1cf1}}, - {{0x292f400e, 0x04dba975, 0x3c77ffbc, 0x27bbe3fb, 0x2dde1747, 0x0dca99ad, 0x063865f4, 0x36bcc5c7, 0xd6ff}}}, + {{{0x1e19aaed, 0x19272dab, 0x199cc9c0, 0x1759bd18, 0x0a920459, 0x0017b703, 0x0366a7bb, 0x194a2d04, 0x1cf138}}, + {{0x092f400e, 0x09b752eb, 0x11dffef0, 0x1ddf1fdf, 0x1de17479, 0x195335b6, 0x0e197d0d, 0x1e62e38c, 0xd6ffda}}}, /* 11*16^45*G: */ - {{{0x36a8aa39, 0x3db03a7e, 0x278fac55, 0x2998ded2, 0x1990d937, 0x16825a12, 0x0d412c87, 0x21af97d0, 0xb586}}, - {{0x2b493c1f, 0x3f1e4d74, 0x2db347b8, 0x2f6be639, 0x00a91dab, 0x11e35153, 0x38c2c149, 0x3550c931, 0x5632}}}, + {{{0x16a8aa39, 0x1b6074fd, 0x1e3eb157, 0x0cc6f694, 0x190d937a, 0x104b424c, 0x104b21d6, 0x17cbe81a, 0xb58686}}, + {{0x0b493c1f, 0x1e3c9ae9, 0x16cd1ee3, 0x1b5f31cd, 0x0a91dabb, 0x1c6a2a60, 0x10b05251, 0x086498f1, 0x5632d5}}}, /* 13*16^45*G: */ - {{{0x303b4cc5, 0x3a47af8e, 0x21c77c2e, 0x0a0c6e96, 0x33a80257, 0x16f13f9f, 0x3cc2b67b, 0x276c1ae2, 0x5fc1}}, - {{0x25b57c28, 0x0ece7ee1, 0x0087ec4a, 0x1dbd40f3, 0x3a5ef492, 0x084e3e68, 0x0c7c66ee, 0x21303b26, 0xec8e}}}, + {{{0x103b4cc5, 0x148f5f1d, 0x071df0bb, 0x106374b4, 0x1a802572, 0x1e27f3f9, 0x10ad9ed6, 0x160d7179, 0x5fc19d}}, + {{0x05b57c28, 0x1d9cfdc3, 0x021fb128, 0x0dea0798, 0x05ef4927, 0x09c7cd1d, 0x1f19bb88, 0x181d9318, 0xec8e84}}}, /* 15*16^45*G: */ - {{{0x0cb38cb5, 0x2d2e15f5, 0x1388948b, 0x02dff7d3, 0x3eea1be1, 0x2a2903f4, 0x1e289deb, 0x2dc350bb, 0xb88f}}, - {{0x1965f3d7, 0x1efe9d59, 0x3af8c719, 0x13cf8489, 0x35a8e24d, 0x12ee652c, 0x23280603, 0x0dab51ba, 0xd6c7}}} + {{{0x0cb38cb5, 0x1a5c2bea, 0x0e22522e, 0x16ffbe9a, 0x0ea1be10, 0x05207e9f, 0x0a277aea, 0x01a85dbc, 0xb88fb7}}, + {{0x1965f3d7, 0x1dfd3ab2, 0x0be31c65, 0x1e7c244f, 0x1a8e24d4, 0x1dcca59a, 0x0a0180d2, 0x15a8dd46, 0xd6c736}}} }, { /* 1*16^46*G: */ - {{{0x0526087e, 0x3d501209, 0x2da20308, 0x3edb6220, 0x18b85dfd, 0x26d8105e, 0x2ce97c1c, 0x0373a5fb, 0xff2b}}, - {{0x30c29907, 0x32547807, 0x10e2ceb2, 0x2dfb5bee, 0x107936c7, 0x13137153, 0x0ba188af, 0x04ffbd49, 0x493d}}}, + {{{0x0526087e, 0x1aa02412, 0x16880c23, 0x16db1105, 0x0b85dfdf, 0x1b020bcc, 0x1a5f0726, 0x19d2fdd9, 0xff2b0d}}, + {{0x10c29907, 0x04a8f00f, 0x038b3acb, 0x0fdadf72, 0x07936c7b, 0x026e2a68, 0x08622bd3, 0x1fdea497, 0x493d13}}}, /* 3*16^46*G: */ - {{{0x39d681f9, 0x164153f9, 0x08feb9fc, 0x3383bbeb, 0x2c94b066, 0x1ffc9780, 0x3230888b, 0x3f7c9dd7, 0xc745}}, - {{0x3bbb1247, 0x00c5cd0d, 0x27d45c76, 0x36f4cd71, 0x2818678c, 0x04e531c3, 0x1e5e78a7, 0x08bcbdae, 0x5902}}}, + {{{0x19d681f9, 0x0c82a7f3, 0x03fae7f1, 0x1c1ddf59, 0x094b066c, 0x1f92f016, 0x0c2222df, 0x1e4eebe4, 0xc745fd}}, + {{0x1bbb1247, 0x018b9a1b, 0x1f5171d8, 0x17a66b8c, 0x018678cd, 0x1ca63874, 0x179e29c4, 0x1e5ed73c, 0x590222}}}, /* 5*16^46*G: */ - {{{0x35cd0ea3, 0x38133bb4, 0x0cac4815, 0x111e3a08, 0x32e7f2b3, 0x16797ad9, 0x1050b27a, 0x1e7cea5d, 0xabb2}}, - {{0x3c307bce, 0x1c24c4cd, 0x202f3b64, 0x25da4167, 0x078ed47c, 0x12f8300c, 0x3970d9fb, 0x040eefc5, 0x5dee}}}, + {{{0x15cd0ea3, 0x10267769, 0x12b12057, 0x08f1d041, 0x0e7f2b34, 0x0f2f5b39, 0x142c9e96, 0x1e752ea0, 0xabb279}}, + {{0x1c307bce, 0x1849899b, 0x00bced91, 0x0ed20b3c, 0x18ed47c9, 0x1f060183, 0x1c367ed2, 0x0777e2f2, 0x5dee10}}}, /* 7*16^46*G: */ - {{{0x1bc9ee3e, 0x30b8bcfc, 0x3e7382c5, 0x27e86a58, 0x27ed11ea, 0x2baa9d09, 0x0682827f, 0x0542d67f, 0x3f81}}, - {{0x199aae06, 0x33ab6c31, 0x0da81603, 0x08ecb73f, 0x39566276, 0x06facf11, 0x3a82d467, 0x229a3f6f, 0x19c8}}}, + {{{0x1bc9ee3e, 0x017179f8, 0x19ce0b17, 0x1f4352c7, 0x1ed11ea9, 0x1553a133, 0x00a09feb, 0x016b3f8d, 0x3f8115}}, + {{0x199aae06, 0x0756d862, 0x16a0580f, 0x0765b9f9, 0x15662762, 0x1f59e23c, 0x00b519c6, 0x0d1fb7f5, 0x19c88a}}}, /* 9*16^46*G: */ - {{{0x38e4a007, 0x05c6fbeb, 0x0bb358b6, 0x3b3bb3c2, 0x16c7ec15, 0x12e8cea9, 0x02de6959, 0x04cb7402, 0x5cf8}}, - {{0x1068b883, 0x398fc242, 0x39c7fe8c, 0x251be5b1, 0x0c3df6c8, 0x35056212, 0x1fa0df4a, 0x3b970358, 0xb45a}}}, + {{{0x18e4a007, 0x0b8df7d7, 0x0ecd62d8, 0x19dd9e11, 0x0c7ec15e, 0x1d19d52b, 0x179a5652, 0x05ba0105, 0x5cf813}}, + {{0x1068b883, 0x131f8484, 0x071ffa33, 0x08df2d8f, 0x03df6c89, 0x00ac4246, 0x0837d2b5, 0x0b81ac3f, 0xb45aee}}}, /* 11*16^46*G: */ - {{{0x26c2d4a7, 0x255bf9ec, 0x3cfffb10, 0x30dbe4ce, 0x004ed21b, 0x38ce5cf1, 0x3a494653, 0x3f934352, 0xb6d5}}, - {{0x3ae86371, 0x063739f8, 0x35e3cc81, 0x16df939b, 0x3ffd8e74, 0x33e48277, 0x3d6c14df, 0x1ce84eae, 0x47f3}}}, + {{{0x06c2d4a7, 0x0ab7f3d9, 0x13ffec42, 0x06df2677, 0x04ed21bc, 0x19cb9e20, 0x125194f8, 0x09a1a974, 0xb6d5fe}}, + {{0x1ae86371, 0x0c6e73f1, 0x178f3204, 0x16fc9cde, 0x1fd8e745, 0x1c904eff, 0x1b0537f3, 0x1427577a, 0x47f373}}}, /* 13*16^46*G: */ - {{{0x3c66dd33, 0x024cd88b, 0x1dc76dc5, 0x23ef23fc, 0x29b022ea, 0x2c6c5400, 0x3588706b, 0x2ef019b3, 0x61c8}}, - {{0x36f10bfa, 0x0eeea7ce, 0x2820c8ca, 0x1441bab0, 0x05d3fb6a, 0x1a6652e6, 0x0f703446, 0x2788e795, 0x9359}}}, + {{{0x1c66dd33, 0x0499b117, 0x171db714, 0x1f791fe3, 0x1b022ea8, 0x0d8a8014, 0x021c1aec, 0x180cd9eb, 0x61c8bb}}, + {{0x16f10bfa, 0x1ddd4f9d, 0x00832328, 0x020dd585, 0x1d3fb6a5, 0x0cca5cc2, 0x1c0d119a, 0x0473ca9e, 0x93599e}}}, /* 15*16^46*G: */ - {{{0x1d6b2ff8, 0x2016df33, 0x286c8fa9, 0x18cdb05c, 0x03bdf187, 0x27d4dcfb, 0x2785187c, 0x0ae95d09, 0x94e3}}, - {{0x2ce1af3e, 0x37521554, 0x26bfe13a, 0x0ebc1094, 0x2d9e8cb3, 0x07922198, 0x204e192f, 0x1122d0f6, 0x0d1b}}} + {{{0x1d6b2ff8, 0x002dbe66, 0x01b23ea6, 0x066d82e5, 0x1bdf1876, 0x1a9b9f61, 0x01461f27, 0x14ae84cf, 0x94e32b}}, + {{0x0ce1af3e, 0x0ea42aa9, 0x1aff84eb, 0x15e084a4, 0x19e8cb33, 0x12443316, 0x13864bc7, 0x11687b40, 0xd1b44}}} }, { /* 1*16^47*G: */ - {{{0x3856e241, 0x203978b3, 0x0d6dd287, 0x3c7b8523, 0x1b212b57, 0x0acb98c0, 0x080ea9ed, 0x2ef92c7a, 0x827f}}, - {{0x2ec293ec, 0x1816da2e, 0x2903166d, 0x3de98c61, 0x1d12687f, 0x3bcb19f4, 0x27b0b71b, 0x27248f1c, 0xc60f}}}, + {{{0x1856e241, 0x0072f167, 0x15b74a1e, 0x03dc2919, 0x1212b57f, 0x1973180d, 0x03aa7b4a, 0x1c963d10, 0x827fbb}}, + {{0x0ec293ec, 0x102db45d, 0x040c59b5, 0x0f4c630d, 0x112687ff, 0x19633e8e, 0x0c2dc6fb, 0x12478e4f, 0xc60f9c}}}, /* 3*16^47*G: */ - {{{0x3bb80fa7, 0x0d12172c, 0x30413886, 0x29f69aed, 0x20819f3a, 0x0681af4c, 0x0c2fbc0d, 0x38c7d8c2, 0x0857}}, - {{0x09366b2d, 0x3660847c, 0x0d7016ab, 0x0b8dc10f, 0x0b714717, 0x1f327477, 0x0172092d, 0x24d08eb8, 0xf643}}}, + {{{0x1bb80fa7, 0x1a242e59, 0x0104e218, 0x0fb4d76e, 0x0819f3aa, 0x1035e990, 0x0bef0346, 0x03ec6118, 0x857e3}}, + {{0x09366b2d, 0x0cc108f8, 0x15c05aaf, 0x1c6e0879, 0x17147172, 0x064e8ee5, 0x1c824b5f, 0x08475c02, 0xf64393}}}, /* 5*16^47*G: */ - {{{0x09c70e63, 0x1740b0e8, 0x353d496f, 0x2ee2de39, 0x0a672e9c, 0x171955d9, 0x16004354, 0x333a95af, 0x28aa}}, - {{0x3057da4e, 0x27c0e20b, 0x04da1e8b, 0x3f167391, 0x28ebb7f5, 0x22599f1d, 0x20e1567a, 0x0c8bbe06, 0x2b69}}}, + {{{0x09c70e63, 0x0e8161d0, 0x14f525bd, 0x1716f1ce, 0x0672e9cb, 0x032abb25, 0x0010d517, 0x1d4ad7ac, 0x28aacc}}, + {{0x1057da4e, 0x0f81c417, 0x13687a2e, 0x18b39c88, 0x0ebb7f5f, 0x0b33e3b4, 0x18559ea2, 0x05df0341, 0x2b6932}}}, /* 7*16^47*G: */ - {{{0x33e674b5, 0x007714bd, 0x3060aac6, 0x363da739, 0x2b8a4f92, 0x36cb26f3, 0x1a66145d, 0x2d896815, 0xa2f3}}, - {{0x0e937941, 0x024e3238, 0x033fa53b, 0x08be8c5f, 0x2a7c4b92, 0x112a43cc, 0x068ae800, 0x28565853, 0x620e}}}, + {{{0x13e674b5, 0x00ee297b, 0x0182ab18, 0x11ed39ce, 0x18a4f92d, 0x1964de75, 0x19851776, 0x04b40ab4, 0xa2f3b6}}, + {{0x0e937941, 0x049c6470, 0x0cfe94ec, 0x05f462f8, 0x07c4b922, 0x05487995, 0x02ba0011, 0x0b2c298d, 0x620ea1}}}, /* 9*16^47*G: */ - {{{0x191eb056, 0x1d8058c7, 0x2cfd386c, 0x00bbf6e3, 0x3515f5a0, 0x22d71a8f, 0x259231d9, 0x20f27aab, 0x3c4f}}, - {{0x205cecab, 0x109624f6, 0x1cf6b877, 0x20ad5120, 0x32788019, 0x3595cf0e, 0x28b6a33a, 0x2401d452, 0x9447}}}, + {{{0x191eb056, 0x1b00b18e, 0x13f4e1b1, 0x05dfb71d, 0x115f5a00, 0x1ae351fa, 0x048c7662, 0x193d55cb, 0x3c4f83}}, + {{0x005cecab, 0x012c49ed, 0x13dae1dd, 0x056a8903, 0x07880198, 0x12b9e1d9, 0x0da8ceb5, 0x00ea2951, 0x944790}}}, /* 11*16^47*G: */ - {{{0x3d86dfa9, 0x24187f6e, 0x1b993a71, 0x0e2d2902, 0x103baadc, 0x30780fa0, 0x167d4e29, 0x384a22a6, 0xaff8}}, - {{0x01d12681, 0x1c40f0db, 0x019f9c70, 0x045b6a51, 0x0f53f4f9, 0x0faea87f, 0x37c3fd3d, 0x12ecc84d, 0x8d8b}}}, + {{{0x1d86dfa9, 0x0830fedd, 0x0e64e9c6, 0x11694813, 0x03baadc3, 0x0f01f408, 0x1f538a70, 0x0511532c, 0xaff8e1}}, + {{0x01d12681, 0x1881e1b6, 0x067e71c1, 0x02db5288, 0x153f4f91, 0x15d50fe7, 0x10ff4f4f, 0x166426ef, 0x8d8b4b}}}, /* 13*16^47*G: */ - {{{0x189ba9c1, 0x23c9cdae, 0x09d338e2, 0x03df2968, 0x0ee579e4, 0x16098abb, 0x000b3e84, 0x1e114a37, 0xd3fb}}, - {{0x2b51b267, 0x186e237f, 0x011ade00, 0x073b7570, 0x370fe634, 0x32815d62, 0x2b4e7ca7, 0x350d3be9, 0xf894}}}, + {{{0x189ba9c1, 0x07939b5c, 0x074ce38a, 0x1ef94b41, 0x0e579e40, 0x01315767, 0x02cfa116, 0x08a51b80, 0xd3fb78}}, + {{0x0b51b267, 0x10dc46ff, 0x046b7801, 0x19dbab80, 0x10fe6341, 0x102bac5b, 0x139f29f2, 0x069df4d6, 0xf894d4}}}, /* 15*16^47*G: */ - {{{0x0f2bb909, 0x36a5b074, 0x3598d999, 0x24409f14, 0x187d7f63, 0x1ca620e4, 0x1aa88ff4, 0x0c0382b2, 0x4ec9}}, - {{0x24cf4071, 0x2228e0fe, 0x1ac3827b, 0x0b85a083, 0x0c49bad5, 0x03711461, 0x304dc5c8, 0x2841af86, 0x782b}}} + {{{0x0f2bb909, 0x0d4b60e8, 0x16636667, 0x0204f8a6, 0x07d7f639, 0x14c41c8c, 0x0a23fd1c, 0x01c15935, 0x4ec930}}, + {{0x04cf4071, 0x0451c1fd, 0x0b0e09ee, 0x1c2d041b, 0x049bad52, 0x0e228c26, 0x13717203, 0x00d7c360, 0x782ba1}}} }, { /* 1*16^48*G: */ - {{{0x2120e2b3, 0x3ced63e8, 0x347f9aa7, 0x163f739f, 0x26e5217a, 0x392b8d33, 0x1bdbae7b, 0x127c87d4, 0xeaa6}}, - {{0x3a5ad93d, 0x11e94c16, 0x13f7e59d, 0x29ae597c, 0x39aa5a01, 0x2a03e261, 0x3b03ac69, 0x1e7b56ee, 0xbe32}}}, + {{{0x0120e2b3, 0x19dac7d1, 0x11fe6a9f, 0x11fb9cfe, 0x0e5217a5, 0x0571a673, 0x16eb9ef9, 0x1e43ea37, 0xeaa649}}, + {{0x1a5ad93d, 0x03d2982d, 0x0fdf9675, 0x0d72cbe2, 0x1aa5a01a, 0x007c4c3c, 0x00eb1a6a, 0x1dab7776, 0xbe3279}}}, /* 3*16^48*G: */ - {{{0x3f2e070d, 0x160ff4e8, 0x12a6a98f, 0x2aadc731, 0x1047e229, 0x1cc70ee1, 0x34abff48, 0x297a410b, 0x4b72}}, - {{0x296dd780, 0x112ea0bb, 0x2948c3de, 0x2d197774, 0x0f3c10b0, 0x1deecdb4, 0x2e1cf602, 0x0753875a, 0x599e}}}, + {{{0x1f2e070d, 0x0c1fe9d1, 0x0a9aa63d, 0x156e398a, 0x047e229a, 0x18e1dc28, 0x0affd21c, 0x1d2085e9, 0x4b72a5}}, + {{0x096dd780, 0x025d4177, 0x05230f79, 0x08cbbba5, 0x13c10b0b, 0x1dd9b687, 0x073d809d, 0x09c3ad5c, 0x599e1d}}}, /* 5*16^48*G: */ - {{{0x0a02591c, 0x2739ff61, 0x05125a1e, 0x3d526596, 0x21fd613e, 0x1afefad7, 0x1c8e285a, 0x24ff194e, 0xa9fc}}, - {{0x29bec2dc, 0x242b77bd, 0x3cf72537, 0x22231057, 0x1165e5ca, 0x1305e86a, 0x387173e8, 0x39ce7714, 0x9c2c}}}, + {{{0x0a02591c, 0x0e73fec2, 0x1449687a, 0x0a932cb0, 0x1fd613ef, 0x1fdf5af0, 0x038a169a, 0x1f8ca739, 0xa9fc93}}, + {{0x09bec2dc, 0x0856ef7b, 0x13dc94de, 0x111882bf, 0x165e5ca8, 0x00bd0d48, 0x1c5cfa13, 0x073b8a70, 0x9c2ce7}}}, /* 7*16^48*G: */ - {{{0x2d968b59, 0x0401b838, 0x3cbbc2e1, 0x28a2eb84, 0x1b027709, 0x35eb0482, 0x39f0a6a7, 0x005f069b, 0xc940}}, - {{0x0de572fb, 0x3bf5d902, 0x390c9c8f, 0x210b2d90, 0x35742ce2, 0x2286fe96, 0x3862013b, 0x08940326, 0x39d9}}}, + {{{0x0d968b59, 0x08037071, 0x12ef0b84, 0x05175c27, 0x1027709a, 0x1d60904d, 0x1c29a9f5, 0x0f834df3, 0xc94001}}, + {{0x0de572fb, 0x17ebb204, 0x0432723f, 0x08596c87, 0x1742ce28, 0x10dfd2da, 0x18804ee2, 0x0a019370, 0x39d922}}}, /* 9*16^48*G: */ - {{{0x326b3332, 0x0a1cccd5, 0x3ee5de6a, 0x00e2341c, 0x0bf8e031, 0x1e4e97dc, 0x10024ec6, 0x2ee75fbb, 0x1f84}}, - {{0x14e8d52e, 0x1510a28c, 0x36dc3a25, 0x2f338b50, 0x39edf0c2, 0x1f09fdd6, 0x29ecc254, 0x1b41caf2, 0xee72}}}, + {{{0x126b3332, 0x143999ab, 0x1b9779a8, 0x0711a0e7, 0x1f8e0310, 0x09d2fb85, 0x0093b19e, 0x13afdda0, 0x1f84bb}}, + {{0x14e8d52e, 0x0a214518, 0x1b70e895, 0x199c5a86, 0x1edf0c2b, 0x013fbadc, 0x1b30951f, 0x00e57953, 0xee726d}}}, /* 11*16^48*G: */ - {{{0x0defa98e, 0x336a952b, 0x1ac27995, 0x12111a04, 0x11e9c772, 0x2055ece6, 0x1fcd06ca, 0x38224251, 0x0f13}}, - {{0x3e286767, 0x0229dda6, 0x2ceaccdc, 0x1f9c1785, 0x3362db28, 0x0fe2c29e, 0x27c5035e, 0x087c5d93, 0xadd5}}}, + {{{0x0defa98e, 0x06d52a56, 0x0b09e657, 0x1088d023, 0x1e9c7724, 0x0abd9cc8, 0x1341b2a0, 0x112128bf, 0xf13e0}}, + {{0x1e286767, 0x0453bb4d, 0x13ab3370, 0x1ce0bc2d, 0x162db287, 0x1c5853d9, 0x1140d78f, 0x1e2ec9cf, 0xadd521}}}, /* 13*16^48*G: */ - {{{0x29f59b6b, 0x178700ef, 0x1888e2fa, 0x2ce318f0, 0x1826d3e9, 0x0a2874b5, 0x1ec7db37, 0x24695477, 0xdde1}}, - {{0x26cb1410, 0x1ab658a4, 0x3154fecf, 0x15ce2ef9, 0x12e14e8b, 0x1d5f5871, 0x275cbe0a, 0x3ede00a0, 0x5b2b}}}, + {{{0x09f59b6b, 0x0f0e01df, 0x02238be9, 0x0718c783, 0x026d3e9b, 0x050e96ac, 0x11f6cdca, 0x14aa3bbd, 0xdde191}}, + {{0x06cb1410, 0x156cb149, 0x0553fb3d, 0x0e7177ce, 0x0e14e8b5, 0x0beb0e29, 0x172f829d, 0x0f00504e, 0x5b2bfb}}}, /* 15*16^48*G: */ - {{{0x09c6b699, 0x1a3157f7, 0x3e46871b, 0x1bd5cd5a, 0x341682a8, 0x1b5efe5e, 0x36f7a5a1, 0x004bbb60, 0x5fab}}, - {{0x01c6c3aa, 0x05cc854b, 0x2883519b, 0x2ac45ffa, 0x162f7b90, 0x2ed044c3, 0x3d144e9e, 0x3e9c28f0, 0x2d9b}}} + {{{0x09c6b699, 0x1462afee, 0x191a1c6d, 0x1eae6ad7, 0x01682a86, 0x0bdfcbda, 0x1de9685b, 0x05ddb06d, 0x5fab01}}, + {{0x01c6c3aa, 0x0b990a96, 0x020d466c, 0x1622ffd5, 0x02f7b90a, 0x1a08986b, 0x0513a7ae, 0x0e14787a, 0x2d9bfa}}} }, { /* 1*16^49*G: */ - {{{0x1a34d24f, 0x388d8cb7, 0x1a137401, 0x2db63c32, 0x342ee541, 0x077db7b3, 0x3169d939, 0x0b50f173, 0xe4a4}}, - {{0x1eba9414, 0x29fdc4c7, 0x0d8e4f13, 0x21bbb7ea, 0x0ad34ce8, 0x326733ee, 0x1c73526f, 0x24b9c5b4, 0x4d9f}}}, + {{{0x1a34d24f, 0x111b196e, 0x084dd007, 0x0db1e193, 0x02ee541b, 0x0fb6f67a, 0x1a764e47, 0x0878b9e2, 0xe4a42d}}, + {{0x1eba9414, 0x13fb898e, 0x16393c4e, 0x0dddbf51, 0x0d34ce88, 0x0ce67dc5, 0x1cd49bf2, 0x1ce2da38, 0x4d9f92}}}, /* 3*16^49*G: */ - {{{0x3bea0c68, 0x321042bc, 0x37b392b5, 0x10c048d9, 0x396faf09, 0x26f23a34, 0x2a3a2494, 0x258d3855, 0x3e41}}, - {{0x1a45edb6, 0x32edbfdc, 0x03cda1ab, 0x2846518c, 0x0693062f, 0x0f2ff8dc, 0x321f7f37, 0x31676492, 0x0123}}}, + {{{0x1bea0c68, 0x04208579, 0x1ece4ad7, 0x060246ce, 0x16faf094, 0x1e47469c, 0x0e892526, 0x069c2ad4, 0x3e4196}}, + {{0x1a45edb6, 0x05db7fb8, 0x0f3686af, 0x02328c60, 0x093062fa, 0x05ff1b83, 0x07dfcdcf, 0x13b24964, 0x123c5}}}, /* 5*16^49*G: */ - {{{0x139824d7, 0x3dd748f2, 0x11c9897a, 0x2ded930d, 0x3f0b576e, 0x128f98bd, 0x17508eed, 0x0e3d5157, 0x8d94}}, - {{0x1366489f, 0x28013d22, 0x26b063d8, 0x2e78ae0c, 0x36ef6f8f, 0x182f4c6a, 0x26c2a2ca, 0x381cd3fb, 0x3261}}}, + {{{0x139824d7, 0x1bae91e4, 0x072625eb, 0x0f6c986a, 0x10b576eb, 0x11f317bf, 0x1423bb52, 0x1ea8abae, 0x8d9438}}, + {{0x1366489f, 0x10027a44, 0x1ac18f62, 0x13c57064, 0x0ef6f8fb, 0x05e98d5b, 0x10a8b298, 0x0e69fdcd, 0x3261e0}}}, /* 7*16^49*G: */ - {{{0x18d713de, 0x39201c6a, 0x028e6208, 0x1830bedd, 0x25454393, 0x2a44a8bf, 0x254420d4, 0x0931563b, 0xb725}}, - {{0x1b8350e9, 0x1bff9496, 0x04a5fcb7, 0x20b49bf9, 0x16941504, 0x0b460ba7, 0x03e45104, 0x2ce6a28a, 0x4c51}}}, + {{{0x18d713de, 0x124038d4, 0x0a398823, 0x0185f6e8, 0x14543936, 0x089517f2, 0x1108352a, 0x18ab1dca, 0xb72524}}, + {{0x1b8350e9, 0x17ff292c, 0x1297f2dd, 0x05a4dfc8, 0x09415048, 0x08c174eb, 0x1914410b, 0x13514507, 0x4c51b3}}}, /* 9*16^49*G: */ - {{{0x3e3b2cb4, 0x331b0a4f, 0x37210402, 0x127cd6fc, 0x21149e30, 0x31db8e04, 0x112519ad, 0x17d6885b, 0x3de4}}, - {{0x307eb02f, 0x1878ceb0, 0x287044cf, 0x0f8a3996, 0x3c910682, 0x022a92a5, 0x2addc50e, 0x21661017, 0xba2a}}}, + {{{0x1e3b2cb4, 0x0636149f, 0x1c84100b, 0x13e6b7e6, 0x1149e304, 0x1b71c090, 0x09466b71, 0x0b442da2, 0x3de45f}}, + {{0x107eb02f, 0x10f19d61, 0x01c1133d, 0x1c51ccb5, 0x09106823, 0x055254be, 0x17714382, 0x13080bd5, 0xba2a85}}}, /* 11*16^49*G: */ - {{{0x2ce4e5bf, 0x08d1d9bd, 0x09005b17, 0x19f2a1a8, 0x0906ae9b, 0x0ff38dd2, 0x1be87c1e, 0x3c71a256, 0x8511}}, - {{0x01789c08, 0x3f24a513, 0x05365262, 0x2a1e226f, 0x2a00232d, 0x377dfb1a, 0x0d4874c1, 0x3d73e46f, 0xecdf}}}, + {{{0x0ce4e5bf, 0x11a3b37b, 0x04016c5c, 0x0f950d41, 0x106ae9b6, 0x1e71ba44, 0x1a1f078f, 0x18d12b37, 0x8511f1}}, + {{0x01789c08, 0x1e494a26, 0x14d9498b, 0x10f11378, 0x000232da, 0x0fbf6355, 0x121d3077, 0x19f2379a, 0xecdff5}}}, /* 13*16^49*G: */ - {{{0x3d3258ab, 0x06d59a28, 0x2bc14dc3, 0x3490a062, 0x14ab5957, 0x2871cbb8, 0x360222cf, 0x014ba073, 0x8c5a}}, - {{0x022d0f8f, 0x15f8214c, 0x0d944ade, 0x36ba3e70, 0x0c08c246, 0x2a031e41, 0x3bda1079, 0x36d2ed10, 0x6811}}}, + {{{0x1d3258ab, 0x0dab3451, 0x0f05370c, 0x04850315, 0x0ab5957d, 0x0e39770a, 0x0088b3e8, 0x05d039ec, 0x8c5a05}}, + {{0x022d0f8f, 0x0bf04298, 0x16512b79, 0x15d1f381, 0x008c246d, 0x0063c826, 0x16841e6a, 0x09768877, 0x6811db}}}, /* 15*16^49*G: */ - {{{0x3f91bcee, 0x1630a82a, 0x20c0d841, 0x33c763c7, 0x2bf137f5, 0x18f3b155, 0x13560bdc, 0x3e05b7af, 0xcef7}}, - {{0x01966b33, 0x2ed36a7e, 0x172f6ac6, 0x0f92c0a8, 0x1d245fa6, 0x0ecce700, 0x08701246, 0x1320d8dd, 0x67e7}}} + {{{0x1f91bcee, 0x0c615055, 0x03036105, 0x1e3b1e3c, 0x1f137f5c, 0x1e762ab5, 0x1582f718, 0x02dbd7a6, 0xcef7f8}}, + {{0x01966b33, 0x1da6d4fc, 0x1cbdab1a, 0x1c960542, 0x1245fa63, 0x199ce00e, 0x1c04918e, 0x106c6e90, 0x67e74c}}} }, { /* 1*16^50*G: */ - {{{0x0300bf19, 0x1c5cee75, 0x08fea494, 0x2d4d5daa, 0x352b6b92, 0x183eb6ac, 0x0bdd9541, 0x03fbcd83, 0x1ec8}}, - {{0x0107cefd, 0x1c737073, 0x295a07b6, 0x11b9dfd8, 0x2bbf5e01, 0x2925629e, 0x1340d2f3, 0x3a4dd5ad, 0xaeef}}}, + {{{0x0300bf19, 0x18b9dcea, 0x03fa9251, 0x0a6aed51, 0x12b6b92b, 0x07d6d59a, 0x17655058, 0x1de6c197, 0x1ec80f}}, + {{0x0107cefd, 0x18e6e0e6, 0x05681ed9, 0x0dcefec5, 0x1bf5e014, 0x04ac53d5, 0x1034bce9, 0x06ead6a6, 0xaeefe9}}}, /* 3*16^50*G: */ - {{{0x12fea1f9, 0x2c5f2ef1, 0x00452b94, 0x3fc2d423, 0x106531c4, 0x3f76ad9c, 0x1f2e83bc, 0x22029574, 0xa6dc}}, - {{0x3bc345e9, 0x2c705391, 0x268f7e63, 0x1ee276df, 0x2cbc5005, 0x1a0e845a, 0x367c3038, 0x2a151f70, 0x7ef1}}}, + {{{0x12fea1f9, 0x18be5de2, 0x0114ae52, 0x1e16a118, 0x06531c4f, 0x0ed5b388, 0x0ba0ef3f, 0x014aba3e, 0xa6dc88}}, + {{0x1bc345e9, 0x18e0a723, 0x1a3df98e, 0x1713b6fc, 0x0bc50057, 0x01d08b56, 0x1f0c0e1a, 0x0a8fb86c, 0x7ef1a8}}}, /* 5*16^50*G: */ - {{{0x06d6c9b3, 0x235030fc, 0x0865637c, 0x1b133a1d, 0x2481ba8c, 0x308a71e2, 0x245992bd, 0x2a4ffa90, 0xfe6b}}, - {{0x2948bdfb, 0x30b1e23e, 0x1c2e9b00, 0x203c6fc1, 0x013b56d9, 0x2d06cd15, 0x39872b6b, 0x0635d014, 0x7ee9}}}, + {{{0x06d6c9b3, 0x06a061f8, 0x01958df2, 0x1899d0e9, 0x081ba8c6, 0x114e3c52, 0x1664af70, 0x07fd4848, 0xfe6ba9}}, + {{0x0948bdfb, 0x0163c47d, 0x10ba6c03, 0x01e37e0b, 0x13b56d98, 0x00d9a2a0, 0x01cadaed, 0x1ae80a73, 0x7ee918}}}, /* 7*16^50*G: */ - {{{0x0cf95151, 0x08bc41cc, 0x02c4b644, 0x19201b91, 0x08ded1b9, 0x03230b70, 0x098bfb02, 0x38bc51bf, 0x15d5}}, - {{0x2ff8ecf2, 0x20a81f30, 0x1d8c0f94, 0x0813ee5f, 0x1023f9bb, 0x038425e2, 0x3d4ec7f9, 0x0b8c6457, 0xa5b7}}}, + {{{0x0cf95151, 0x11788398, 0x0b12d910, 0x0900dc88, 0x0ded1b96, 0x04616e04, 0x02fec083, 0x1e28df93, 0x15d5e2}}, + {{0x0ff8ecf2, 0x01503e61, 0x16303e52, 0x009f72fb, 0x023f9bb2, 0x1084bc48, 0x13b1fe43, 0x06322bfa, 0xa5b72e}}}, /* 9*16^50*G: */ - {{{0x296a5658, 0x35e042e4, 0x1ef65643, 0x052c9490, 0x2e29be38, 0x1f80249e, 0x0447ad8c, 0x3a1c95a2, 0x84c0}}, - {{0x181b80d1, 0x3659ca6f, 0x34f1fd22, 0x2986a607, 0x13725ed3, 0x1f8c6419, 0x022c4a08, 0x20e03058, 0x2659}}}, + {{{0x096a5658, 0x0bc085c9, 0x1bd9590f, 0x0964a483, 0x029be381, 0x100493d7, 0x11eb631f, 0x0e4ad108, 0x84c0e8}}, + {{0x181b80d1, 0x0cb394de, 0x13c7f48b, 0x0c35303e, 0x1725ed3a, 0x118c8329, 0x0b12821f, 0x10182c04, 0x265983}}}, /* 11*16^50*G: */ - {{{0x14dc6a0f, 0x1d6ed722, 0x2fe15753, 0x10d06450, 0x0077c274, 0x09939e8b, 0x3731d565, 0x2c71c6a4, 0xfed6}}, - {{0x176fc7e0, 0x32e35cb6, 0x23fc409c, 0x1d3564c2, 0x13ae2313, 0x24606b93, 0x3ff0a847, 0x2af9ac3f, 0x8de2}}}, + {{{0x14dc6a0f, 0x1addae44, 0x1f855d4d, 0x06832285, 0x077c2744, 0x1273d160, 0x0c755949, 0x18e3526e, 0xfed6b1}}, + {{0x176fc7e0, 0x05c6b96c, 0x0ff10273, 0x09ab2614, 0x1ae23137, 0x0c0d7269, 0x1c2a11e4, 0x1cd61fff, 0x8de2ab}}}, /* 13*16^50*G: */ - {{{0x18e29355, 0x2ce217c4, 0x1720d86d, 0x0723a4ce, 0x23b9d82f, 0x3be18100, 0x3cbc70fc, 0x137664b4, 0x2a6a}}, - {{0x35cc2872, 0x014f803e, 0x0c4c76c0, 0x24168e99, 0x28f90dfe, 0x3f720789, 0x27e0c760, 0x37ee9f12, 0x8677}}}, + {{{0x18e29355, 0x19c42f88, 0x1c8361b6, 0x191d2672, 0x1b9d82f1, 0x1c302011, 0x0f1c3f3b, 0x1b325a79, 0x2a6a4d}}, + {{0x15cc2872, 0x029f007d, 0x1131db00, 0x00b474c9, 0x0f90dfe9, 0x0e40f134, 0x1831d83f, 0x174f894f, 0x8677df}}}, /* 15*16^50*G: */ - {{{0x2148dabf, 0x3e7ea23f, 0x09d78eb1, 0x2b74ae4d, 0x3ae735c1, 0x193b08d7, 0x27546d97, 0x24c09b24, 0xe42d}}, - {{0x011e1361, 0x1dcb1d5a, 0x1e77eb9d, 0x1c9d5c06, 0x33853032, 0x0e33aff7, 0x184b0d8b, 0x218b1b8b, 0x6413}}} + {{{0x0148dabf, 0x1cfd447f, 0x075e3ac7, 0x1ba57269, 0x0e735c1a, 0x07611afd, 0x151b65d9, 0x004d924e, 0xe42d93}}, + {{0x011e1361, 0x1b963ab4, 0x19dfae75, 0x04eae033, 0x18530327, 0x0675fef9, 0x12c362ce, 0x058dc5b0, 0x641386}}} }, { /* 1*16^51*G: */ - {{{0x366642be, 0x376d64a0, 0x158ba889, 0x0d241c5f, 0x0dfa8bce, 0x002bd1a0, 0x30c2f91b, 0x1de30119, 0x146a}}, - {{0x3d83efd0, 0x02ca5d20, 0x37e5ed1d, 0x2aa5c74b, 0x14b2870a, 0x1a609fe7, 0x0028add6, 0x383b0cd5, 0xb318}}}, + {{{0x166642be, 0x0edac941, 0x162ea227, 0x0920e2fa, 0x1fa8bce3, 0x057a3406, 0x10be46c0, 0x11808ce1, 0x146a77}}, + {{0x1d83efd0, 0x0594ba41, 0x1f97b474, 0x152e3a5e, 0x0b2870aa, 0x0c13fcea, 0x0a2b759a, 0x1d866a80, 0xb318e0}}}, /* 3*16^51*G: */ - {{{0x27315443, 0x364e1ce0, 0x2e867299, 0x1e6ef552, 0x2142a13d, 0x32266082, 0x0935ff42, 0x1b010198, 0xfc69}}, - {{0x17d28960, 0x1243582d, 0x09bd1b17, 0x1ffd2184, 0x1677b548, 0x0387375a, 0x35892bbf, 0x09fafe0e, 0xe0ce}}}, + {{{0x07315443, 0x0c9c39c1, 0x1a19ca67, 0x1377aa95, 0x142a13d7, 0x04cc1050, 0x0d7fd0b2, 0x0080cc12, 0xfc696c}}, + {{0x17d28960, 0x0486b05a, 0x06f46c5d, 0x1fe90c21, 0x077b5487, 0x10e6eb4b, 0x024aefc3, 0x1d7f076b, 0xe0ce27}}}, /* 5*16^51*G: */ - {{{0x16fdb4eb, 0x06ecbd70, 0x22e6a79d, 0x28f75e71, 0x3eb0928f, 0x15a8d58a, 0x3f2ad1ae, 0x3c887fd3, 0x974a}}, - {{0x29f6f484, 0x10270f7e, 0x3ffc2348, 0x0715ca8e, 0x0090ed11, 0x0790f40b, 0x003ca64d, 0x0e1f54d4, 0x5552}}}, + {{{0x16fdb4eb, 0x0dd97ae0, 0x0b9a9e74, 0x07baf38c, 0x0b0928fa, 0x151ab15f, 0x0ab46b95, 0x043fe9fe, 0x974af2}}, + {{0x09f6f484, 0x004e1efd, 0x1ff08d21, 0x18ae5477, 0x090ed111, 0x121e8160, 0x0f299347, 0x0faa6a00, 0x555238}}}, /* 7*16^51*G: */ - {{{0x1d5aeee3, 0x0e412b6d, 0x258c8137, 0x0a12f0d9, 0x1270c5e8, 0x086ce99a, 0x2398b091, 0x2d66d277, 0x5baa}}, - {{0x30f69717, 0x0b4a6bed, 0x3d31eed8, 0x1777276a, 0x3fdaf721, 0x28021987, 0x37e856e5, 0x1fd85f03, 0x8a57}}}, + {{{0x1d5aeee3, 0x1c8256da, 0x163204dc, 0x109786cc, 0x070c5e82, 0x0d9d3349, 0x062c2448, 0x13693bc7, 0x5baab5}}, + {{0x10f69717, 0x1694d7db, 0x14c7bb60, 0x1bb93b57, 0x1daf7215, 0x004330ff, 0x1a15b968, 0x0c2f81ef, 0x8a577f}}}, /* 9*16^51*G: */ - {{{0x35726890, 0x146c7913, 0x0837d158, 0x24097fab, 0x110a0ee5, 0x0cbf3afe, 0x1c43d010, 0x17e9fad2, 0xfb68}}, - {{0x3835783a, 0x01baa3ce, 0x10e79b26, 0x29b2c4ba, 0x24ba094f, 0x3285b661, 0x25e2e869, 0x37c8b263, 0xd750}}}, + {{{0x15726890, 0x08d8f227, 0x00df4561, 0x004bfd59, 0x10a0ee59, 0x17e75fc8, 0x10f4040c, 0x14fd6938, 0xfb685f}}, + {{0x1835783a, 0x0375479d, 0x039e6c98, 0x0d9625d2, 0x0ba094fa, 0x10b6cc32, 0x18ba1a72, 0x045931cb, 0xd750df}}}, /* 11*16^51*G: */ - {{{0x28bca48a, 0x1192fc4e, 0x03df62f5, 0x2d357d3a, 0x07f71d78, 0x09ee470a, 0x2995a0ab, 0x23fd9678, 0x5de5}}, - {{0x12fd41cd, 0x21e53a03, 0x20f8aa95, 0x396f6713, 0x2d3c843f, 0x2988f094, 0x19b55309, 0x0ecf600d, 0x685a}}}, + {{{0x08bca48a, 0x0325f89d, 0x0f7d8bd5, 0x09abe9d0, 0x1f71d78b, 0x1dc8e143, 0x05682ac9, 0x1ecb3c53, 0x5de58f}}, + {{0x12fd41cd, 0x03ca7406, 0x03e2aa56, 0x0b7b389c, 0x13c843fe, 0x111e1296, 0x0d54c269, 0x07b006b3, 0x685a3b}}}, /* 13*16^51*G: */ - {{{0x25ef63b6, 0x378e0d13, 0x31b182eb, 0x2d34059c, 0x0fc1c85a, 0x2dff68ed, 0x218bfaf1, 0x09737ab5, 0x6f18}}, - {{0x05c655f3, 0x0b211b3d, 0x27f94541, 0x22569900, 0x3334553c, 0x108135e0, 0x1911b98f, 0x1f9f7564, 0xff09}}}, + {{{0x05ef63b6, 0x0f1c1a27, 0x06c60baf, 0x09a02ce6, 0x1c1c85ab, 0x1fed1da7, 0x02febc6d, 0x19bd5ac3, 0x6f1825}}, + {{0x05c655f3, 0x1642367a, 0x1fe51504, 0x12b4c804, 0x134553c8, 0x1026bc19, 0x046e63d0, 0x0fbab232, 0xff097e}}}, /* 15*16^51*G: */ - {{{0x34a63f3b, 0x2d411fb7, 0x178f9727, 0x080ec066, 0x36c76583, 0x1c457d79, 0x2a376b58, 0x2e257dd8, 0xc5ec}}, - {{0x05005024, 0x14fcdd1a, 0x230bee5b, 0x3ad97b97, 0x1233ec8b, 0x290163fe, 0x081f374e, 0x0946065e, 0x2225}}} + {{{0x14a63f3b, 0x1a823f6f, 0x1e3e5c9e, 0x00760332, 0x0c765832, 0x08afaf3b, 0x0ddad61c, 0x12beec54, 0xc5ecb8}}, + {{0x05005024, 0x09f9ba34, 0x0c2fb96d, 0x16cbdcbc, 0x033ec8be, 0x002c7fc9, 0x07cdd3a9, 0x03032f10, 0x222525}}} }, { /* 1*16^52*G: */ - {{{0x3180eef9, 0x35daa1e4, 0x228b9776, 0x00048826, 0x207b128d, 0x2b3aec6a, 0x2e5f07e3, 0x303d8748, 0xfa50}}, - {{0x3f4f2811, 0x233635f4, 0x17a213b3, 0x1a0ca4e9, 0x01a68a5e, 0x334a1c8a, 0x3eba9b72, 0x31a488e5, 0x6b84}}}, + {{{0x1180eef9, 0x0bb543c9, 0x0a2e5ddb, 0x00244134, 0x07b128d0, 0x075d8d50, 0x17c1f8eb, 0x1ec3a45c, 0xfa50c0}}, + {{0x1f4f2811, 0x066c6be9, 0x1e884ece, 0x1065274a, 0x1a68a5e6, 0x09439140, 0x0ea6dcb3, 0x124472fd, 0x6b84c6}}}, /* 3*16^52*G: */ - {{{0x11da5e12, 0x07b838ce, 0x1cacb297, 0x31829005, 0x1ca2b6a9, 0x0ca7e4e8, 0x1e31bcda, 0x0b8f10de, 0xf750}}, - {{0x0385f4eb, 0x292e717a, 0x325cebc7, 0x21b4cbbd, 0x1672047b, 0x1c25170f, 0x0fafd599, 0x3d7b759f, 0x3c57}}}, + {{{0x11da5e12, 0x0f70719c, 0x12b2ca5c, 0x0c14802b, 0x0a2b6a9c, 0x14fc9d0e, 0x0c6f368c, 0x07886f3c, 0xf7502e}}, + {{0x0385f4eb, 0x125ce2f4, 0x0973af1e, 0x0da65dee, 0x072047b8, 0x04a2e1eb, 0x0bf5665c, 0x1dbacf9f, 0x3c57f5}}}, /* 5*16^52*G: */ - {{{0x10b7d105, 0x01d24cc4, 0x0e57c9f2, 0x329712e5, 0x3455b3f4, 0x13d98938, 0x25862a3a, 0x1e3e60eb, 0x12fe}}, - {{0x1f794a60, 0x162b1bee, 0x2ee90b84, 0x3b389975, 0x27cb771d, 0x2d6a8666, 0x2bcf7786, 0x3c68ce35, 0x2062}}}, + {{{0x10b7d105, 0x03a49988, 0x195f27c8, 0x14b89729, 0x055b3f4c, 0x1b31271a, 0x018a8e93, 0x1f3075cb, 0x12fe78}}, + {{0x1f794a60, 0x0c5637dc, 0x1ba42e11, 0x19c4cbad, 0x1cb771de, 0x0d50ccd3, 0x13dde1ad, 0x14671ad7, 0x2062f1}}}, /* 7*16^52*G: */ - {{{0x1e0c5d05, 0x188760ce, 0x2572daff, 0x039b142a, 0x084b1a48, 0x12ec40a0, 0x3473d58c, 0x30c4d1f7, 0x76aa}}, - {{0x11ece63e, 0x159866dd, 0x15e6ee35, 0x048973c0, 0x02625f4b, 0x3ccb20c8, 0x070efabe, 0x1dbbc357, 0xef55}}}, + {{{0x1e0c5d05, 0x110ec19c, 0x15cb6bfd, 0x1cd8a154, 0x04b1a480, 0x1d881404, 0x1cf56312, 0x0268fbe8, 0x76aac3}}, + {{0x11ece63e, 0x0b30cdba, 0x179bb8d5, 0x044b9e02, 0x0625f4b1, 0x19641901, 0x03beafbc, 0x1de1ab8e, 0xef5576}}}, /* 9*16^52*G: */ - {{{0x3c53c086, 0x389bd217, 0x09a1aec9, 0x2d570d27, 0x288104c6, 0x1830c517, 0x05ccc87e, 0x3f96ef97, 0xa663}}, - {{0x25016201, 0x1a7140ca, 0x3994fc0e, 0x07b3295c, 0x023dc399, 0x2c40b226, 0x11fbf5d1, 0x265fdac8, 0xb541}}}, + {{{0x1c53c086, 0x1137a42f, 0x0686bb27, 0x0ab86939, 0x08104c6b, 0x0618a2f4, 0x13321f98, 0x0b77cb8b, 0xa663fe}}, + {{0x05016201, 0x14e28195, 0x0653f039, 0x1d994ae7, 0x03dc3991, 0x081644c1, 0x1efd746c, 0x0fed6423, 0xb54199}}}, /* 11*16^52*G: */ - {{{0x0b758574, 0x2b6007b5, 0x34f9c6e9, 0x0c99a250, 0x22bdf3d8, 0x328409eb, 0x2cd825b7, 0x149e8081, 0xde95}}, - {{0x3b67232a, 0x2df7c7f3, 0x15a2deb4, 0x39a84145, 0x169ed7ba, 0x077211fc, 0x3d14e4e2, 0x3815ab24, 0x4cd3}}}, + {{{0x0b758574, 0x16c00f6a, 0x13e71ba6, 0x04cd1286, 0x0bdf3d83, 0x10813d71, 0x16096df2, 0x0f4040d9, 0xde9552}}, + {{0x1b67232a, 0x1bef8fe7, 0x168b7ad2, 0x0d420a2a, 0x09ed7bae, 0x0e423f8b, 0x05393887, 0x0ad5927a, 0x4cd3e0}}}, /* 13*16^52*G: */ - {{{0x3d85474f, 0x1de6e2af, 0x1634668d, 0x13128ae2, 0x385aea89, 0x3732f911, 0x32addbfe, 0x2f3819b4, 0x8da6}}, - {{0x3d7b4ef7, 0x3f7e71f4, 0x1dbdd7a5, 0x073164c1, 0x1dfff10b, 0x377d741c, 0x2d4ff84f, 0x1b1abcc7, 0x13fc}}}, + {{{0x1d85474f, 0x1bcdc55f, 0x18d19a35, 0x18945712, 0x05aea894, 0x065f223c, 0x0b76ffb7, 0x1c0cda65, 0x8da6bc}}, + {{0x1d7b4ef7, 0x1efce3e9, 0x16f75e97, 0x198b260b, 0x1fff10b1, 0x0fae838e, 0x13fe13f7, 0x0d5e63da, 0x13fc6c}}}, /* 15*16^52*G: */ - {{{0x3dd042ea, 0x2d750959, 0x18eafd06, 0x3e89a991, 0x3c93beeb, 0x3599278c, 0x3ba39b1b, 0x2b31f3ec, 0x7329}}, - {{0x2f5c94a1, 0x36a33fb0, 0x1fab4f0a, 0x1225dcc7, 0x2b68ee18, 0x2139e53e, 0x36f14892, 0x124d506d, 0x9272}}} + {{{0x1dd042ea, 0x1aea12b3, 0x03abf41a, 0x144d4c8b, 0x093beebf, 0x1324f19e, 0x08e6c6f5, 0x18f9f677, 0x7329ac}}, + {{0x0f5c94a1, 0x0d467f61, 0x1ead3c2b, 0x112ee63b, 0x168ee184, 0x073ca7d5, 0x1c5224a1, 0x06a836ed, 0x927249}}} }, { /* 1*16^53*G: */ - {{{0x1f067ec2, 0x394f4cad, 0x1bba5220, 0x0a22ad75, 0x08e8421a, 0x16fdadf6, 0x21a11b1a, 0x1874329c, 0xda1d}}, - {{0x1ad836f1, 0x157ee83c, 0x279b48a6, 0x29ce2674, 0x091e2966, 0x01d98587, 0x1306c79c, 0x3d569f26, 0x8157}}}, + {{{0x1f067ec2, 0x129e995a, 0x0ee94883, 0x11156bab, 0x0e8421a2, 0x1fb5bec4, 0x0846c696, 0x1a194e43, 0xda1d61}}, + {{0x1ad836f1, 0x0afdd078, 0x1e6d2299, 0x0e7133a4, 0x11e2966a, 0x1b30b0e4, 0x01b1e701, 0x0b4f9326, 0x8157f5}}}, /* 3*16^53*G: */ - {{{0x3a95a8db, 0x1761dccb, 0x39d36f61, 0x0fb03111, 0x1b1723b8, 0x25991a64, 0x3dd0419e, 0x036918c0, 0xe3e9}}, - {{0x1b0d1cf9, 0x005b3dfc, 0x0984d3d1, 0x2c7be5f3, 0x02e76afb, 0x3eaa431c, 0x0178bb00, 0x0ef0015b, 0xfbe5}}}, + {{{0x1a95a8db, 0x0ec3b997, 0x074dbd85, 0x1d81888f, 0x11723b83, 0x13234c8d, 0x141067a5, 0x148c607b, 0xe3e90d}}, + {{0x1b0d1cf9, 0x00b67bf8, 0x06134f44, 0x03df2f99, 0x0e76afbb, 0x15486381, 0x1e2ec03e, 0x1800ad82, 0xfbe53b}}}, /* 5*16^53*G: */ - {{{0x112ee214, 0x1eabf590, 0x19315401, 0x0a93a5e5, 0x00c01c78, 0x19437f57, 0x3d775a8b, 0x3fb1ccb8, 0x9f4f}}, - {{0x1085f37a, 0x3bd10889, 0x3c880283, 0x066da4c2, 0x35c69d97, 0x259a0bf5, 0x22f2e60e, 0x38b84c63, 0x639c}}}, + {{{0x112ee214, 0x1d57eb20, 0x04c55005, 0x149d2f2b, 0x0c01c782, 0x086feae0, 0x1dd6a2d9, 0x18e65c7a, 0x9f4ffe}}, + {{0x1085f37a, 0x17a21112, 0x12200a0f, 0x136d2617, 0x1c69d971, 0x13417eba, 0x1cb983a5, 0x1c2631c5, 0x639ce2}}}, /* 7*16^53*G: */ - {{{0x1f61a0a5, 0x22da0514, 0x3c14e3ef, 0x0494f86c, 0x040b2c4b, 0x0682907d, 0x34ac1b17, 0x188b5044, 0x431f}}, - {{0x38cef899, 0x1adedff9, 0x15657724, 0x2eaa810d, 0x23aa7241, 0x3799465c, 0x2438f6d6, 0x0c9ff9ea, 0xa298}}}, + {{{0x1f61a0a5, 0x05b40a28, 0x10538fbe, 0x04a7c367, 0x00b2c4b1, 0x10520fa2, 0x0b06c5c6, 0x05a82269, 0x431f62}}, + {{0x18cef899, 0x15bdbff3, 0x1595dc91, 0x1554086a, 0x1aa7241b, 0x1328cb91, 0x0e3db5b7, 0x0ffcf548, 0xa29832}}}, /* 9*16^53*G: */ - {{{0x27748503, 0x2b099f55, 0x31328e7c, 0x1b8391dc, 0x0a12ac0e, 0x18bbce7e, 0x38fb86cb, 0x2eb77b39, 0x993d}}, - {{0x3eb0cee2, 0x2e9cd84d, 0x38adaa49, 0x3e1efda6, 0x21f51a17, 0x3de11e1e, 0x1eeeb785, 0x2a7ba15a, 0xa521}}}, + {{{0x07748503, 0x16133eab, 0x04ca39f2, 0x1c1c8ee6, 0x012ac0e6, 0x1779cfc5, 0x1ee1b2d8, 0x1bbd9cf1, 0x993dba}}, + {{0x1eb0cee2, 0x1d39b09b, 0x02b6a926, 0x10f7ed37, 0x1f51a17f, 0x1c23c3d0, 0x1bade17d, 0x1dd0ad3d, 0xa521a9}}}, /* 11*16^53*G: */ - {{{0x26d23d80, 0x37a889d6, 0x2474d478, 0x02f447c9, 0x0962c0e1, 0x250c72e4, 0x15ea5a33, 0x1eae81ab, 0x75f1}}, - {{0x280dd57e, 0x21aa16c0, 0x34ea5909, 0x0bfefb6e, 0x1b629237, 0x31f42fc6, 0x39a80c7f, 0x18bf8558, 0xa07a}}}, + {{{0x06d23d80, 0x0f5113ad, 0x11d351e3, 0x17a23e4c, 0x162c0e10, 0x018e5c84, 0x1a968ce5, 0x1740d5ab, 0x75f17a}}, + {{0x080dd57e, 0x03542d81, 0x13a96426, 0x1ff7db76, 0x16292372, 0x1e85f8cd, 0x0a031ff1, 0x1fc2ac73, 0xa07a62}}}, /* 13*16^53*G: */ - {{{0x21ad3413, 0x38ae6db5, 0x327d684a, 0x2e700100, 0x387b7a8d, 0x257d2172, 0x1f4a0a6e, 0x15578476, 0x6678}}, - {{0x3ebca672, 0x09204081, 0x2dc66601, 0x338b454e, 0x0bdf9ea6, 0x099b649f, 0x0f646925, 0x368f789e, 0x510d}}}, + {{{0x01ad3413, 0x115cdb6b, 0x09f5a12b, 0x13800806, 0x07b7a8db, 0x0fa42e5c, 0x12829ba5, 0x0bc23b3e, 0x667855}}, + {{0x1ebca672, 0x12408103, 0x17199804, 0x1c5a2a75, 0x1df9ea6c, 0x136c93e5, 0x191a4949, 0x07bc4f1e, 0x510dda}}}, /* 15*16^53*G: */ - {{{0x06cc8563, 0x3002bd6c, 0x3e101eaa, 0x0937d6ff, 0x16368892, 0x320af606, 0x27748ada, 0x128d8b36, 0xebdc}}, - {{0x2394ccfa, 0x26c5ef3a, 0x1204f924, 0x3101e492, 0x1d4f07be, 0x3b8d79b3, 0x2d35f9b1, 0x0c513a15, 0x659a}}} + {{{0x06cc8563, 0x00057ad8, 0x18407aab, 0x09beb7ff, 0x03688922, 0x015ec0cb, 0x1d22b6b2, 0x06c59b4e, 0xebdc4a}}, + {{0x0394ccfa, 0x0d8bde75, 0x0813e492, 0x080f2492, 0x14f07bec, 0x11af366e, 0x0d7e6c7b, 0x089d0ada, 0x659a31}}} }, { /* 1*16^54*G: */ - {{{0x0d064e13, 0x29cec184, 0x06f1e062, 0x0c477811, 0x3d416615, 0x17fe63a3, 0x30690721, 0x20bfc325, 0xa8e2}}, - {{0x11f4cc0c, 0x3bdf1cc4, 0x0dd6bd6c, 0x19e68f94, 0x2515888b, 0x2dfcf16c, 0x01c09abf, 0x0d56e36e, 0x7f97}}}, + {{{0x0d064e13, 0x139d8308, 0x1bc7818a, 0x023bc088, 0x14166153, 0x1fcc747e, 0x1a41c857, 0x1fe192e0, 0xa8e282}}, + {{0x11f4cc0c, 0x17be3988, 0x175af5b3, 0x0f347ca1, 0x115888b6, 0x1f9e2d92, 0x1026afed, 0x0b71b703, 0x7f9735}}}, /* 3*16^54*G: */ - {{{0x3a3979b5, 0x0a8666c2, 0x27e829e2, 0x0a23e379, 0x240e50ba, 0x0dfc2c7b, 0x1e26327f, 0x01f1736b, 0xae22}}, - {{0x0450fa6f, 0x23cf359a, 0x3d4f8896, 0x2a1edf4d, 0x2d7060fc, 0x3249148e, 0x39f71ad4, 0x3f944301, 0xea91}}}, + {{{0x1a3979b5, 0x150ccd85, 0x1fa0a788, 0x111f1bcc, 0x00e50ba2, 0x1f858f72, 0x098c9fcd, 0x18b9b5bc, 0xae2207}}, + {{0x0450fa6f, 0x079e6b34, 0x153e225a, 0x10f6fa6f, 0x17060fca, 0x092291d6, 0x1dc6b532, 0x0a2180f3, 0xea91fe}}}, /* 5*16^54*G: */ - {{{0x0efca824, 0x10406440, 0x22164fae, 0x2f8313fa, 0x185461e0, 0x31504019, 0x2ace59ce, 0x3b432b5c, 0xcb8d}}, - {{0x0f227361, 0x0502f416, 0x3931742f, 0x2b47f7f1, 0x2ccbc496, 0x05b121e8, 0x188c85b3, 0x0023dd03, 0x33a5}}}, + {{{0x0efca824, 0x0080c880, 0x08593eb9, 0x1c189fd4, 0x05461e0b, 0x0a08032c, 0x139673b1, 0x0195ae55, 0xcb8ded}}, + {{0x0f227361, 0x0a05e82c, 0x04c5d0bc, 0x1a3fbf8f, 0x0cbc496a, 0x16243d16, 0x03216cc5, 0x11ee81b1, 0x33a500}}}, /* 7*16^54*G: */ - {{{0x3bcbd327, 0x1046d368, 0x1e4aaee9, 0x13821488, 0x276ed6b0, 0x2524035f, 0x1836708e, 0x0eca62bc, 0xb0c5}}, - {{0x2d7be436, 0x185af128, 0x0636a0f1, 0x0a88831d, 0x26b2afd8, 0x3da9806d, 0x17ea1638, 0x25d007ef, 0xee2a}}}, + {{{0x1bcbd327, 0x008da6d1, 0x192abba5, 0x1c10a443, 0x16ed6b04, 0x04806bf3, 0x0d9c23a5, 0x05315e30, 0xb0c53b}}, + {{0x0d7be436, 0x10b5e251, 0x18da83c5, 0x144418e8, 0x0b2afd82, 0x15300db3, 0x1a858e3d, 0x0803f7af, 0xee2a97}}}, /* 9*16^54*G: */ - {{{0x17b836a1, 0x39bbed8e, 0x3679ef7d, 0x019017fd, 0x37f526c8, 0x2218bb39, 0x1b920d4d, 0x29cfcca7, 0x6f6b}}, - {{0x06832b84, 0x36f7cbec, 0x0e1ff934, 0x264314a2, 0x3ee9c0d8, 0x02e29016, 0x3c18e3db, 0x2285ffd7, 0xdc77}}}, + {{{0x17b836a1, 0x1377db1c, 0x19e7bdf7, 0x0c80bfee, 0x1f526c80, 0x0317673b, 0x04835362, 0x07e653b7, 0x6f6ba7}}, + {{0x06832b84, 0x0def97d8, 0x187fe4d3, 0x1218a511, 0x0e9c0d89, 0x1c5202df, 0x0638f6c2, 0x02ffebf8, 0xdc778a}}}, /* 11*16^54*G: */ - {{{0x1eb39ede, 0x2bb8d082, 0x30612d42, 0x02200cb5, 0x02436031, 0x3fd19f84, 0x22af4bbc, 0x069f71d0, 0x7d47}}, - {{0x2bf6607e, 0x326f3652, 0x022a8fd0, 0x2573df47, 0x3c86fa77, 0x2088c7bf, 0x2856507b, 0x1ec67ce9, 0x004a}}}, + {{{0x1eb39ede, 0x1771a104, 0x0184b50a, 0x110065ae, 0x04360310, 0x1a33f081, 0x0bd2ef3f, 0x0fb8e845, 0x7d471a}}, + {{0x0bf6607e, 0x04de6ca5, 0x08aa3f43, 0x0b9efa38, 0x086fa779, 0x1118f7fe, 0x15941ee0, 0x033e74d0, 0x4a7b}}}, /* 13*16^54*G: */ - {{{0x165eb1c1, 0x15b52789, 0x1ae5c5aa, 0x335d59f3, 0x02f0967f, 0x03f30c66, 0x33fac707, 0x1458fe6d, 0xf002}}, - {{0x2dde2ae0, 0x369f5c11, 0x2cd11e57, 0x1dbfd735, 0x26afed85, 0x1ad29768, 0x120df4c6, 0x2a7a220f, 0x054e}}}, + {{{0x165eb1c1, 0x0b6a4f12, 0x0b9716a9, 0x1aeacf9b, 0x0f0967fc, 0x1e618cc1, 0x1eb1c1c3, 0x0c7f36e7, 0xf00251}}, + {{0x0dde2ae0, 0x0d3eb823, 0x1344795f, 0x0dfeb9ad, 0x0afed857, 0x1a52ed13, 0x037d319a, 0x1d1107a4, 0x54ea9}}}, /* 15*16^54*G: */ - {{{0x1ac32c64, 0x33cd424f, 0x0ae4bf84, 0x0dbf80fb, 0x07715e0e, 0x013a543d, 0x123aa0f7, 0x0500007b, 0xac12}}, - {{0x1eb1a867, 0x204ab6eb, 0x253f0898, 0x16974e96, 0x0499a3ed, 0x02da55cc, 0x38baf187, 0x2f32eb0c, 0xce8e}}} + {{{0x1ac32c64, 0x079a849e, 0x0b92fe13, 0x0dfc07d9, 0x1715e0e3, 0x074a87a3, 0x0ea83dc1, 0x00003da4, 0xac1214}}, + {{0x1eb1a867, 0x00956dd6, 0x14fc2262, 0x14ba74b4, 0x099a3ed5, 0x1b4ab982, 0x0ebc61c2, 0x19758671, 0xce8ebc}}} }, { /* 1*16^55*G: */ - {{{0x0319497c, 0x0bce0b7a, 0x12508c02, 0x166c7e94, 0x13cab15d, 0x2795b9a4, 0x285872d3, 0x14ee7268, 0x174a}}, - {{0x079afa73, 0x0f684eb0, 0x0b985438, 0x1ace8763, 0x07f9e664, 0x10557cb1, 0x09c1657b, 0x370deaff, 0xccc9}}}, + {{{0x0319497c, 0x179c16f4, 0x09423008, 0x1363f4a2, 0x1cab15d5, 0x12b73489, 0x161cb4e7, 0x17393450, 0x174a53}}, + {{0x079afa73, 0x1ed09d60, 0x0e6150e0, 0x16743b19, 0x1f9e6646, 0x0aaf9623, 0x10595ed0, 0x06f57f93, 0xccc9dc}}}, /* 3*16^55*G: */ - {{{0x354b8367, 0x25201cf5, 0x3d506bfe, 0x1d6ddf59, 0x036a5db7, 0x2a975161, 0x2526e40c, 0x0252b911, 0x5e5a}}, - {{0x11ce85ca, 0x14ca6a76, 0x1e5ffa44, 0x1aaa7bcf, 0x2a4b7a79, 0x2407c55c, 0x15e05c2c, 0x3e32691e, 0xae8a}}}, + {{{0x154b8367, 0x0a4039eb, 0x1541affa, 0x0b6efacf, 0x16a5db77, 0x12ea2c21, 0x09b9032a, 0x095c88ca, 0x5e5a09}}, + {{0x11ce85ca, 0x0994d4ec, 0x197fe911, 0x1553de7b, 0x04b7a796, 0x00f8ab95, 0x18170b24, 0x19348f2b, 0xae8af8}}}, /* 5*16^55*G: */ - {{{0x17b10d9d, 0x06615e4e, 0x11f8fcaf, 0x294bc627, 0x0cb82de6, 0x332e0cc4, 0x02e859de, 0x382b6e5c, 0x00d4}}, - {{0x3140dced, 0x20840121, 0x0e2d923e, 0x1626325e, 0x2287f70b, 0x0be1190c, 0x3640947d, 0x0066060d, 0x87b8}}}, + {{{0x17b10d9d, 0x0cc2bc9c, 0x07e3f2bc, 0x0a5e313a, 0x0b82de6a, 0x05c19886, 0x1a1677b3, 0x15b72e05, 0xd4e0}}, + {{0x1140dced, 0x01080243, 0x18b648fa, 0x113192f1, 0x087f70b5, 0x1c232191, 0x10251f4b, 0x130306ec, 0x87b801}}}, /* 7*16^55*G: */ - {{{0x1c9caee8, 0x02046982, 0x1a270bb2, 0x0b88116c, 0x04a66763, 0x1e866bbb, 0x374c0f6f, 0x1484da3b, 0x0366}}, - {{0x3772b711, 0x2a7b1a8e, 0x295ba7f0, 0x32ea624c, 0x26944501, 0x27f1a06e, 0x3ded9994, 0x30cacaa4, 0x1f18}}}, + {{{0x1c9caee8, 0x0408d304, 0x089c2ec8, 0x1c408b63, 0x0a667632, 0x10cd7762, 0x1303dbde, 0x026d1dee, 0x36652}}, + {{0x1772b711, 0x14f6351d, 0x056e9fc2, 0x17531265, 0x0944501c, 0x1e340dd3, 0x1b666527, 0x0565527b, 0x1f18c3}}}, /* 9*16^55*G: */ - {{{0x1446c85c, 0x0ffe5d46, 0x201c0635, 0x0df78239, 0x36c6eade, 0x19db114f, 0x38f1faa0, 0x24415bf6, 0x0e58}}, - {{0x2148972e, 0x3db1df9c, 0x0cddadd5, 0x2408d3a0, 0x081898f4, 0x1d062ebd, 0x27bda0ec, 0x1217c47e, 0xe39a}}}, + {{{0x1446c85c, 0x1ffcba8c, 0x007018d4, 0x0fbc11cc, 0x0c6eade3, 0x1b6229fb, 0x1c7ea819, 0x00adfb71, 0xe5891}}, + {{0x0148972e, 0x1b63bf39, 0x1376b757, 0x00469d01, 0x01898f49, 0x00c5d7a4, 0x0f683b1d, 0x0be23f4f, 0xe39a48}}}, /* 11*16^55*G: */ - {{{0x022e1259, 0x3c62b7cf, 0x281362af, 0x05ce6901, 0x07777193, 0x33d7ea80, 0x1463f2b6, 0x049b49bc, 0xa740}}, - {{0x334a5f43, 0x3ddc5c90, 0x31d6dad5, 0x21979d4e, 0x3c7ee517, 0x17c5d299, 0x0f1ff1b0, 0x3feebc65, 0x05a9}}}, + {{{0x022e1259, 0x18c56f9e, 0x004d8abf, 0x0e73480d, 0x17771931, 0x1afd5003, 0x18fcadb3, 0x0da4de28, 0xa74012}}, + {{0x134a5f43, 0x1bb8b921, 0x075b6b57, 0x0cbcea76, 0x07ee5178, 0x18ba533e, 0x07fc6c17, 0x175e329e, 0x5a9ff}}}, /* 13*16^55*G: */ - {{{0x0b08f1fe, 0x22285e8f, 0x3a087bfd, 0x339fb9c2, 0x02d177d7, 0x1015d976, 0x074e4a65, 0x2e085b65, 0x87e4}}, - {{0x2ed5e2ec, 0x17dd2b26, 0x2786d9d7, 0x0bc8f6f5, 0x38c2cc6e, 0x35fe3a8b, 0x348cecd7, 0x0eb01d98, 0xf74e}}}, + {{{0x0b08f1fe, 0x0450bd1e, 0x0821eff6, 0x1cfdce17, 0x0d177d7c, 0x02bb2ec1, 0x13929950, 0x042db28e, 0x87e4b8}}, + {{0x0ed5e2ec, 0x0fba564d, 0x1e1b675d, 0x1e47b7ac, 0x0c2cc6e2, 0x1fc7517c, 0x033b35f5, 0x180ecc69, 0xf74e3a}}}, /* 15*16^55*G: */ - {{{0x21c4d15c, 0x2a1c039a, 0x3c0e74b9, 0x17a9efc1, 0x254a4410, 0x308b0304, 0x279a5a92, 0x06d18ffa, 0x35ea}}, - {{0x3f3fe1ea, 0x324e6ebd, 0x065095ed, 0x18cea80c, 0x0d3b185d, 0x23e97f5d, 0x2d2cd788, 0x245946e7, 0xad21}}} + {{{0x01c4d15c, 0x14380735, 0x1039d2e6, 0x1d4f7e0f, 0x14a44105, 0x11606092, 0x0696a4b0, 0x08c7fd4f, 0x35ea1b}}, + {{0x1f3fe1ea, 0x049cdd7b, 0x194257b7, 0x06754060, 0x13b185d6, 0x1d2feba6, 0x0b35e223, 0x0ca373da, 0xad2191}}} }, { /* 1*16^56*G: */ - {{{0x1475b7ba, 0x213f7fc2, 0x0918b3d8, 0x0e79cc39, 0x018cdbe0, 0x395fb7d4, 0x3785c3d3, 0x25a60650, 0x9593}}, - {{0x3524f2fd, 0x26e2afe1, 0x0709385e, 0x194fd932, 0x1cd6849c, 0x00e1a92e, 0x331dd8ba, 0x154a2230, 0x2e7e}}}, + {{{0x1475b7ba, 0x027eff84, 0x0462cf62, 0x13ce61c9, 0x18cdbe03, 0x0bf6fa80, 0x0170f4f9, 0x1303286f, 0x959396}}, + {{0x1524f2fd, 0x0dc55fc3, 0x1c24e17a, 0x0a7ec990, 0x0d6849c6, 0x1c3525ce, 0x07762e80, 0x05111866, 0x2e7e55}}}, /* 3*16^56*G: */ - {{{0x0fd69985, 0x02717764, 0x1df72aea, 0x0c2732db, 0x0ccf149f, 0x3da437ef, 0x32f7e788, 0x1d9d73ad, 0x0ae9}}, - {{0x1409a003, 0x2723ad04, 0x2ee1aff8, 0x2e67505e, 0x1a54c5d0, 0x237fb814, 0x08d14e9b, 0x265cfdb9, 0x9121}}}, + {{{0x0fd69985, 0x04e2eec8, 0x17dcaba8, 0x013996db, 0x0cf149f3, 0x1486fde6, 0x1df9e23d, 0x0eb9d6e5, 0xae976}}, + {{0x1409a003, 0x0e475a08, 0x1b86bfe2, 0x133a82f5, 0x054c5d0b, 0x0ff7028d, 0x1453a6e3, 0x0e7edc91, 0x912199}}}, /* 5*16^56*G: */ - {{{0x19262b90, 0x37064f7f, 0x23cc29a9, 0x08f1307f, 0x025d1fb7, 0x197c5de0, 0x1612ec9b, 0x218a96b0, 0x2b15}}, - {{0x083d7557, 0x24665b99, 0x19489a49, 0x14d25c3e, 0x0749066f, 0x0c354b6a, 0x233faa7a, 0x014f6a82, 0x2eb0}}}, + {{{0x19262b90, 0x0e0c9efe, 0x0f30a6a7, 0x078983fc, 0x05d1fb72, 0x0f8bbc01, 0x04bb26d9, 0x054b582c, 0x2b1586}}, + {{0x083d7557, 0x08ccb732, 0x05226926, 0x0692e1f3, 0x149066f5, 0x06a96d43, 0x0fea9e8c, 0x07b54146, 0x2eb005}}}, /* 7*16^56*G: */ - {{{0x28e7be40, 0x0fe5c532, 0x1040ee59, 0x34b22524, 0x24769af2, 0x2570585b, 0x2ee677ee, 0x3abb46a5, 0x6af9}}, - {{0x2e387e1c, 0x2905b809, 0x0f59569f, 0x38fd99a8, 0x07dc8145, 0x27a90a0d, 0x06649670, 0x0a845a40, 0xb381}}}, + {{{0x08e7be40, 0x1fcb8a65, 0x0103b964, 0x05912922, 0x0769af2d, 0x0e0b0b72, 0x199dfba5, 0x1da352dd, 0x6af9ea}}, + {{0x0e387e1c, 0x120b7013, 0x1d655a7e, 0x07eccd41, 0x1dc8145e, 0x152141a3, 0x19259c27, 0x022d200c, 0xb3812a}}}, /* 9*16^56*G: */ - {{{0x3482801e, 0x09adbe83, 0x1bd4155d, 0x1e53e2f1, 0x38d6f940, 0x2aad0932, 0x0144eeb3, 0x1a3b8111, 0x5966}}, - {{0x04870c37, 0x11dc523c, 0x3d3535ad, 0x2db072d8, 0x31304e8d, 0x23e5821d, 0x2ef5f1ec, 0x282a16ee, 0x949a}}}, + {{{0x1482801e, 0x135b7d07, 0x0f505574, 0x129f178b, 0x0d6f9407, 0x15a1265c, 0x113bacea, 0x1dc08882, 0x596668}}, + {{0x04870c37, 0x03b8a478, 0x14d4d6b5, 0x0d8396c7, 0x1304e8db, 0x1cb043b8, 0x1d7c7b23, 0x150b775d, 0x949aa0}}}, /* 11*16^56*G: */ - {{{0x032c19fd, 0x1326cb9f, 0x18028c3e, 0x32ae3a41, 0x170b5b4a, 0x3d345ead, 0x050762fd, 0x346206d4, 0xbe84}}, - {{0x32f1281f, 0x1da5294d, 0x250dc376, 0x1569fd57, 0x08399479, 0x3997d20c, 0x050944d1, 0x1832ccb7, 0xeff9}}}, + {{{0x032c19fd, 0x064d973e, 0x000a30f9, 0x1571d20b, 0x10b5b4ac, 0x068bd5ab, 0x01d8bf7d, 0x11036a0a, 0xbe84d1}}, + {{0x12f1281f, 0x1b4a529b, 0x14370dd9, 0x0b4feabc, 0x03994795, 0x12fa4184, 0x02513479, 0x19665b8a, 0xeff960}}}, /* 13*16^56*G: */ - {{{0x16c69482, 0x346dd7f5, 0x32fa167b, 0x3aad5004, 0x32bc88cb, 0x15c9d32b, 0x17ee541f, 0x280c5303, 0x9867}}, - {{0x2f792cd7, 0x1bc18451, 0x15628a91, 0x189173d4, 0x3a99639e, 0x24b556c6, 0x0834f9c7, 0x18568ec4, 0xd02e}}}, + {{{0x16c69482, 0x08dbafea, 0x0be859ef, 0x156a8026, 0x0bc88cbe, 0x193a6579, 0x1b9507d5, 0x062981af, 0x9867a0}}, + {{0x0f792cd7, 0x178308a3, 0x158a2a45, 0x048b9ea2, 0x099639e6, 0x16aad8dd, 0x0d3e71e4, 0x0b476210, 0xd02e61}}}, /* 15*16^56*G: */ - {{{0x1d557aa1, 0x2288e764, 0x101fc297, 0x0764bfb3, 0x19d6abdf, 0x1fcba802, 0x0815a592, 0x3c915036, 0xa866}}, - {{0x01430634, 0x2606eed3, 0x0611a4b7, 0x3ada719f, 0x30e13961, 0x0f63e976, 0x22b44d79, 0x0e7daa00, 0xb587}}} + {{{0x1d557aa1, 0x0511cec8, 0x007f0a5e, 0x1b25fd9a, 0x1d6abdf1, 0x1975004c, 0x0569649f, 0x08a81b10, 0xa866f2}}, + {{0x01430634, 0x0c0ddda6, 0x184692de, 0x16d38cf8, 0x0e13961e, 0x0c7d2ed8, 0x0d135e4f, 0x1ed50045, 0xb58739}}} }, { /* 1*16^57*G: */ - {{{0x1d82b151, 0x2d44d032, 0x21fba2db, 0x28290f55, 0x109a8fcc, 0x168454ec, 0x01e56d64, 0x0e942b90, 0xd2a6}}, - {{0x1cf89405, 0x105085d3, 0x084ca52d, 0x03dd42bd, 0x148220a7, 0x2bb962ca, 0x3fcb7565, 0x21bed910, 0xe82d}}}, + {{{0x1d82b151, 0x1a89a064, 0x07ee8b6e, 0x01487aac, 0x09a8fcca, 0x108a9d88, 0x195b5916, 0x0a15c803, 0xd2a63a}}, + {{0x1cf89405, 0x00a10ba6, 0x013294b5, 0x1eea15e9, 0x08220a70, 0x172c594a, 0x12dd596b, 0x1f6c887f, 0xe82d86}}}, /* 3*16^57*G: */ - {{{0x2e4b3ba0, 0x2167d8d7, 0x18bf1f17, 0x0aafbd7c, 0x3f245f5c, 0x385c3cc6, 0x3fb73bef, 0x04414887, 0x4108}}, - {{0x17525595, 0x21a58770, 0x1a064554, 0x0d926159, 0x2b849813, 0x2996b875, 0x35668f2c, 0x3cda5dbf, 0xdc37}}}, + {{{0x0e4b3ba0, 0x02cfb1af, 0x02fc7c5e, 0x157debe3, 0x1245f5c2, 0x0b8798df, 0x0dcefbf8, 0x00a443ff, 0x410811}}, + {{0x17525595, 0x034b0ee0, 0x08191552, 0x0c930acb, 0x18498133, 0x12d70eb5, 0x19a3cb29, 0x0d2edfea, 0xdc37f3}}}, /* 5*16^57*G: */ - {{{0x13d98ded, 0x18a726e2, 0x38a02184, 0x37c8a0ce, 0x31d65edb, 0x3c8a6414, 0x0c0c8c8c, 0x2884285b, 0x63a2}}, - {{0x20d1cfc2, 0x06465f53, 0x1c7873a5, 0x2afda802, 0x2d94461f, 0x140cc953, 0x2c76fd06, 0x10b8b9ff, 0x882b}}}, + {{{0x13d98ded, 0x114e4dc4, 0x02808611, 0x1e450677, 0x1d65edbd, 0x114c8298, 0x0323233c, 0x02142d98, 0x63a2a2}}, + {{0x00d1cfc2, 0x0c8cbea7, 0x11e1ce94, 0x17ed4013, 0x194461fa, 0x01992a76, 0x1dbf4194, 0x1c5cffd8, 0x882b42}}}, /* 7*16^57*G: */ - {{{0x38045445, 0x2a186942, 0x01e8d7ee, 0x3fdcdc64, 0x17bef080, 0x04b8b975, 0x167ca3df, 0x20575127, 0x0c15}}, - {{0x0054a206, 0x053e1f55, 0x258cea32, 0x0c15390d, 0x23cd28ba, 0x24f0ed99, 0x14115d0a, 0x35828eba, 0x2f30}}}, + {{{0x18045445, 0x1430d285, 0x07a35fba, 0x1ee6e320, 0x1bef080f, 0x17172eab, 0x1f28f7c4, 0x0ba893ac, 0xc1581}}, + {{0x0054a206, 0x0a7c3eaa, 0x1633a8c8, 0x00a9c86c, 0x1cd28ba3, 0x1e1db331, 0x045742a4, 0x01475d28, 0x2f30d6}}}, /* 9*16^57*G: */ - {{{0x03857faf, 0x3a448e73, 0x29619701, 0x0bf2b787, 0x28ef7f88, 0x1eea3d20, 0x28a9c0d5, 0x3adae26b, 0xc757}}, - {{0x20584ca4, 0x07676c32, 0x01894c10, 0x1f4c4344, 0x3ec61b62, 0x0da7c822, 0x3ff36257, 0x1673f348, 0xf03a}}}, + {{{0x03857faf, 0x14891ce6, 0x05865c07, 0x1f95bc3d, 0x0ef7f882, 0x1d47a414, 0x0a70355e, 0x0d7135d1, 0xc757eb}}, + {{0x00584ca4, 0x0eced865, 0x06253040, 0x1a621a20, 0x0c61b627, 0x14f9045f, 0x1cd895cd, 0x19f9a47f, 0xf03a59}}}, /* 11*16^57*G: */ - {{{0x1459225d, 0x3934613d, 0x18858d10, 0x3ebddf8b, 0x1c02a244, 0x17502646, 0x3a0d0f81, 0x18ebab6b, 0xfa80}}, - {{0x3ece1507, 0x28adf8ed, 0x007c59c3, 0x0adb0db4, 0x0c425c0a, 0x37888209, 0x0c069160, 0x07e415f0, 0x0ba7}}}, + {{{0x1459225d, 0x1268c27a, 0x02163443, 0x15eefc5b, 0x002a244f, 0x0a04c8ce, 0x0343e057, 0x15d5b5f4, 0xfa8063}}, + {{0x1ece1507, 0x115bf1db, 0x01f1670e, 0x16d86da0, 0x0425c0a2, 0x11104126, 0x01a45837, 0x120af818, 0xba71f}}}, /* 13*16^57*G: */ - {{{0x16f0d044, 0x19e7fa50, 0x09e61a79, 0x2ea7f524, 0x2ee0a5aa, 0x3da73e18, 0x257a89e2, 0x28f16740, 0x658c}}, - {{0x37cb872d, 0x3747ccbb, 0x018ce89a, 0x2859d8f1, 0x3bd37655, 0x197589c4, 0x225460f1, 0x304ddeba, 0xae5c}}}, + {{{0x16f0d044, 0x13cff4a0, 0x079869e5, 0x153fa921, 0x0e0a5aab, 0x14e7c317, 0x1ea278bd, 0x18b3a04a, 0x658ca3}}, + {{0x17cb872d, 0x0e8f9977, 0x0633a26b, 0x02cec788, 0x1d37655a, 0x0eb1389d, 0x15183c59, 0x06ef5d44, 0xae5cc1}}}, /* 15*16^57*G: */ - {{{0x3696756d, 0x2d6b255c, 0x2561417a, 0x1abc5815, 0x3f305c67, 0x30660d74, 0x1f2bace4, 0x12d2abe4, 0x31c9}}, - {{0x1e08ae78, 0x2f117a37, 0x2ad1070a, 0x2bb7f2b9, 0x34160683, 0x2e2d66ab, 0x283a9bf4, 0x2212d55b, 0xf80f}}} + {{{0x1696756d, 0x1ad64ab9, 0x158505ea, 0x15e2c0ac, 0x1305c676, 0x0cc1ae9f, 0x0aeb3930, 0x0955f23e, 0x31c94b}}, + {{0x1e08ae78, 0x1e22f46e, 0x0b441c2a, 0x1dbf95cd, 0x0160683a, 0x05acd57a, 0x0ea6fd2e, 0x096aadd0, 0xf80f88}}} }, { /* 1*16^58*G: */ - {{{0x1617e073, 0x10dbe6d1, 0x039317b3, 0x2b2f6f4e, 0x0fdc866b, 0x39e25b5f, 0x31eb890e, 0x1f88cd51, 0x6458}}, - {{0x1faf6589, 0x20a6797a, 0x33aeab35, 0x2e428e44, 0x0299a185, 0x1b75911f, 0x102e2ae9, 0x33756fda, 0xd99f}}}, + {{{0x1617e073, 0x01b7cda2, 0x0e4c5ecd, 0x197b7a70, 0x1dc866ba, 0x1c4b6be7, 0x1ae243b9, 0x0466a8e3, 0x64587e}}, + {{0x1faf6589, 0x014cf2f4, 0x0ebaacd6, 0x12147226, 0x099a185b, 0x0eb223e1, 0x0b8aba5b, 0x1ab7ed20, 0xd99fcd}}}, /* 3*16^58*G: */ - {{{0x0e103dd6, 0x37dc51c8, 0x0004859a, 0x1181301f, 0x12a17ac3, 0x084f3f16, 0x203f836a, 0x1ef55690, 0xbc47}}, - {{0x16f7c343, 0x0e420b63, 0x23b44ac6, 0x0a4d5cb1, 0x1ea6395d, 0x2b154b1b, 0x0dd526cb, 0x07890a6a, 0xe31e}}}, + {{{0x0e103dd6, 0x0fb8a390, 0x0012166b, 0x0c0980f8, 0x0a17ac34, 0x09e7e2c9, 0x0fe0da88, 0x1aab4840, 0xbc477b}}, + {{0x16f7c343, 0x1c8416c6, 0x0ed12b18, 0x126ae58c, 0x0a6395d2, 0x02a9636f, 0x1549b2eb, 0x0485351b, 0xe31e1e}}}, /* 5*16^58*G: */ - {{{0x144eab31, 0x34370ec3, 0x0e634907, 0x316bc501, 0x3bf8e80a, 0x0ed08c99, 0x3b838030, 0x2d3f969a, 0x589d}}, - {{0x11361f6a, 0x106baf9d, 0x148f8db9, 0x18439548, 0x3d90f31f, 0x1c188092, 0x2a2a4f60, 0x11170422, 0x6255}}}, + {{{0x144eab31, 0x086e1d86, 0x198d241f, 0x0b5e2809, 0x1f8e80ac, 0x1a11933d, 0x00e00c0e, 0x1fcb4d77, 0x589db4}}, + {{0x11361f6a, 0x00d75f3a, 0x123e36e5, 0x021caa42, 0x190f31f6, 0x0310125e, 0x0a93d81c, 0x0b821154, 0x625544}}}, /* 7*16^58*G: */ - {{{0x1a0c2c41, 0x2fe585ca, 0x20336c67, 0x20c70715, 0x2edb7c42, 0x286182b5, 0x22fa2ea8, 0x2ccdf45b, 0x1339}}, - {{0x29f1bc2b, 0x217c152e, 0x1e923a41, 0x0489fe1f, 0x13a3406b, 0x0c903f44, 0x3ae5ba7a, 0x0a58d8b1, 0x9f9b}}}, + {{{0x1a0c2c41, 0x1fcb0b94, 0x00cdb19e, 0x063838ac, 0x0db7c428, 0x0c3056b7, 0x1e8baa28, 0x06fa2dc5, 0x1339b3}}, + {{0x09f1bc2b, 0x02f82a5d, 0x1a48e906, 0x044ff0fb, 0x1a3406b1, 0x1207e889, 0x196e9e8c, 0x0c6c58f5, 0x9f9b29}}}, /* 9*16^58*G: */ - {{{0x18fc47af, 0x1c12c7e1, 0x2c0cdec3, 0x377fb20c, 0x01b568a8, 0x00ca6d40, 0x3cf17cc5, 0x2ee844d8, 0x7ff3}}, - {{0x39ba43a7, 0x3e185933, 0x18bac297, 0x294ec6b4, 0x33446b17, 0x32246dd1, 0x0a629a0b, 0x29eba006, 0x1f6b}}}, + {{{0x18fc47af, 0x18258fc2, 0x10337b0d, 0x1bfd9065, 0x1b568a8d, 0x194da800, 0x1c5f3140, 0x14226c79, 0x7ff3bb}}, + {{0x19ba43a7, 0x1c30b267, 0x02eb0a5f, 0x0a7635a3, 0x1446b17a, 0x048dba39, 0x18a682f2, 0x15d00314, 0x1f6ba7}}}, /* 11*16^58*G: */ - {{{0x15213775, 0x06135802, 0x3d42a990, 0x2d0a4ec8, 0x2c7f6100, 0x07a4e57f, 0x360bb614, 0x1c118f3a, 0x8ec6}}, - {{0x3841ffff, 0x38043cf9, 0x0cf51e90, 0x36a6282f, 0x2dee0e71, 0x190d0573, 0x25be306e, 0x299be836, 0x8f58}}}, + {{{0x15213775, 0x0c26b004, 0x150aa640, 0x08527647, 0x07f6100b, 0x149caff6, 0x02ed8507, 0x08c79d6c, 0x8ec670}}, + {{0x1841ffff, 0x100879f3, 0x13d47a43, 0x15314179, 0x1ee0e71d, 0x01a0ae76, 0x0f8c1b99, 0x0df41b4b, 0x8f58a6}}}, /* 13*16^58*G: */ - {{{0x3452abbb, 0x32cffe34, 0x2b95c2e3, 0x1aa9cbf8, 0x15d495ae, 0x2eb0ffb6, 0x301bb89d, 0x186d1079, 0x83de}}, - {{0x054eb66e, 0x28145dac, 0x3ce42918, 0x2717cdae, 0x0e1563d7, 0x3edabe31, 0x0609fa6b, 0x38cd28d3, 0x32f0}}}, + {{{0x1452abbb, 0x059ffc69, 0x0e570b8f, 0x154e5fc5, 0x1d495ae6, 0x161ff6ca, 0x06ee276e, 0x16883ce0, 0x83de61}}, + {{0x054eb66e, 0x1028bb58, 0x1390a462, 0x18be6d77, 0x01563d79, 0x1b57c627, 0x027e9afe, 0x0694698c, 0x32f0e3}}}, /* 15*16^58*G: */ - {{{0x359276f1, 0x25a2309b, 0x2a17b15e, 0x2b896ca4, 0x3cd86833, 0x2ed7003d, 0x0c1db1a8, 0x18e263d4, 0x3d76}}, - {{0x059cbcb3, 0x0792996e, 0x1b197860, 0x08660806, 0x18333ef3, 0x1db8d36b, 0x07ddb609, 0x1a5cde86, 0xd376}}} + {{{0x159276f1, 0x0b446137, 0x085ec57a, 0x1c4b6525, 0x0d86833a, 0x1ae007be, 0x076c6a2e, 0x1131ea18, 0x3d7663}}, + {{0x059cbcb3, 0x0f2532dc, 0x0c65e180, 0x03304033, 0x0333ef32, 0x171a6d6c, 0x176d825d, 0x0e6f430f, 0xd37669}}} }, { /* 1*16^59*G: */ - {{{0x1d45e458, 0x1635b21b, 0x250e7fd3, 0x02a9b3a8, 0x09de042f, 0x151b4f95, 0x0d885b3a, 0x2f783939, 0x8481}}, - {{0x1779057e, 0x3592c6d6, 0x3262e556, 0x029e710a, 0x2cb2ca90, 0x096fce73, 0x004dd84a, 0x1ee32e95, 0x38ee}}}, + {{{0x1d45e458, 0x0c6b6436, 0x1439ff4d, 0x154d9d44, 0x1de042f0, 0x0369f2a4, 0x0216ce95, 0x1c1c9c9b, 0x8481bd}}, + {{0x1779057e, 0x0b258dac, 0x098b955b, 0x14f38856, 0x0b2ca900, 0x0df9ce76, 0x13761289, 0x11974a80, 0x38ee7b}}}, /* 3*16^59*G: */ - {{{0x152da17d, 0x18283e90, 0x0d0646b1, 0x3704f6c2, 0x200bc811, 0x139ac17f, 0x18c5f089, 0x3b4783d4, 0x3bea}}, - {{0x2cc768d2, 0x39c12617, 0x1fec416c, 0x3379dee3, 0x00e1b554, 0x12a2fafa, 0x37acdfef, 0x35fd56bf, 0xc3b0}}}, + {{{0x152da17d, 0x10507d20, 0x14191ac5, 0x1827b611, 0x00bc811d, 0x13582ff0, 0x117c2253, 0x03c1ea31, 0x3beaed}}, + {{0x0cc768d2, 0x13824c2f, 0x1fb105b3, 0x1bcef71b, 0x0e1b554c, 0x145f5f40, 0x0b37fbd2, 0x1eab5fef, 0xc3b0d7}}}, /* 5*16^59*G: */ - {{{0x3a4edcc5, 0x0d3e85f6, 0x20311b72, 0x138c8850, 0x275997e7, 0x0b7f00e4, 0x09d61875, 0x36e832f7, 0x6e73}}, - {{0x159da0e4, 0x2cc7df37, 0x00679037, 0x229df69c, 0x02869327, 0x11542222, 0x2cc48bea, 0x307f127b, 0xee0a}}}, + {{{0x1a4edcc5, 0x1a7d0bed, 0x00c46dc8, 0x1c644284, 0x15997e74, 0x0fe01c93, 0x15861d4b, 0x14197b93, 0x6e73db}}, + {{0x159da0e4, 0x198fbe6e, 0x019e40de, 0x14efb4e0, 0x08693278, 0x0a844441, 0x1122fa91, 0x1f893dd9, 0xee0ac1}}}, /* 7*16^59*G: */ - {{{0x0a80b979, 0x02713109, 0x29abb314, 0x243d7e8c, 0x07c31004, 0x1f65faa9, 0x1b592762, 0x37624df9, 0x7706}}, - {{0x0126cfde, 0x133d2041, 0x17efe321, 0x3e828d3f, 0x2a9c7117, 0x2375e647, 0x3b714777, 0x2a609f56, 0x8a02}}}, + {{{0x0a80b979, 0x04e26212, 0x06aecc50, 0x01ebf465, 0x1c310049, 0x0cbf5523, 0x1649d89f, 0x1126fcb6, 0x7706dd}}, + {{0x0126cfde, 0x067a4082, 0x1fbf8c85, 0x141469fa, 0x09c7117f, 0x0ebcc8f5, 0x1c51dde3, 0x104fab76, 0x8a02a9}}}, /* 9*16^59*G: */ - {{{0x326fe285, 0x336e712d, 0x13ef127d, 0x16eb0a50, 0x39e06aa4, 0x3cf1e907, 0x3c0f80d2, 0x08b164a6, 0x16d4}}, - {{0x0155b441, 0x0f83ff9b, 0x3364d423, 0x0fc3044d, 0x3531b1e9, 0x2df9a698, 0x22641a8a, 0x223e9478, 0x0df8}}}, + {{{0x126fe285, 0x06dce25b, 0x0fbc49f7, 0x17585282, 0x1e06aa45, 0x1e3d20fc, 0x03e034bc, 0x18b25378, 0x16d422}}, + {{0x0155b441, 0x1f07ff36, 0x0d93508c, 0x1e18226e, 0x131b1e93, 0x1f34d31a, 0x1906a2ad, 0x1f4a3c44, 0xdf888}}}, /* 11*16^59*G: */ - {{{0x3acfa513, 0x38c42f2a, 0x260e3aea, 0x0901e7e6, 0x356a9c4e, 0x28d11d43, 0x36d63aa5, 0x0391fbb1, 0x1fcc}}, - {{0x107afc9c, 0x141d6e90, 0x09839187, 0x3b7b7459, 0x39f9b44b, 0x38e1d50c, 0x35478b48, 0x30681078, 0x165d}}}, + {{{0x1acfa513, 0x11885e55, 0x1838ebab, 0x080f3f34, 0x16a9c4e2, 0x1a23a87a, 0x158ea968, 0x08fdd8ed, 0x1fcc0e}}, + {{0x107afc9c, 0x083add20, 0x060e461d, 0x1bdba2c9, 0x1f9b44be, 0x1c3aa19c, 0x11e2d238, 0x14083c6a, 0x165dc1}}}, /* 13*16^59*G: */ - {{{0x3edc69b2, 0x0689c1f3, 0x26b77172, 0x0298226c, 0x0aa386a5, 0x190c10d7, 0x0b8a1730, 0x241ceb5b, 0xc12b}}, - {{0x20dd41dd, 0x0caba6c0, 0x127b2a00, 0x3b876f8f, 0x094976b8, 0x1cb7227e, 0x0cdf1d97, 0x310ff94d, 0x3173}}}, + {{{0x1edc69b2, 0x0d1383e7, 0x1addc5c8, 0x14c11364, 0x0a386a50, 0x01821ae5, 0x0285cc19, 0x0e75ad97, 0xc12b90}}, + {{0x00dd41dd, 0x19574d81, 0x09eca800, 0x1c3b7c7a, 0x14976b8e, 0x16e44fc4, 0x17c765dc, 0x07fca699, 0x3173c4}}}, /* 15*16^59*G: */ - {{{0x3961fe4d, 0x2dbd6177, 0x3107197a, 0x05221be2, 0x2ca73e8a, 0x0fa4c4c4, 0x27a8fa3f, 0x2fe1770c, 0xd059}}, - {{0x2ae823c2, 0x264d6c19, 0x0dab64cb, 0x0e22e87d, 0x0955b4fd, 0x01d97721, 0x3525e3fe, 0x1e983022, 0x4510}}} + {{{0x1961fe4d, 0x1b7ac2ef, 0x041c65ea, 0x0910df16, 0x0a73e8a1, 0x14989896, 0x0a3e8fcf, 0x10bb864f, 0xd059bf}}, + {{0x0ae823c2, 0x0c9ad833, 0x16ad932e, 0x111743e9, 0x155b4fd3, 0x1b2ee424, 0x0978ff81, 0x0c18116a, 0x45107a}}} }, { /* 1*16^60*G: */ - {{{0x2caf666b, 0x3358c0fd, 0x0b1ce30b, 0x3f3fb4f1, 0x17f4637f, 0x1a5e6ba0, 0x102aa62b, 0x1295e9e0, 0x1346}}, - {{0x3f6ecc27, 0x3d256a41, 0x10942e13, 0x3cc02a07, 0x0cb0ca48, 0x390cd14f, 0x14580ef7, 0x05640118, 0x69be}}}, + {{{0x0caf666b, 0x06b181fb, 0x0c738c2f, 0x19fda789, 0x1f4637ff, 0x0bcd740b, 0x0aa98ada, 0x0af4f020, 0x13464a}}, + {{0x1f6ecc27, 0x1a4ad483, 0x0250b84f, 0x0601503a, 0x0b0ca48f, 0x019a29e6, 0x1603bdf9, 0x12008c28, 0x69be15}}}, /* 3*16^60*G: */ - {{{0x0eca5f51, 0x085ac826, 0x0fc9aebf, 0x3a85c6e5, 0x05b5cfdd, 0x3b5acafc, 0x2e6962c6, 0x35453767, 0xdde9}}, - {{0x10c638f7, 0x2b5a69cf, 0x289571f9, 0x3fbafa37, 0x3f8f0950, 0x07cd2c29, 0x28111d89, 0x1a44cf38, 0xb84e}}}, + {{{0x0eca5f51, 0x10b5904c, 0x1f26bafc, 0x142e3729, 0x1b5cfdde, 0x0b595f82, 0x1a58b1bb, 0x029bb3dc, 0xdde9d5}}, + {{0x10c638f7, 0x16b4d39e, 0x0255c7e6, 0x1dd7d1bd, 0x18f0950f, 0x19a5853f, 0x04476247, 0x02679c50, 0xb84e69}}}, /* 5*16^60*G: */ - {{{0x199c88e4, 0x3e41ac16, 0x0ad46ec2, 0x3b544f88, 0x204b179a, 0x3d01bac4, 0x193736e9, 0x188408da, 0xfd1a}}, - {{0x195bc8df, 0x27232459, 0x1cc00f29, 0x1adc7525, 0x177782dc, 0x0f01a552, 0x0c20bfb1, 0x1ed52e72, 0x1ac9}}}, + {{{0x199c88e4, 0x1c83582c, 0x0b51bb0b, 0x1aa27c41, 0x04b179ae, 0x00375890, 0x0dcdba7d, 0x02046d32, 0xfd1a62}}, + {{0x195bc8df, 0x0e4648b2, 0x13003ca6, 0x16e3a92b, 0x17782dc6, 0x0034aa4b, 0x082fec4f, 0x0a973918, 0x1ac97b}}}, /* 7*16^60*G: */ - {{{0x1f8018ce, 0x35456d6d, 0x1892d68b, 0x0b695ce3, 0x086dc7cf, 0x3ff393cb, 0x296b9f13, 0x214c7630, 0x4ee4}}, - {{0x1e48381f, 0x30d6986c, 0x0e806013, 0x01d25c6d, 0x07c5e671, 0x2d102343, 0x3f8b5fc7, 0x27b52042, 0xb68f}}}, + {{{0x1f8018ce, 0x0a8adada, 0x024b5a2f, 0x1b4ae71b, 0x06dc7cf2, 0x1e727964, 0x1ae7c4ff, 0x063b1852, 0x4ee485}}, + {{0x1e48381f, 0x01ad30d8, 0x1a01804f, 0x0e92e369, 0x1c5e6710, 0x02046863, 0x02d7f1ed, 0x1a90217f, 0xb68f9e}}}, /* 9*16^60*G: */ - {{{0x31473678, 0x0a14ba47, 0x14392f70, 0x2815e542, 0x38c070cb, 0x38c53156, 0x000dbff5, 0x33270d31, 0xfd76}}, - {{0x0d144f4f, 0x38593baa, 0x001c8437, 0x18a3bb85, 0x032cd660, 0x3b829cf4, 0x143dae0f, 0x1950de1c, 0xf204}}}, + {{{0x11473678, 0x1429748f, 0x10e4bdc0, 0x00af2a12, 0x0c070cba, 0x18a62adc, 0x036ffd78, 0x13869880, 0xfd76cc}}, + {{0x0d144f4f, 0x10b27754, 0x007210df, 0x051ddc28, 0x12cd6606, 0x10539e81, 0x0f6b83fb, 0x086f0e28, 0xf20465}}}, /* 11*16^60*G: */ - {{{0x0d7a2193, 0x3c02dc52, 0x197546ed, 0x1a47913c, 0x34ea212c, 0x1b3a09d2, 0x3b40219e, 0x2ae8cc48, 0x85a2}}, - {{0x30cdcf3a, 0x3c320f52, 0x03b12427, 0x31b6b7e7, 0x0c029fe1, 0x31820b47, 0x30516d82, 0x2615faca, 0x9c12}}}, + {{{0x0d7a2193, 0x1805b8a4, 0x05d51bb7, 0x123c89e3, 0x0ea212c6, 0x07413a5a, 0x1008679b, 0x14662476, 0x85a2ab}}, + {{0x10cdcf3a, 0x18641ea5, 0x0ec4909f, 0x0db5bf38, 0x0029fe1c, 0x104168e6, 0x145b60b1, 0x0afd6560, 0x9c1298}}}, /* 13*16^60*G: */ - {{{0x377568b0, 0x16c0c16c, 0x1e03b053, 0x2ba37406, 0x03650f35, 0x2db5b15e, 0x3fe74440, 0x36ff1cf3, 0xd25d}}, - {{0x1f39929c, 0x0284e49b, 0x23c3f006, 0x089ce207, 0x27d92b83, 0x2bbdd337, 0x048938be, 0x3fdd64fe, 0x7a3a}}}, + {{{0x177568b0, 0x0d8182d9, 0x180ec14d, 0x1d1ba033, 0x1650f35a, 0x16b62bc1, 0x19d1102d, 0x1f8e79ff, 0xd25ddb}}, + {{0x1f39929c, 0x0509c936, 0x0f0fc018, 0x04e7103c, 0x1d92b832, 0x17ba66f3, 0x024e2fab, 0x0eb27f09, 0x7a3aff}}}, /* 15*16^60*G: */ - {{{0x271d7c13, 0x17f94462, 0x20ffa385, 0x06ad7dfe, 0x2ac80564, 0x01fa6a5e, 0x14a7255f, 0x0d4c50fa, 0x4581}}, - {{0x3aff63cf, 0x18e2f154, 0x2bd96b99, 0x08019550, 0x1d69c970, 0x3d43c5df, 0x39ad8b57, 0x163b0525, 0x9f58}}} + {{{0x071d7c13, 0x0ff288c5, 0x03fe8e15, 0x156beff4, 0x0c805641, 0x1f4d4bd5, 0x09c957c1, 0x06287d29, 0x458135}}, + {{0x1aff63cf, 0x11c5e2a9, 0x0f65ae65, 0x000caa85, 0x169c9702, 0x0878bbee, 0x0b62d5fd, 0x1d8292f3, 0x9f5858}}} }, { /* 1*16^61*G: */ - {{{0x2d83f366, 0x2b68e834, 0x2f28588c, 0x36733b78, 0x1dc97a0c, 0x3d0c2f30, 0x3fe2e9ae, 0x277d6dc4, 0xbc4a}}, - {{0x181f33c1, 0x1d635999, 0x2547b16d, 0x3a2a7efe, 0x3798caa6, 0x24deb7d2, 0x05c06383, 0x20729b9e, 0x0d3a}}}, + {{{0x0d83f366, 0x16d1d069, 0x1ca16232, 0x1399dbc5, 0x1c97a0cd, 0x0185e60e, 0x18ba6bbd, 0x1eb6e27f, 0xbc4a9d}}, + {{0x181f33c1, 0x1ac6b332, 0x151ec5b5, 0x1153f7f4, 0x198caa6e, 0x1bd6fa5b, 0x1018e0e4, 0x194dcf0b, 0xd3a81}}}, /* 3*16^61*G: */ - {{{0x3712be3c, 0x01a8b8cb, 0x2146a66b, 0x257c63b6, 0x00153472, 0x1c976eac, 0x1b378d3c, 0x0d2764cc, 0x39d7}}, - {{0x1c6ff65c, 0x30c067d0, 0x0a41644c, 0x17bde97b, 0x2812e8ef, 0x09d55319, 0x33bf7fb1, 0x26d3d5bb, 0x8f92}}}, + {{{0x1712be3c, 0x03517197, 0x051a99ac, 0x0be31db4, 0x01534729, 0x12edd580, 0x0de34f1c, 0x13b26636, 0x39d734}}, + {{0x1c6ff65c, 0x0180cfa0, 0x09059133, 0x1def4bd9, 0x012e8ef5, 0x1aaa6334, 0x0fdfec49, 0x09eadde7, 0x8f929b}}}, /* 5*16^61*G: */ - {{{0x1f77f22b, 0x2ab93ef3, 0x0f82e035, 0x265c8e65, 0x15af26c6, 0x0735b0a6, 0x01dd09e5, 0x2985fdf7, 0xf0cb}}, - {{0x1909a03c, 0x3f238b1d, 0x0a095661, 0x3c631fa4, 0x16d04004, 0x0c9b0d94, 0x1df989ef, 0x2ad0c4fe, 0x1a25}}}, + {{{0x1f77f22b, 0x15727de6, 0x1e0b80d6, 0x12e47329, 0x1af26c69, 0x06b614ca, 0x17427947, 0x02fefb83, 0xf0cba6}}, + {{0x1909a03c, 0x1e47163a, 0x08255987, 0x0318fd21, 0x0d04004f, 0x1361b28b, 0x1e627bcc, 0x08627f3b, 0x1a25ab}}}, /* 7*16^61*G: */ - {{{0x06509c12, 0x22b37353, 0x3d1f4765, 0x1aff88d6, 0x3268ed8d, 0x05c3a361, 0x154d321d, 0x1eae76c8, 0x381d}}, - {{0x2eb46102, 0x1190aa38, 0x0e6eaf75, 0x160a161b, 0x2581e720, 0x34915ce9, 0x23da9eb5, 0x2ad6dff6, 0xa47a}}}, + {{{0x06509c12, 0x0566e6a6, 0x147d1d96, 0x17fc46b7, 0x068ed8d6, 0x18746c39, 0x134c8745, 0x173b642a, 0x381d7a}}, + {{0x0eb46102, 0x03215471, 0x19babdd5, 0x1050b0d9, 0x181e7205, 0x122b9d32, 0x16a7ad74, 0x0b6ffb47, 0xa47aab}}}, /* 9*16^61*G: */ - {{{0x384fe955, 0x36ced358, 0x063bce48, 0x2655a968, 0x0c8a53f6, 0x0edcf9a5, 0x387e6479, 0x3c1519ea, 0xa703}}, - {{0x161344bd, 0x09acbbef, 0x197277fa, 0x27858a71, 0x19199b53, 0x29e4b5ac, 0x047adc0e, 0x3e4d68ac, 0xd500}}}, + {{{0x184fe955, 0x0d9da6b1, 0x18ef3923, 0x12ad4b40, 0x08a53f69, 0x1b9f34a6, 0x1f991e4e, 0x0a8cf570, 0xa703f0}}, + {{0x161344bd, 0x135977de, 0x05c9dfe8, 0x1c2c538b, 0x1199b539, 0x1c96b58c, 0x1eb703a9, 0x06b45608, 0xd500f9}}}, /* 11*16^61*G: */ - {{{0x06eace58, 0x126595b0, 0x2f3211d3, 0x1f9158e8, 0x13a03f1b, 0x1ab435c1, 0x150d746c, 0x2cf16ab5, 0x73c6}}, - {{0x2af8654e, 0x05c2a45c, 0x3b8d2917, 0x1aa1e36e, 0x2d91c6aa, 0x242644d9, 0x24f741ba, 0x2d291cce, 0x3a2f}}}, + {{{0x06eace58, 0x04cb2b60, 0x1cc8474d, 0x1c8ac745, 0x1a03f1b7, 0x1686b829, 0x035d1b1a, 0x18b55aaa, 0x73c6b3}}, + {{0x0af8654e, 0x0b8548b9, 0x0e34a45c, 0x150f1b77, 0x191c6aa6, 0x04c89b36, 0x1dd06ea4, 0x148e6749, 0x3a2fb4}}}, /* 13*16^61*G: */ - {{{0x00181d5e, 0x12ce22fc, 0x15aaf205, 0x1c6cea6e, 0x0eddb8de, 0x0034e870, 0x147fda1d, 0x3cf9d41b, 0xc627}}, - {{0x369f886d, 0x09e40298, 0x1cbe2c39, 0x3dac0152, 0x21f7d68e, 0x1a5804e2, 0x02a63b2d, 0x2775c791, 0xd78f}}}, + {{{0x00181d5e, 0x059c45f8, 0x16abc815, 0x03675372, 0x0ddb8de7, 0x069d0e07, 0x1ff68740, 0x1cea0da8, 0xc627f3}}, + {{0x169f886d, 0x13c80531, 0x12f8b0e4, 0x0d600a93, 0x1f7d68ef, 0x0b009c50, 0x098ecb5a, 0x1ae3c885, 0xd78f9d}}}, /* 15*16^61*G: */ - {{{0x37828b16, 0x138a367e, 0x0a4847f3, 0x11e563ca, 0x06de53a0, 0x17d029bc, 0x3d233fa2, 0x3eaf83b7, 0xbb88}}, - {{0x0aea5df7, 0x1451ce88, 0x3a1e969c, 0x12a05d38, 0x159163ec, 0x37165804, 0x1e8dd345, 0x1dacc13d, 0xb736}}} + {{{0x17828b16, 0x07146cfd, 0x09211fcd, 0x0f2b1e51, 0x0de53a04, 0x1a053783, 0x08cfe897, 0x17c1dbfa, 0xbb88fa}}, + {{0x0aea5df7, 0x08a39d10, 0x087a5a71, 0x1502e9c7, 0x19163ec4, 0x02cb008a, 0x0374d177, 0x16609ebd, 0xb73676}}} }, { /* 1*16^62*G: */ - {{{0x25324caa, 0x152acc3f, 0x29472a39, 0x12d978c2, 0x12a32e69, 0x3631d251, 0x18bc0d23, 0x2a5efe0a, 0x8c28}}, - {{0x0bef9482, 0x39c771cf, 0x11cb9459, 0x39e13c11, 0x3cc0eb7a, 0x3fb7cc7d, 0x05193378, 0x0118e8cc, 0x40a3}}}, + {{{0x05324caa, 0x0a55987f, 0x051ca8e5, 0x16cbc615, 0x0a32e694, 0x063a4a29, 0x0f0348f6, 0x0f7f0531, 0x8c28a9}}, + {{0x0bef9482, 0x138ee39e, 0x072e5167, 0x0f09e08a, 0x0c0eb7ae, 0x16f98fbe, 0x064cde3f, 0x0c74660a, 0x40a304}}}, /* 3*16^62*G: */ - {{{0x0754dd40, 0x18fa1c55, 0x03466cf8, 0x10898c7f, 0x32f6e9a2, 0x12107f35, 0x0dfcf45b, 0x091c0cb0, 0x9729}}, - {{0x2aa36143, 0x212d24bc, 0x1acaf493, 0x36ba1495, 0x14df3690, 0x171d772f, 0x3ea1dcd1, 0x28910997, 0x91d1}}}, + {{{0x0754dd40, 0x11f438aa, 0x0d19b3e1, 0x044c63f8, 0x0f6e9a24, 0x020fe6b9, 0x1f3d16d2, 0x0e06581b, 0x972924}}, + {{0x0aa36143, 0x025a4979, 0x0b2bd24e, 0x15d0a4ab, 0x0df3690d, 0x03aee5ea, 0x08773457, 0x0884cbfd, 0x91d1a2}}}, /* 5*16^62*G: */ - {{{0x0c2ca7ff, 0x30b60bae, 0x1df021a3, 0x00d91765, 0x2f27af18, 0x1e46b568, 0x2796e050, 0x1fe5d602, 0x8963}}, - {{0x30493e68, 0x3b505785, 0x242eab7b, 0x1ef1a8e3, 0x357489f8, 0x2e73c550, 0x08424d57, 0x38492322, 0x2d1f}}}, + {{{0x0c2ca7ff, 0x016c175c, 0x17c0868f, 0x06c8bb2b, 0x127af180, 0x08d6ad17, 0x05b8141e, 0x12eb014f, 0x89637f}}, + {{0x10493e68, 0x16a0af0b, 0x10baadef, 0x178d471c, 0x17489f87, 0x0e78aa1a, 0x109355ee, 0x04919110, 0x2d1fe1}}}, /* 7*16^62*G: */ - {{{0x0ca8dd7f, 0x061b58e8, 0x2a1381a6, 0x31ca00d5, 0x1357421b, 0x327680f5, 0x25e092fd, 0x0e39c6f8, 0x3081}}, - {{0x0a92c7f2, 0x1057c91e, 0x34ad915e, 0x05959190, 0x008e18c8, 0x27b11745, 0x0fc925e3, 0x38b4a20a, 0x28d1}}}, + {{{0x0ca8dd7f, 0x0c36b1d0, 0x084e0698, 0x0e5006ad, 0x157421bc, 0x0ed01ea9, 0x1824bf72, 0x1ce37c4b, 0x308138}}, + {{0x0a92c7f2, 0x00af923c, 0x12b64579, 0x0cac8c86, 0x08e18c81, 0x1622e8a0, 0x124978e7, 0x1a51051f, 0x28d1e2}}}, /* 9*16^62*G: */ - {{{0x066a3fb1, 0x037315a2, 0x192e206c, 0x30024a06, 0x36862f6e, 0x15d43216, 0x1eb65d1e, 0x313a0a9b, 0x575f}}, - {{0x102655ad, 0x26e3a42a, 0x2a3af2f0, 0x0ced5cf1, 0x0e87daed, 0x076f0a5e, 0x2fca2d67, 0x36e410a9, 0x6f6e}}}, + {{{0x066a3fb1, 0x06e62b44, 0x04b881b0, 0x00125033, 0x0862f6ec, 0x1a8642db, 0x0d974795, 0x1d054dbd, 0x575fc4}}, + {{0x102655ad, 0x0dc74854, 0x08ebcbc2, 0x076ae78d, 0x087daed3, 0x0de14bc7, 0x128b59c7, 0x120854df, 0x6f6edb}}}, /* 11*16^62*G: */ - {{{0x390117df, 0x06daa291, 0x22010292, 0x094eeef3, 0x2a2a8fda, 0x3c9be07b, 0x2ab7a227, 0x240dad93, 0xa5ec}}, - {{0x386462fe, 0x204a04cf, 0x214a363d, 0x21187c15, 0x1fa0f71c, 0x25e60eb4, 0x140400c5, 0x319897b0, 0xb79d}}}, + {{{0x190117df, 0x0db54523, 0x08040a48, 0x0a77779c, 0x02a8fda2, 0x137c0f75, 0x0de889fc, 0x06d6c9d5, 0xa5ec90}}, + {{0x186462fe, 0x0094099f, 0x0528d8f6, 0x08c3e0ac, 0x1a0f71c8, 0x1cc1d68f, 0x01003165, 0x0c4bd828, 0xb79dc6}}}, /* 13*16^62*G: */ - {{{0x172ad712, 0x2c3e5d70, 0x21047290, 0x0e632c37, 0x2349b95a, 0x39e5d851, 0x10b0949d, 0x37fa44cc, 0xa153}}, - {{0x0d48fdd2, 0x2297d94e, 0x2f0b329c, 0x014fca16, 0x31b89abd, 0x0c6357c7, 0x05b2fc48, 0x36104fec, 0xfd94}}}, + {{{0x172ad712, 0x187cbae0, 0x0411ca42, 0x131961bc, 0x149b95a3, 0x1cbb0a31, 0x0c252779, 0x1d226621, 0xa153df}}, + {{0x0d48fdd2, 0x052fb29c, 0x1c2cca72, 0x0a7e50b5, 0x1b89abd0, 0x0c6af8f8, 0x0cbf120c, 0x0827f60b, 0xfd94d8}}}, /* 15*16^62*G: */ - {{{0x11cf5b3a, 0x0c30dc04, 0x1b5a7810, 0x10cea0ef, 0x2dc824c4, 0x30d34223, 0x14615935, 0x06b1abde, 0x9a54}}, - {{0x36a44ae4, 0x0fd55d7c, 0x21ea52d6, 0x123fb894, 0x0f475f55, 0x386bcda2, 0x06ab7caf, 0x123072c4, 0xb661}}} + {{{0x11cf5b3a, 0x1861b808, 0x0d69e040, 0x0675077b, 0x1c824c44, 0x1a684476, 0x18564d70, 0x18d5ef28, 0x9a541a}}, + {{0x16a44ae4, 0x1faabaf9, 0x07a94b58, 0x11fdc4a4, 0x1475f554, 0x0d79b447, 0x0adf2bf8, 0x1839620d, 0xb66148}}} }, { /* 1*16^63*G: */ - {{{0x1faccae0, 0x2312e844, 0x24bb3374, 0x22cd4316, 0x071fd23c, 0x3653393c, 0x127a8c1d, 0x259984e5, 0x08ea}}, - {{0x0e62b945, 0x16bcd28c, 0x0f0f8e95, 0x2de0efa7, 0x15c5d735, 0x39f033ee, 0x22782e24, 0x3eaef23b, 0x620e}}}, + {{{0x1faccae0, 0x0625d088, 0x12eccdd2, 0x166a18b4, 0x11fd23c8, 0x0a672783, 0x1ea30776, 0x0cc272a4, 0x8ea96}}, + {{0x0e62b945, 0x0d79a518, 0x1c3e3a55, 0x0f077d39, 0x1c5d735b, 0x1e067dca, 0x1e0b8939, 0x17791dc4, 0x620efa}}}, /* 3*16^63*G: */ - {{{0x26a06f5e, 0x06902d65, 0x2a083702, 0x1064945b, 0x23b716a3, 0x2c350849, 0x0253ac37, 0x093efa85, 0x383b}}, - {{0x13c6e772, 0x227d1e1b, 0x38c2b040, 0x3dab9d2e, 0x2a5a19e8, 0x3d59b553, 0x1ba2044c, 0x1c1ab13b, 0x54cf}}}, + {{{0x06a06f5e, 0x0d205acb, 0x0820dc08, 0x0324a2dd, 0x1b716a34, 0x06a10931, 0x14eb0dec, 0x1f7d4284, 0x383b24}}, + {{0x13c6e772, 0x04fa3c36, 0x030ac102, 0x0d5ce977, 0x05a19e8f, 0x0b36aa75, 0x0881133d, 0x0d589db7, 0x54cf70}}}, /* 5*16^63*G: */ - {{{0x0638a136, 0x1e5d7075, 0x2838195c, 0x034738cd, 0x0d790c2b, 0x39671ad8, 0x2ed6d789, 0x0cb40f80, 0xe684}}, - {{0x0c6c2584, 0x2bf46042, 0x3357336a, 0x0278faf6, 0x01e6472e, 0x0a9cc0e8, 0x35a6624d, 0x3904e638, 0xca5b}}}, + {{{0x0638a136, 0x1cbae0ea, 0x00e06571, 0x1a39c66d, 0x1790c2b0, 0x0ce35b06, 0x15b5e279, 0x1a07c05d, 0xe68432}}, + {{0x0c6c2584, 0x17e8c084, 0x0d5ccdaa, 0x13c7d7b6, 0x1e6472e0, 0x13981d00, 0x0998934a, 0x02731c6b, 0xca5be4}}}, /* 7*16^63*G: */ - {{{0x16e8c10c, 0x33a1f110, 0x11bd6807, 0x1ca617ce, 0x306e7fb4, 0x3ef7b39c, 0x25c2a0ee, 0x355678bf, 0x395d}}, - {{0x05fe638e, 0x30f5b64c, 0x066922cb, 0x24270137, 0x3a4e274c, 0x04fa1ebf, 0x12ac5d04, 0x37352d16, 0xfd62}}}, + {{{0x16e8c10c, 0x0743e220, 0x06f5a01f, 0x0530be72, 0x06e7fb47, 0x1ef67398, 0x10a83bbe, 0x0b3c5fcb, 0x395dd5}}, + {{0x05fe638e, 0x01eb6c98, 0x19a48b2f, 0x013809b8, 0x04e274c9, 0x1f43d7fd, 0x0b174104, 0x1a968b25, 0xfd62dc}}}, /* 9*16^63*G: */ - {{{0x0d6c14ef, 0x059936c8, 0x2f93c8f5, 0x163f1d41, 0x22648008, 0x3bb56fbb, 0x25dcb9f6, 0x12b70d54, 0x7a51}}, - {{0x0b3fbd13, 0x2b4f861c, 0x2a6e24f7, 0x2fabbdca, 0x0f5c3729, 0x1fc2e532, 0x2e4d8e89, 0x347fb454, 0x56ed}}}, + {{{0x0d6c14ef, 0x0b326d90, 0x1e4f23d4, 0x11f8ea0d, 0x06480085, 0x16adf771, 0x172e7dbb, 0x1b86aa4b, 0x7a514a}}, + {{0x0b3fbd13, 0x169f0c38, 0x09b893de, 0x1d5dee55, 0x15c3729b, 0x185ca647, 0x1363a25f, 0x1fda2a5c, 0x56edd1}}}, /* 11*16^63*G: */ - {{{0x0f6d65eb, 0x2a518f41, 0x04021524, 0x26441dd5, 0x108f235a, 0x23bcefd2, 0x1d90d8ea, 0x3f5610c9, 0x1ee1}}, - {{0x1d22941c, 0x380dae49, 0x23582b11, 0x0cbd3a61, 0x02fcfaca, 0x2ae7f13d, 0x2c73c1cf, 0x0a246f75, 0xbb69}}}, + {{{0x0f6d65eb, 0x14a31e82, 0x10085492, 0x1220eea8, 0x08f235a9, 0x179dfa48, 0x04363aa3, 0x0b0864bb, 0x1ee1fd}}, + {{0x1d22941c, 0x101b5c92, 0x0d60ac47, 0x05e9d30c, 0x0fcfaca3, 0x1cfe27a1, 0x1cf073ea, 0x1237bad8, 0xbb6928}}}, /* 13*16^63*G: */ - {{{0x0e36cb44, 0x3c6543bc, 0x1ca20191, 0x1fa2db23, 0x03357d61, 0x163f4362, 0x3aaa8bc0, 0x158d34e3, 0x1551}}, - {{0x1f495a68, 0x0a6bd194, 0x020c1e53, 0x30dc5d7c, 0x23205da8, 0x038fc2d1, 0x35215e37, 0x3ff1d555, 0xab4f}}}, + {{{0x0e36cb44, 0x18ca8778, 0x12880647, 0x1d16d91b, 0x1357d617, 0x07e86c41, 0x0aa2f016, 0x069a71f5, 0x155156}}, + {{0x1f495a68, 0x14d7a328, 0x0830794c, 0x06e2ebe0, 0x1205da8c, 0x11f85a31, 0x08578dc3, 0x18eaaaea, 0xab4fff}}}, /* 15*16^63*G: */ - {{{0x3427bacc, 0x07e51841, 0x12d62e15, 0x1ccc5937, 0x0dc4aa9e, 0x163ac256, 0x35201363, 0x2f1911af, 0x3bc6}}, - {{0x2ad6fda6, 0x130cff57, 0x28beb471, 0x06dd6948, 0x16c02bd7, 0x18bb889b, 0x2c305cdb, 0x17301c5d, 0x8e30}}} + {{{0x1427bacc, 0x0fca3083, 0x0b58b854, 0x0662c9ba, 0x1c4aa9e7, 0x07584ac6, 0x0804d8d6, 0x0c88d7ea, 0x3bc6bc}}, + {{0x0ad6fda6, 0x0619feaf, 0x02fad1c5, 0x16eb4a45, 0x0c02bd71, 0x1771136b, 0x0c1736d8, 0x180e2ed8, 0x8e305c}}} }, diff --git a/crypto/tests/test_bignum.py b/crypto/tests/test_bignum.py new file mode 100755 index 0000000000..b9ae52315d --- /dev/null +++ b/crypto/tests/test_bignum.py @@ -0,0 +1,1028 @@ +#!/usr/bin/python +import ctypes +import os +import random +from ctypes import ( + c_bool, + c_int, + c_size_t, + c_uint, + c_uint8, + c_uint16, + c_uint32, + c_uint64, +) +from math import floor, log, sqrt + +import pytest + +dir = os.path.abspath(os.path.dirname(__file__)) +lib = ctypes.cdll.LoadLibrary(os.path.join(dir, "libtrezor-crypto.so")) + +limbs_number = 9 +bits_per_limb = 29 + + +@pytest.fixture() +def prime(request): + return 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC2F + + +@pytest.fixture(params=range(limbs_number * bits_per_limb)) +def bignum_bit_index(request): + return request.param + + +max_decimal_digits = floor(limbs_number * bits_per_limb * log(2, 10)) + + +@pytest.fixture(params=range(max_decimal_digits)) +def bignum_decimal_digit_index(request): + return request.param + + +iterations = int(os.environ.get("ITERS", 1000)) + + +@pytest.fixture(params=range(iterations)) +def r(request): + return Random(request.param) + + +def implication(p, c): + return not p or c + + +def uint32_p_to_int(pointer): + return pointer.contents.value + + +def uint32_p(): + return ctypes.POINTER(c_int)(c_int()) + + +limb_type = c_uint32 + + +def bignum(limbs_number=limbs_number): + return (limbs_number * limb_type)() + + +def limbs_to_bignum(limbs): + return (limbs_number * limb_type)(*limbs) + + +def int_to_bignum(number, limbs_number=limbs_number): + assert number >= 0 + assert number.bit_length() <= limbs_number * bits_per_limb + + bn = (limbs_number * limb_type)() + for i in range(limbs_number): + bn[i] = number % 2 ** bits_per_limb + number //= 2 ** bits_per_limb + + return bn + + +def bignum_to_int(bignum, limbs_number=limbs_number): + number = 0 + + for i in reversed(range(limbs_number)): + number *= 2 ** bits_per_limb + number += bignum[i] + + return number + + +def raw_number(): + return (32 * c_uint8)() + + +def raw_number_to_integer(raw_number, endianess): + return int.from_bytes(raw_number, endianess) + + +def integer_to_raw_number(number, endianess): + return (32 * c_uint8)(*number.to_bytes(32, endianess)) + + +def bignum_is_normalised(bignum): + for limb in bignum: + if limb > 2 ** bits_per_limb: + return False + return True + + +def number_is_partly_reduced(number, prime): + return number < 2 * prime + + +def number_is_fully_reduced(number, prime): + return number < prime + + +class Random(random.Random): + def rand_int_normalized(self): + return self.randrange(0, 2 ** (limbs_number * bits_per_limb)) + + def rand_int_256(self): + return self.randrange(0, 2 ** 256) + + def rand_int_reduced(self, p): + return self.randrange(0, 2 * p) + + def rand_int_bitsize(self, bitsize): + return self.randrange(0, 2 ** bitsize) + + def rand_bit_index(self): + return self.randrange(0, limbs_number * bits_per_limb) + + def rand_bignum(self, limbs_number=limbs_number): + return (limb_type * limbs_number)( + *[self.randrange(0, 256 ** 4) for _ in range(limbs_number)] + ) + + +def assert_bn_read_be(in_number): + raw_in_number = integer_to_raw_number(in_number, "big") + bn_out_number = bignum() + lib.bn_read_be(raw_in_number, bn_out_number) + out_number = bignum_to_int(bn_out_number) + + assert bignum_is_normalised(bn_out_number) + assert out_number == in_number + + +def assert_bn_read_le(in_number): + raw_in_number = integer_to_raw_number(in_number, "little") + bn_out_number = bignum() + lib.bn_read_le(raw_in_number, bn_out_number) + out_number = bignum_to_int(bn_out_number) + + assert bignum_is_normalised(bn_out_number) + assert out_number == in_number + + +def assert_bn_write_be(in_number): + bn_in_number = int_to_bignum(in_number) + raw_out_number = raw_number() + lib.bn_write_be(bn_in_number, raw_out_number) + out_number = raw_number_to_integer(raw_out_number, "big") + + assert out_number == in_number + + +def assert_bn_write_le(in_number): + bn_in_number = int_to_bignum(in_number) + raw_out_number = raw_number() + lib.bn_write_le(bn_in_number, raw_out_number) + out_number = raw_number_to_integer(raw_out_number, "little") + + assert out_number == in_number + + +def assert_bn_read_uint32(x): + bn_out_number = bignum() + lib.bn_read_uint32(c_uint32(x), bn_out_number) + out_number = bignum_to_int(bn_out_number) + + assert bignum_is_normalised(bn_out_number) + assert out_number == x + + +def assert_bn_read_uint64(x): + bn_out_number = bignum() + lib.bn_read_uint64(c_uint64(x), bn_out_number) + out_number = bignum_to_int(bn_out_number) + + assert bignum_is_normalised(bn_out_number) + assert out_number == x + + +def assert_bn_bitcount(x): + bn_x = int_to_bignum(x) + return_value = lib.bn_bitcount(bn_x) + + assert return_value == x.bit_length() + + +def assert_bn_digitcount(x): + bn_x = int_to_bignum(x) + return_value = lib.bn_digitcount(bn_x) + + assert return_value == len(str(x)) + + +def assert_bn_zero(): + bn_x = bignum() + lib.bn_zero(bn_x) + x = bignum_to_int(bn_x) + + assert bignum_is_normalised(bn_x) + assert x == 0 + + +def assert_bn_one(): + bn_x = bignum() + lib.bn_one(bn_x) + x = bignum_to_int(bn_x) + + assert bignum_is_normalised(bn_x) + assert x == 1 + + +def assert_bn_is_zero(x): + bn_x = int_to_bignum(x) + return_value = lib.bn_is_zero(bn_x) + + assert return_value == (x == 0) + + +def assert_bn_is_one(x): + bn_x = int_to_bignum(x) + return_value = lib.bn_is_one(bn_x) + + assert return_value == (x == 1) + + +def assert_bn_is_less(x, y): + bn_x = int_to_bignum(x) + bn_y = int_to_bignum(y) + return_value = lib.bn_is_less(bn_x, bn_y) + + assert return_value == (x < y) + + +def assert_bn_is_equal(x, y): + bn_x = int_to_bignum(x) + bn_y = int_to_bignum(y) + return_value = lib.bn_is_equal(bn_x, bn_y) + + assert return_value == (x == y) + + +def assert_bn_cmov(cond, truecase, falsecase): + bn_res = bignum() + bn_truecase = int_to_bignum(truecase) + bn_falsecase = int_to_bignum(falsecase) + lib.bn_cmov(bn_res, c_uint32(cond), bn_truecase, bn_falsecase) + res = bignum_to_int(bn_res) + + assert res == truecase if cond else falsecase + + +def assert_bn_cnegate(cond, x_old, prime): + bn_x = int_to_bignum(x_old) + bn_prime = int_to_bignum(prime) + lib.bn_cnegate(c_uint32(cond), bn_x, bn_prime) + x_new = bignum_to_int(bn_x) + + assert bignum_is_normalised(bn_x) + assert number_is_partly_reduced(x_new, prime) + assert x_new % prime == -x_old % prime if cond else x_old % prime + + +def assert_bn_lshift(x_old): + bn_x = int_to_bignum(x_old) + lib.bn_lshift(bn_x) + x_new = bignum_to_int(bn_x) + + assert bignum_is_normalised(bn_x) + assert x_new == (x_old << 1) + + +def assert_bn_rshift(x_old): + bn_x = int_to_bignum(x_old) + lib.bn_rshift(bn_x) + x_new = bignum_to_int(bn_x) + + assert bignum_is_normalised(bn_x) + assert x_new == (x_old >> 1) + + +def assert_bn_setbit(x_old, i): + bn_x = int_to_bignum(x_old) + lib.bn_setbit(bn_x, c_uint16(i)) + x_new = bignum_to_int(bn_x) + + assert bignum_is_normalised(bn_x) + assert x_new == x_old | (1 << i) + + +def assert_bn_clearbit(x_old, i): + bn_x = int_to_bignum(x_old) + lib.bn_clearbit(bn_x, c_uint16(i)) + x_new = bignum_to_int(bn_x) + + assert bignum_is_normalised(bn_x) + assert x_new == x_old & ~(1 << i) + + +def assert_bn_testbit(x_old, i): + bn_x = int_to_bignum(x_old) + return_value = lib.bn_testbit(bn_x, c_uint16(i)) + + assert return_value == x_old >> i & 1 + + +def assert_bn_xor(x, y): + bn_res = bignum() + bn_x = int_to_bignum(x) + bn_y = int_to_bignum(y) + lib.bn_xor(bn_res, bn_x, bn_y) + res = bignum_to_int(bn_res) + + assert res == x ^ y + + +def assert_bn_mult_half(x_old, prime): + bn_x = int_to_bignum(x_old) + bn_prime = int_to_bignum(prime) + lib.bn_mult_half(bn_x, bn_prime) + x_new = bignum_to_int(bn_x) + + assert implication( + number_is_partly_reduced(x_old, prime), number_is_partly_reduced(x_new, prime) + ) + assert x_new == (x_old + prime) >> 1 if x_old & 1 else x_old >> 1 + + +def assert_bn_mult_k(x_old, k, prime): + bn_x = int_to_bignum(x_old) + bn_prime = int_to_bignum(prime) + lib.bn_mult_k(bn_x, c_uint8(k), bn_prime) + x_new = bignum_to_int(bn_x) + + assert bignum_is_normalised(bn_x) + assert number_is_partly_reduced(x_new, prime) + assert x_new == (x_old * k) % prime + + +def assert_bn_mod(x_old, prime): + bn_x = int_to_bignum(x_old) + bn_prime = int_to_bignum(prime) + lib.bn_mod(bn_x, bn_prime) + x_new = bignum_to_int(bn_x) + + assert bignum_is_normalised(bn_x) + assert number_is_fully_reduced(x_new, prime) + assert x_new == x_old % prime + + +def assert_bn_multiply_long(k_old, x_old): + bn_k = int_to_bignum(k_old) + bn_x = int_to_bignum(x_old) + bn_res = bignum(2 * limbs_number) + lib.bn_multiply_long(bn_k, bn_x, bn_res) + res = bignum_to_int(bn_res, 2 * limbs_number) + + assert res == k_old * x_old + + +def assert_bn_multiply_reduce_step(res_old, prime, d): + bn_res = int_to_bignum(res_old, 2 * limbs_number) + bn_prime = int_to_bignum(prime) + lib.bn_multiply_reduce_step(bn_res, bn_prime, d) + res_new = bignum_to_int(bn_res, 2 * limbs_number) + + assert bignum_is_normalised(bn_res) + assert res_new < 2 * prime * 2 ** (d * bits_per_limb) + + +def assert_bn_multiply(k, x_old, prime): + bn_k = int_to_bignum(k) + bn_x = int_to_bignum(x_old) + bn_prime = int_to_bignum(prime) + lib.bn_multiply(bn_k, bn_x, bn_prime) + x_new = bignum_to_int(bn_x) + + assert bignum_is_normalised(bn_x) + assert number_is_partly_reduced(x_new, prime) + assert x_new == (k * x_old) % prime + + +def assert_bn_fast_mod(x_old, prime): + bn_x = int_to_bignum(x_old) + bn_prime = int_to_bignum(prime) + lib.bn_fast_mod(bn_x, bn_prime) + x_new = bignum_to_int(bn_x) + + assert bignum_is_normalised(bn_x) + assert number_is_partly_reduced(x_new, prime) + assert x_new % prime == x_old % prime + + +def assert_bn_fast_mod_bn(bn_x, prime): + bn_x + x_old = bignum_to_int(bn_x) + bn_prime = int_to_bignum(prime) + lib.bn_fast_mod(bn_x, bn_prime) + x_new = bignum_to_int(bn_x) + + assert bignum_is_normalised(bn_x) + assert number_is_partly_reduced(x_new, prime) + assert x_new % prime == x_old % prime + + +def assert_bn_power_mod(x, e, prime): + bn_x = int_to_bignum(x) + bn_e = int_to_bignum(e) + bn_prime = int_to_bignum(prime) + bn_res_new = bignum() + lib.bn_power_mod(bn_x, bn_e, bn_prime, bn_res_new) + res_new = bignum_to_int(bn_res_new) + + assert bignum_is_normalised(bn_res_new) + assert number_is_partly_reduced(res_new, prime) + assert res_new % prime == pow(x, e, prime) + + +def assert_bn_sqrt(x_old, prime): + bn_x = int_to_bignum(x_old) + bn_prime = int_to_bignum(prime) + lib.bn_sqrt(bn_x, bn_prime) + x_new = bignum_to_int(bn_x) + + assert bignum_is_normalised(bn_x) + assert number_is_fully_reduced(x_new, prime) + assert x_new ** 2 % prime == x_old % prime + + +def assert_inverse_mod_power_two(x, m): + return_value = lib.inverse_mod_power_two(c_uint32(x), c_uint32(m)) + + assert return_value * x % 2 ** m == 1 + + +def assert_bn_divide_base(x_old, prime): + bn_x = int_to_bignum(x_old) + bn_prime = int_to_bignum(prime) + lib.bn_divide_base(bn_x, bn_prime) + x_new = bignum_to_int(bn_x) + + assert implication( + number_is_fully_reduced(x_old, prime), number_is_fully_reduced(x_new, prime) + ) + assert implication( + number_is_partly_reduced(x_old, prime), number_is_partly_reduced(x_new, prime) + ) + assert x_new * 2 ** bits_per_limb % prime == x_old % prime + + +def assert_bn_inverse(x_old, prime): + bn_x = int_to_bignum(x_old) + bn_prime = int_to_bignum(prime) + lib.bn_inverse(bn_x, bn_prime) + x_new = bignum_to_int(bn_x) + + assert bignum_is_normalised(bn_x) + assert number_is_fully_reduced(x_new, prime) + assert (x_old == 0 and x_new == 0) or (x_old != 0 and (x_old * x_new) % prime == 1) + + +def assert_bn_normalize(bn_x): + x_old = bignum_to_int(bn_x) + lib.bn_normalize(bn_x) + x_new = bignum_to_int(bn_x) + + assert x_new == x_old % 2 ** (bits_per_limb * limbs_number) + assert bignum_is_normalised(bn_x) + + +def assert_bn_add(x_old, y): + bn_x = int_to_bignum(x_old) + bn_y = int_to_bignum(y) + lib.bn_add(bn_x, bn_y) + x_new = bignum_to_int(bn_x) + y = bignum_to_int(bn_y) + + assert bignum_is_normalised(bn_x) + assert x_new == x_old + y + + +def assert_bn_addmod(x_old, y, prime): + bn_x = int_to_bignum(x_old) + bn_y = int_to_bignum(y) + bn_prime = int_to_bignum(prime) + lib.bn_addmod(bn_x, bn_y, bn_prime) + x_new = bignum_to_int(bn_x) + + assert bignum_is_normalised(bn_x) + assert number_is_partly_reduced(x_new, prime) + assert x_new % prime == (x_old + y) % prime + + +def assert_bn_addi(x_old, y): + bn_x = int_to_bignum(x_old) + lib.bn_addi(bn_x, c_uint32(y)) + x_new = bignum_to_int(bn_x) + + assert bignum_is_normalised(bn_x) + assert x_new == x_old + y + + +def assert_bn_subi(x_old, y, prime): + bn_x = int_to_bignum(x_old) + bn_prime = int_to_bignum(prime) + lib.bn_subi(bn_x, c_uint32(y), bn_prime) + x_new = bignum_to_int(bn_x) + + assert bignum_is_normalised(bn_x) + assert implication( + number_is_fully_reduced(x_old, prime), number_is_partly_reduced(x_new, prime) + ) + assert x_new % prime == (x_old - y) % prime + + +def assert_bn_subtractmod(x, y, prime): + bn_x = int_to_bignum(x) + bn_y = int_to_bignum(y) + bn_prime = int_to_bignum(prime) + bn_res = bignum() + lib.bn_subtractmod(bn_x, bn_y, bn_res, bn_prime) + res = bignum_to_int(bn_res) + + assert bignum_is_normalised(bn_x) + assert res % prime == (x - y) % prime + + +def assert_bn_subtract(x, y): + bn_x = int_to_bignum(x) + bn_y = int_to_bignum(y) + bn_res = bignum() + lib.bn_subtract(bn_x, bn_y, bn_res) + res = bignum_to_int(bn_res) + + assert bignum_is_normalised(bn_x) + assert res == x - y + + +def assert_bn_long_division(x, d): + bn_x = int_to_bignum(x) + bn_q = bignum() + uint32_p_r = uint32_p() + lib.bn_long_division(bn_x, d, bn_q, uint32_p_r) + r = uint32_p_to_int(uint32_p_r) + q = bignum_to_int(bn_q) + + assert bignum_is_normalised(bn_q) + assert q == x // d + assert r == x % d + + +def assert_bn_divmod58(x_old): + bn_x = int_to_bignum(x_old) + uint32_p_r = uint32_p() + lib.bn_divmod58(bn_x, uint32_p_r) + x_new = bignum_to_int(bn_x) + r = uint32_p_to_int(uint32_p_r) + + assert bignum_is_normalised(bn_x) + assert x_new == x_old // 58 + assert r == x_old % 58 + + +def assert_bn_divmod1000(x_old): + bn_x = int_to_bignum(x_old) + uint32_p_r = uint32_p() + lib.bn_divmod1000(bn_x, uint32_p_r) + x_new = bignum_to_int(bn_x) + r = uint32_p_to_int(uint32_p_r) + + assert bignum_is_normalised(bn_x) + assert x_new == x_old // 1000 + assert r == x_old % 1000 + + +def assert_bn_divmod10(x_old): + bn_x = int_to_bignum(x_old) + uint32_p_r = uint32_p() + lib.bn_divmod10(bn_x, uint32_p_r) + x_new = bignum_to_int(bn_x) + r = uint32_p_to_int(uint32_p_r) + + assert bignum_is_normalised(bn_x) + assert x_new == x_old // 10 + assert r == x_old % 10 + + +def assert_bn_format(x, prefix, suffix, decimals, exponent, trailing): + def format(amount, prefix, suffix, decimals, exponent, trailing): + if exponent >= 0: + amount *= 10 ** exponent + else: + amount //= 10 ** (-exponent) + + d = pow(10, decimals) + + if decimals: + output = "%d.%0*d" % (amount // d, decimals, amount % d) + if not trailing: + output = output.rstrip("0").rstrip(".") + else: + output = "%d" % (amount // d) + + return prefix + output + suffix + + def string_to_char_p(string): + return ctypes.create_string_buffer(string.encode("ascii")) + + def char_p_to_string(pointer): + return str(pointer.value, "ascii") + + bn_x = int_to_bignum(x) + output_length = 100 + output = string_to_char_p("?" * output_length) + return_value = lib.bn_format( + bn_x, + string_to_char_p(prefix), + string_to_char_p(suffix), + c_uint(decimals), + c_int(exponent), + c_bool(trailing), + output, + c_size_t(output_length), + ) + + correct_output = format(x, prefix, suffix, decimals, exponent, trailing) + correct_return_value = len(correct_output) + if len(correct_output) >= output_length: + correct_output = "" + correct_return_value = 0 + + assert char_p_to_string(output) == correct_output + assert return_value == correct_return_value + + +def test_bn_read_be(r): + assert_bn_read_be(r.rand_int_256()) + + +def test_bn_read_le(r): + assert_bn_read_le(r.rand_int_256()) + + +def test_bn_write_be(r): + assert_bn_write_be(r.rand_int_256()) + + +def test_bn_write_le(r): + assert_bn_write_le(r.rand_int_256()) + + +def test_bn_read_uint32(r): + assert_bn_read_uint32(r.rand_int_bitsize(32)) + + +def test_bn_read_uint64(r): + assert_bn_read_uint64(r.rand_int_bitsize(64)) + + +def test_bn_bitcount_1(r): + assert_bn_bitcount(r.rand_int_normalized()) + + +def test_bn_bitcount_2(bignum_bit_index): + assert_bn_bitcount(2 ** bignum_bit_index - 1) + assert_bn_bitcount(2 ** bignum_bit_index) + + +def test_bn_digitcount_1(r): + assert_bn_digitcount(r.rand_int_normalized()) + + +def test_bn_digitcount_2(bignum_decimal_digit_index): + assert_bn_digitcount(10 ** bignum_decimal_digit_index - 1) + assert_bn_digitcount(10 ** bignum_decimal_digit_index) + + +def test_bn_zero(): + assert_bn_zero() + + +def test_bn_one(): + assert_bn_one() + + +def test_bn_is_zero_1(): + assert_bn_is_zero(0) + assert_bn_is_zero(1) + + +def test_bn_is_zero_2(bignum_bit_index): + assert_bn_is_zero(2 ** bignum_bit_index) + + +def test_bn_is_one_1(): + assert_bn_is_one(0) + assert_bn_is_one(1) + + +def test_bn_is_one_2(bignum_bit_index): + assert_bn_is_one(2 ** bignum_bit_index) + + +def test_bn_is_less_1(r): + a = r.rand_int_normalized() + b = r.rand_int_normalized() + assert_bn_is_less(a, a) + assert_bn_is_less(a, b) + assert_bn_is_less(b, a) + + +def test_bn_is_less_2(r): + a = r.rand_int_normalized() + i = r.rand_bit_index() + b = a ^ 2 ** i + assert_bn_is_less(a, b) + + +def test_bn_is_less_3(): + assert_bn_is_less(0, 0) + assert_bn_is_less(1, 0) + assert_bn_is_less(0, 1) + assert_bn_is_less(1, 1) + + +def test_bn_is_equal_1(r): + a = r.rand_int_normalized() + b = r.rand_int_normalized() + assert_bn_is_equal(a, a) + assert_bn_is_equal(a, b) + + +def test_bn_is_equal_2(): + assert_bn_is_equal(0, 0) + assert_bn_is_equal(1, 0) + assert_bn_is_equal(0, 1) + assert_bn_is_equal(1, 1) + + +def test_bn_cmov(r): + a = r.rand_int_normalized() + b = r.rand_int_normalized() + assert_bn_cmov(0, a, b) + assert_bn_cmov(1, a, b) + + +def test_bn_cnegate(r, prime): + a = r.rand_int_reduced(prime) + assert_bn_cnegate(0, a, prime) + assert_bn_cnegate(1, a, prime) + + +def test_bn_lshift(r): + assert_bn_lshift(r.rand_int_normalized() // 2) + + +def test_bn_rshift(r): + assert_bn_rshift(r.rand_int_normalized()) + + +def test_bn_testbit(r): + assert_bn_testbit(r.rand_int_normalized(), r.rand_bit_index()) + + +def test_bn_setbit(r): + assert_bn_setbit(r.rand_int_normalized(), r.rand_bit_index()) + + +def test_bn_clearbit(r): + assert_bn_clearbit(r.rand_int_normalized(), r.rand_bit_index()) + + +def test_bn_xor(r): + assert_bn_xor(r.rand_int_normalized(), r.rand_int_normalized()) + + +def test_bn_mult_half_1(r, prime): + assert_bn_mult_half(r.rand_int_reduced(prime), prime) + + +def test_bn_mult_half_2(r, prime): + assert_bn_mult_half(r.rand_int_normalized(), prime) + + +def test_bn_mult_k(r, prime): + assert_bn_mult_k(r.rand_int_normalized(), r.randrange(9), prime) + + +def test_bn_mod_1(r, prime): + assert_bn_mod(r.rand_int_reduced(prime), prime) + + +def test_bn_mod_2(r, prime): + for x in [ + 0, + 1, + 2, + prime - 2, + prime - 1, + prime, + prime + 1, + prime + 2, + 2 * prime - 2, + 2 * prime - 1, + ]: + assert_bn_mod(x, prime) + + +def test_bn_multiply_long(r, prime): + x = r.randrange(floor(sqrt(2 ** 519))) + k = r.randrange(floor(sqrt(2 ** 519))) + assert_bn_multiply_long(k, x) + + +def test_bn_multiply_reduce_step(r, prime): + k = r.randrange(0, limbs_number) + res = r.randrange(2 ** (256 + 29 * k + 31)) + assert_bn_multiply_reduce_step(res, prime, k) + + +def test_bn_multiply(r, prime): + x = r.randrange(floor(sqrt(2 ** 519))) + k = r.randrange(floor(sqrt(2 ** 519))) + assert_bn_multiply(k, x, prime) + + +def test_bn_fast_mod_1(r, prime): + assert_bn_fast_mod(r.rand_int_normalized(), prime) + + +def test_bn_fast_mod_2(r, prime): + bn_x = r.rand_bignum() + assert_bn_fast_mod_bn(bn_x, prime) + + +def test_bn_power_mod(r, prime): + x = r.rand_int_bitsize(259) + e = r.rand_int_normalized() + assert_bn_power_mod(x, e, prime) + + +def test_bn_sqrt_1(prime): + assert_bn_sqrt(0, prime) + assert_bn_sqrt(1, prime) + + +def test_bn_sqrt_2(r, prime): + def is_quadratic_residuum(x, p): + return pow(x, (p - 1) // 2, p) == 1 + + while True: + x = r.rand_int_bitsize(259) + if is_quadratic_residuum(x, prime): + break + + assert_bn_sqrt(x, prime) + + +def test_inverse_mod_power_two(r): + m = r.randrange(1, 33) + i = r.randrange(1, 2 ** 29, 2) + assert_inverse_mod_power_two(i, m) + + +def test_bn_divide_base(r, prime): + assert_bn_divide_base(r.rand_int_256(), prime) + + +def test_bn_inverse_1(prime): + assert_bn_inverse(0, prime) + assert_bn_inverse(1, prime) + + +def test_bn_inverse_2(r, prime): + from math import gcd + + while True: + n = r.randrange(0, prime) + if gcd(n, prime) == 1: + break + + assert_bn_inverse(n, prime) + + +def test_bn_normalize(r): + assert_bn_normalize(r.rand_bignum()) + + +def test_bn_add_1(r): + assert_bn_add(r.rand_int_256(), r.rand_int_256()) + + +def test_bn_add_2(r): + while True: + a = r.rand_int_normalized() + b = r.rand_int_normalized() + if a + b < 2 ** (limbs_number * bits_per_limb): + break + assert_bn_add(a, b) + + +def test_bn_add_3(): + a = Random().rand_int_normalized() + b = 2 ** (limbs_number * bits_per_limb) - 1 - a + assert_bn_add(a, b) + + +def test_bn_addmod(r, prime): + assert_bn_addmod(r.rand_int_normalized(), r.rand_int_normalized(), prime) + + +def test_bn_addi_1(r): + while True: + a = r.rand_int_normalized() + b = r.randrange(2 ** 32 - 2 ** bits_per_limb + 1) + if a + b < 2 ** (limbs_number * bits_per_limb): + break + assert_bn_addi(a, b) + + +def test_bn_addi_2(): + b = 2 ** 32 - 2 ** bits_per_limb + a = 2 ** (limbs_number * bits_per_limb) - 1 - b + assert_bn_addi(a, b) + + +def test_bn_subi_1(r, prime): + while True: + a = r.rand_int_normalized() + b = r.randrange(prime % 2 ** bits_per_limb) + if a + prime - b < 2 ** (limbs_number * bits_per_limb): + break + assert_bn_subi(a, b, prime) + + +def test_bn_subi_2(prime): + b = (prime % 2 ** bits_per_limb) - 1 + a = 2 ** (limbs_number * bits_per_limb) - 1 - prime + b + assert_bn_subi(a, b, prime) + + +def test_bn_subtractmod_1(r, prime): + assert_bn_subtractmod(r.rand_int_256(), r.rand_int_256(), prime) + + +def test_bn_subtractmod_2(r, prime): + while True: + a = r.rand_int_normalized() + b = r.rand_int_reduced(prime) + if a + 2 * prime - b < 2 ** (limbs_number * bits_per_limb): + break + assert_bn_subtractmod(a, b, prime) + + +def test_bn_subtractmod_3(prime): + b = 2 * prime - 1 + a = 2 ** (limbs_number * bits_per_limb) - 1 - (2 * prime - b) + assert_bn_subtractmod(a, b, prime) + + +def test_bn_subtract_1(r): + a = r.rand_int_256() + b = r.rand_int_256() + if a < b: + a, b = b, a + assert_bn_subtract(a, b) + + +def test_bn_subtract_2(r): + a = r.rand_int_normalized() + b = r.rand_int_normalized() + if a < b: + a, b = b, a + assert_bn_subtract(a, b) + + +def test_bn_long_division(r): + x = r.rand_int_normalized() + d = r.randrange(1, 61304 + 1) + assert_bn_long_division(x, d) + + +def test_bn_divmod58(r): + x = r.rand_int_normalized() + assert_bn_divmod58(x) + + +def test_bn_divmod1000(r): + x = r.rand_int_normalized() + assert_bn_divmod1000(x) + + +def test_bn_divmod10(r): + x = r.rand_int_normalized() + assert_bn_divmod10(x) + + +def test_bn_format(): + for decimals in range(0, 5): + for exponent in range(-5, 5): + for trailing in [True, False]: + for prefix in ["", "prefix"]: + for suffix in ["", "suffix"]: + for value in [123, 120]: + assert_bn_format( + value, prefix, suffix, decimals, exponent, trailing + ) diff --git a/crypto/tests/test_check.c b/crypto/tests/test_check.c index 34431fe013..ef7457523f 100644 --- a/crypto/tests/test_check.c +++ b/crypto/tests/test_check.c @@ -131,8 +131,8 @@ START_TEST(test_bignum_read_be) { bn_read_be(input, &a); - bignum256 b = {{0x286d8bd5, 0x380c7c17, 0x3c6a2ec1, 0x2d787ef5, 0x14437cd3, - 0x25a043f8, 0x1dd5263f, 0x33a162c3, 0x0000c55e}}; + bignum256 b = {{0x086d8bd5, 0x1018f82f, 0x11a8bb07, 0x0bc3f7af, 0x0437cd3b, + 0x14087f0a, 0x15498fe5, 0x10b161bb, 0xc55ece}}; for (int i = 0; i < 9; i++) { ck_assert_int_eq(a.val[i], b.val[i]); @@ -141,8 +141,8 @@ START_TEST(test_bignum_read_be) { END_TEST START_TEST(test_bignum_write_be) { - bignum256 a = {{0x286d8bd5, 0x380c7c17, 0x3c6a2ec1, 0x2d787ef5, 0x14437cd3, - 0x25a043f8, 0x1dd5263f, 0x33a162c3, 0x0000c55e}}; + bignum256 a = {{0x086d8bd5, 0x1018f82f, 0x11a8bb07, 0x0bc3f7af, 0x0437cd3b, + 0x14087f0a, 0x15498fe5, 0x10b161bb, 0xc55ece}}; uint8_t tmp[32]; bn_write_be(&a, tmp); @@ -156,10 +156,10 @@ START_TEST(test_bignum_write_be) { END_TEST START_TEST(test_bignum_is_equal) { - bignum256 a = {{0x286d8bd5, 0x380c7c17, 0x3c6a2ec1, 0x2d787ef5, 0x14437cd3, - 0x25a043f8, 0x1dd5263f, 0x33a162c3, 0x0000c55e}}; - bignum256 b = {{0x286d8bd5, 0x380c7c17, 0x3c6a2ec1, 0x2d787ef5, 0x14437cd3, - 0x25a043f8, 0x1dd5263f, 0x33a162c3, 0x0000c55e}}; + bignum256 a = {{0x086d8bd5, 0x1018f82f, 0x11a8bb07, 0x0bc3f7af, 0x0437cd3b, + 0x14087f0a, 0x15498fe5, 0x10b161bb, 0xc55ece}}; + bignum256 b = {{0x086d8bd5, 0x1018f82f, 0x11a8bb07, 0x0bc3f7af, 0x0437cd3b, + 0x14087f0a, 0x15498fe5, 0x10b161bb, 0xc55ece}}; bignum256 c = {{ 0, }}; @@ -339,6 +339,13 @@ END_TEST START_TEST(test_bignum_write_uint32) { bignum256 a; + // lowest 29 bits set + bn_read_be( + fromhex( + "000000000000000000000000000000000000000000000000000000001fffffff"), + &a); + ck_assert_int_eq(bn_write_uint32(&a), 0x1fffffff); + // lowest 30 bits set bn_read_be( fromhex( @@ -637,8 +644,8 @@ START_TEST(test_bignum_format) { "0000000000000000000000000000000000000000000000000000000000000000"), &a); r = bn_format(&a, NULL, NULL, 18, 0, false, buf, sizeof(buf)); - ck_assert_int_eq(r, 3); - ck_assert_str_eq(buf, "0.0"); + ck_assert_int_eq(r, 1); + ck_assert_str_eq(buf, "0"); bn_read_be( fromhex( @@ -757,8 +764,8 @@ START_TEST(test_bignum_format) { "0000000000000000000000000000000000000000000000000000000000989680"), &a); r = bn_format(&a, NULL, NULL, 7, 0, false, buf, sizeof(buf)); - ck_assert_int_eq(r, 3); - ck_assert_str_eq(buf, "1.0"); + ck_assert_int_eq(r, 1); + ck_assert_str_eq(buf, "1"); bn_read_be( fromhex( @@ -805,10 +812,10 @@ START_TEST(test_bignum_format) { "fffffffffffffffffffffffffffffffffffffffffffffffffffffffffe3bbb00"), &a); r = bn_format(&a, NULL, NULL, 8, 0, false, buf, sizeof(buf)); - ck_assert_int_eq(r, 72); + ck_assert_int_eq(r, 70); ck_assert_str_eq(buf, "11579208923731619542357098500868790785326998466564056403945" - "75840079131.0"); + "75840079131"); bn_read_be( fromhex( @@ -825,9 +832,9 @@ START_TEST(test_bignum_format) { "fffffffffffffffffffffffffffffffffffffffffffffffff7e52fe5afe40000"), &a); r = bn_format(&a, NULL, NULL, 18, 0, false, buf, sizeof(buf)); - ck_assert_int_eq(r, 62); + ck_assert_int_eq(r, 60); ck_assert_str_eq( - buf, "115792089237316195423570985008687907853269984665640564039457.0"); + buf, "115792089237316195423570985008687907853269984665640564039457"); bn_read_be( fromhex( @@ -875,7 +882,69 @@ START_TEST(test_bignum_format) { memset(buf, 'a', sizeof(buf)); r = bn_format(&a, "prefix", "suffix", 10, 0, false, buf, 30); ck_assert_int_eq(r, 0); - ck_assert_str_eq(buf, "prefix198552.9216486895suffix"); + ck_assert_str_eq(buf, ""); +} +END_TEST + +START_TEST(test_bignum_sqrt) { + uint32_t quadratic_residua[] = { + 1, 2, 4, 8, 9, 11, 15, 16, 17, 18, 19, 21, 22, 25, 29, + 30, 31, 32, 34, 35, 36, 38, 39, 42, 43, 44, 47, 49, 50, 58, + 59, 60, 61, 62, 64, 65, 67, 68, 69, 70, 71, 72, 76, 78, 81, + 83, 84, 86, 88, 91, 94, 98, 99, 100, 103, 107, 111, 115, 116, 118, + 120, 121, 122, 123, 124, 127, 128, 130, 131, 134, 135, 136, 137, 138, 139, + 140, 142, 144, 149, 152, 153, 156, 159, 161, 162, 165, 166, 167, 168, 169, + 171, 172, 176, 181, 182, 185, 187, 188, 189, 191, 193, 196, 197, 198, 200, + 205, 206, 209, 214, 219, 222, 223, 225, 229, 230, 231, 232, 233, 236, 237, + 239, 240, 242, 244, 246, 248, 254, 255, 256, 259, 260, 261, 262, 265, 267, + 268, 269, 270, 272, 274, 275, 276, 277, 278, 279, 280, 281, 284, 285, 287, + 288, 289, 291, 293, 298, 299, 303, 304, 306, 311, 312, 315, 318, 319, 322, + 323, 324, 327, 330, 331, 332, 334, 336, 337, 338, 339, 341, 342, 344, 349, + 351, 352, 353, 357, 359, 361, 362, 364, 365, 370, 371, 373, 374, 375, 376, + 378, 379, 382, 383, 385, 386, 387, 389, 392, 394, 395, 396, 399, 400, 409, + 410, 412, 418, 421, 423, 425, 428, 429, 431, 435, 438, 439, 441, 443, 444, + 445, 446, 450, 453, 458, 460, 461, 462, 463, 464, 465, 466, 467, 471, 472, + 473, 474, 475, 478, 479, 480, 481, 484, 485, 487, 488, 489, 492, 493, 496, + 503, 505, 508, 510, 511, 512, 517, 518, 519, 520, 521, 522, 523, 524, 525, + 527, 529, 530, 531, 533, 534, 536, 537, 538, 539, 540, 541, 544, 545, 547, + 548, 549, 550, 551, 552, 553, 554, 556, 557, 558, 560, 562, 563, 565, 568, + 570, 571, 574, 576, 578, 582, 585, 586, 587, 589, 595, 596, 597, 598, 599, + 603, 606, 607, 608, 609, 612, 613, 619, 621, 622, 623, 624, 625, 630, 633, + 636, 638, 639, 644, 645, 646, 648, 649, 651, 653, 654, 660, 662, 663, 664, + 665, 668, 671, 672, 673, 674, 676, 678, 679, 681, 682, 684, 688, 689, 698, + 702, 704, 705, 706, 707, 714, 715, 718, 722, 723, 724, 725, 728, 729, 730, + 731, 733, 735, 737, 740, 741, 742, 746, 747, 748, 750, 751, 752, 753, 755, + 756, 758, 759, 761, 763, 764, 766, 769, 770, 771, 772, 774, 775, 778, 781, + 784, 785, 788, 789, 790, 791, 792, 797, 798, 799, 800, 813, 815, 817, 818, + 819, 820, 823, 824, 833, 836, 841, 842, 846, 849, 850, 851, 856, 857, 858, + 862, 865, 870, 875, 876, 878, 882, 885, 886, 887, 888, 890, 891, 892, 893, + 895, 899, 900, 903, 906, 907, 911, 913, 915, 916, 919, 920, 921, 922, 924, + 926, 927, 928, 930, 931, 932, 934, 937, 939, 942, 943, 944, 946, 948, 949, + 950, 951, 953, 956, 958, 960, 961, 962, 963, 968, 970, 971, 974, 975, 976, + 977, 978, 984, 986, 987, 992, 995, 999}; + + bignum256 a, b; + + bn_zero(&a); + b = a; + bn_sqrt(&b, &secp256k1.prime); + ck_assert_int_eq(bn_is_equal(&a, &b), 1); + + bn_one(&a); + b = a; + bn_sqrt(&b, &secp256k1.prime); + ck_assert_int_eq(bn_is_equal(&a, &b), 1); + + // test some quadratic residua + for (size_t i = 0; i < sizeof(quadratic_residua) / sizeof(*quadratic_residua); + i++) { + bn_read_uint32(quadratic_residua[i], &a); + b = a; + bn_sqrt(&b, &secp256k1.prime); + bn_multiply(&b, &b, &secp256k1.prime); + bn_mod(&b, &secp256k1.prime); + ck_assert_int_eq(bn_is_equal(&a, &b), 1); + } } END_TEST @@ -1102,12 +1171,16 @@ START_TEST(test_bignum_divmod) { uint32_t r; int i; - bignum256 a = {{0x3fffffff, 0x3fffffff, 0x3fffffff, 0x3fffffff, 0x3fffffff, - 0x3fffffff, 0x3fffffff, 0x3fffffff, 0xffff}}; + bignum256 a; uint32_t ar[] = {15, 14, 55, 29, 44, 24, 53, 49, 18, 55, 2, 28, 5, 4, 12, 43, 18, 37, 28, 14, 30, 46, 12, 11, 17, 10, 10, 13, 24, 45, 4, 33, 44, 42, 2, 46, 34, 43, 45, 28, 21, 18, 13, 17}; + bn_read_be( + fromhex( + "ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff"), + &a); + i = 0; while (!bn_is_zero(&a) && i < 44) { bn_divmod58(&a, &r); @@ -1116,12 +1189,15 @@ START_TEST(test_bignum_divmod) { } ck_assert_int_eq(i, 44); - bignum256 b = {{0x3fffffff, 0x3fffffff, 0x3fffffff, 0x3fffffff, 0x3fffffff, - 0x3fffffff, 0x3fffffff, 0x3fffffff, 0xffff}}; + bignum256 b; uint32_t br[] = {935, 639, 129, 913, 7, 584, 457, 39, 564, 640, 665, 984, 269, 853, 907, 687, 8, 985, 570, 423, 195, 316, 237, 89, 792, 115}; + bn_read_be( + fromhex( + "ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff"), + &b); i = 0; while (!bn_is_zero(&b) && i < 26) { bn_divmod1000(&b, &r); @@ -5904,7 +5980,8 @@ static void test_codepoints_curve(const ecdsa_curve *curve) { for (i = 0; i < 64; i++) { for (j = 0; j < 8; j++) { bn_zero(&a); - a.val[(4 * i) / 30] = (uint32_t)(2 * j + 1) << (4 * i % 30); + a.val[(4 * i) / BN_BITS_PER_LIMB] = (uint32_t)(2 * j + 1) + << (4 * i % BN_BITS_PER_LIMB); bn_normalize(&a); // note that this is not a trivial test. We add 64 curve // points in the table to get that particular curve point. @@ -8670,6 +8747,7 @@ Suite *test_suite(void) { tcase_add_test(tc, test_bignum_is_less); tcase_add_test(tc, test_bignum_format); tcase_add_test(tc, test_bignum_format_uint64); + tcase_add_test(tc, test_bignum_sqrt); suite_add_tcase(s, tc); tc = tcase_create("base32"); diff --git a/crypto/tests/test_curves.py b/crypto/tests/test_curves.py index 2a15bf7790..6897cea870 100755 --- a/crypto/tests/test_curves.py +++ b/crypto/tests/test_curves.py @@ -80,14 +80,29 @@ random_iters = int(os.environ.get("ITERS", 1)) DIR = os.path.abspath(os.path.dirname(__file__)) lib = c.cdll.LoadLibrary(os.path.join(DIR, "libtrezor-crypto.so")) +BIGNUM = c.c_uint32 * 9 + class curve_info(c.Structure): _fields_ = [("bip32_name", c.c_char_p), ("params", c.c_void_p)] -lib.get_curve_by_name.restype = c.POINTER(curve_info) +class curve_point(c.Structure): + _fields_ = [("x", BIGNUM), ("y", BIGNUM)] -BIGNUM = c.c_uint32 * 9 + +class ecdsa_curve(c.Structure): + _fields_ = [ + ("prime", BIGNUM), + ("G", curve_point), + ("order", BIGNUM), + ("order_half", BIGNUM), + ("a", c.c_int), + ("b", BIGNUM), + ] + + +lib.get_curve_by_name.restype = c.POINTER(curve_info) class Random(random.Random): @@ -106,15 +121,15 @@ def int2bn(x, bn_type=BIGNUM): b = bn_type() b._int = x for i in range(len(b)): - b[i] = x % (1 << 30) - x = x >> 30 + b[i] = x % (1 << 29) + x = x >> 29 return b def bn2int(b): x = 0 for i in range(len(b)): - x += b[i] << (30 * i) + x += b[i] << (29 * i) return x @@ -130,7 +145,7 @@ def curve(request): curve_ptr = lib.get_curve_by_name(bytes(name, "ascii")).contents.params assert curve_ptr, "curve {} not found".format(name) curve_obj = curves[name] - curve_obj.ptr = c.c_void_p(curve_ptr) + curve_obj.ptr = c.cast(curve_ptr, c.POINTER(ecdsa_curve)) curve_obj.p = curve_obj.curve.p() # shorthand return curve_obj @@ -148,176 +163,6 @@ def point(request): return curve_obj -def test_inverse(curve, r): - x = r.randrange(1, curve.p) - y = int2bn(x) - lib.bn_inverse(y, int2bn(curve.p)) - y = bn2int(y) - y_ = ecdsa.numbertheory.inverse_mod(x, curve.p) - assert y == y_ - - -def test_is_less(curve, r): - x = r.randrange(0, curve.p) - y = r.randrange(0, curve.p) - x_ = int2bn(x) - y_ = int2bn(y) - - res = lib.bn_is_less(x_, y_) - assert res == (x < y) - - res = lib.bn_is_less(y_, x_) - assert res == (y < x) - - -def test_is_equal(curve, r): - x = r.randrange(0, curve.p) - y = r.randrange(0, curve.p) - x_ = int2bn(x) - y_ = int2bn(y) - - assert lib.bn_is_equal(x_, y_) == (x == y) - assert lib.bn_is_equal(x_, x_) == 1 - assert lib.bn_is_equal(y_, y_) == 1 - - -def test_is_zero(curve, r): - x = r.randrange(0, curve.p) - assert lib.bn_is_zero(int2bn(x)) == (not x) - - -def test_simple_comparisons(): - assert lib.bn_is_zero(int2bn(0)) == 1 - assert lib.bn_is_zero(int2bn(1)) == 0 - - assert lib.bn_is_less(int2bn(0), int2bn(0)) == 0 - assert lib.bn_is_less(int2bn(1), int2bn(0)) == 0 - assert lib.bn_is_less(int2bn(0), int2bn(1)) == 1 - - assert lib.bn_is_equal(int2bn(0), int2bn(0)) == 1 - assert lib.bn_is_equal(int2bn(1), int2bn(0)) == 0 - assert lib.bn_is_equal(int2bn(0), int2bn(1)) == 0 - - -def test_mult_half(curve, r): - x = r.randrange(0, 2 * curve.p) - y = int2bn(x) - lib.bn_mult_half(y, int2bn(curve.p)) - y = bn2int(y) - if y >= curve.p: - y -= curve.p - half = ecdsa.numbertheory.inverse_mod(2, curve.p) - assert y == (x * half) % curve.p - - -def test_subtractmod(curve, r): - x = r.randrange(0, 2 ** 256) - y = r.randrange(0, 2 ** 256) - z = int2bn(0) - lib.bn_subtractmod(int2bn(x), int2bn(y), z, int2bn(curve.p)) - z = bn2int(z) - z_ = x + 2 * curve.p - y - assert z == z_ - - -def test_subtract2(r): - x = r.randrange(0, 2 ** 256) - y = r.randrange(0, 2 ** 256) - x, y = max(x, y), min(x, y) - z = int2bn(0) - lib.bn_subtract(int2bn(x), int2bn(y), z) - z = bn2int(z) - z_ = x - y - assert z == z_ - - -def test_add(curve, r): - x = r.randrange(0, 2 ** 256) - y = r.randrange(0, 2 ** 256) - z_ = x + y - z = int2bn(x) - lib.bn_add(z, int2bn(y)) - z = bn2int(z) - - assert z == z_ - - -def test_addmod(curve, r): - x = r.randrange(0, 2 ** 256) - y = r.randrange(0, 2 ** 256) - z_ = (x + y) % curve.p - z = int2bn(x) - lib.bn_addmod(z, int2bn(y), int2bn(curve.p)) - z = bn2int(z) - if z >= curve.p: - z = z - curve.p - assert z == z_ - - -def test_multiply(curve, r): - k = r.randrange(0, 2 * curve.p) - x = r.randrange(0, 2 * curve.p) - z = (k * x) % curve.p - k = int2bn(k) - z_ = int2bn(x) - p_ = int2bn(curve.p) - lib.bn_multiply(k, z_, p_) - z_ = bn2int(z_) - assert z_ < 2 * curve.p - if z_ >= curve.p: - z_ = z_ - curve.p - assert z_ == z - - -def test_multiply1(curve, r): - k = r.randrange(0, 2 * curve.p) - x = r.randrange(0, 2 * curve.p) - kx = k * x - res = int2bn(0, bn_type=(c.c_uint32 * 18)) - lib.bn_multiply_long(int2bn(k), int2bn(x), res) - res = bn2int(res) - assert res == kx - - -def test_multiply2(curve, r): - x = int2bn(0) - s = r.randrange(0, 2 ** 526) - res = int2bn(s, bn_type=(c.c_uint32 * 18)) - prime = int2bn(curve.p) - lib.bn_multiply_reduce(x, res, prime) - - x = bn2int(x) % curve.p - x_ = s % curve.p - - assert x == x_ - - -def test_fast_mod(curve, r): - x = r.randrange(0, 128 * curve.p) - y = int2bn(x) - lib.bn_fast_mod(y, int2bn(curve.p)) - y = bn2int(y) - assert y < 2 * curve.p - if y >= curve.p: - y -= curve.p - assert x % curve.p == y - - -def test_mod(curve, r): - x = r.randrange(0, 2 * curve.p) - y = int2bn(x) - lib.bn_mod(y, int2bn(curve.p)) - assert bn2int(y) == x % curve.p - - -def test_mod_specific(curve): - p = curve.p - for x in [0, 1, 2, p - 2, p - 1, p, p + 1, p + 2, 2 * p - 2, 2 * p - 1]: - y = int2bn(x) - lib.bn_mod(y, int2bn(curve.p)) - assert bn2int(y) == x % p - - POINT = BIGNUM * 2 @@ -340,6 +185,16 @@ def from_JACOBIAN(p): return (bn2int(p[0]), bn2int(p[1]), bn2int(p[2])) +def test_curve_parameters(curve): + assert curve.curve.p() == bn2int(curve.ptr.contents.prime) + assert curve.generator.x() == bn2int(curve.ptr.contents.G.x) + assert curve.generator.y() == bn2int(curve.ptr.contents.G.y) + assert curve.order == bn2int(curve.ptr.contents.order) + assert curve.order // 2 == bn2int(curve.ptr.contents.order_half) + assert curve.curve.a() == curve.ptr.contents.a + assert curve.curve.b() == bn2int(curve.ptr.contents.b) + + def test_point_multiply(curve, r): p = r.randpoint(curve) k = r.randrange(0, 2 ** 256) @@ -385,15 +240,6 @@ def test_point_to_jacobian(curve, r): assert q == (p.x(), p.y()) -def test_cond_negate(curve, r): - x = r.randrange(0, curve.p) - a = int2bn(x) - lib.conditional_negate(0, a, int2bn(curve.p)) - assert bn2int(a) == x - lib.conditional_negate(-1, a, int2bn(curve.p)) - assert bn2int(a) == 2 * curve.p - x - - def test_jacobian_add(curve, r): p1 = r.randpoint(curve) p2 = r.randpoint(curve) diff --git a/crypto/tools/mktable.c b/crypto/tools/mktable.c index f9ab1c653d..2760d74959 100644 --- a/crypto/tools/mktable.c +++ b/crypto/tools/mktable.c @@ -39,7 +39,8 @@ int main(int argc, char **argv) { curve_point checkresult; bignum256 a; bn_zero(&a); - a.val[(4 * i) / 30] = ((uint32_t)2 * j + 1) << ((4 * i) % 30); + a.val[(4 * i) / BN_BITS_PER_LIMB] = ((uint32_t)2 * j + 1) + << ((4 * i) % BN_BITS_PER_LIMB); bn_normalize(&a); point_multiply(curve, &a, &curve->G, &checkresult); assert(point_is_equal(&checkresult, &ng)); From 610dedca745fa1b7118fc5ee555ff566af1db735 Mon Sep 17 00:00:00 2001 From: Tomas Susanka Date: Wed, 20 May 2020 12:29:09 +0000 Subject: [PATCH 21/24] tests/signing: fix mixed inputs test --- tests/device_tests/test_msg_signtx_mixed_inputs.py | 11 ++++------- 1 file changed, 4 insertions(+), 7 deletions(-) diff --git a/tests/device_tests/test_msg_signtx_mixed_inputs.py b/tests/device_tests/test_msg_signtx_mixed_inputs.py index 7724ba16ed..d5ebb033a0 100644 --- a/tests/device_tests/test_msg_signtx_mixed_inputs.py +++ b/tests/device_tests/test_msg_signtx_mixed_inputs.py @@ -142,7 +142,7 @@ def test_segwit_non_segwit_segwit_inputs(client): ) inp3 = messages.TxInputType( address_n=parse_path("84'/1'/0'/0/0"), - amount=123123, + amount=1603000, prev_hash=TXHASH_31bc1c, prev_index=0, script_type=messages.InputScriptType.SPENDWITNESS, @@ -169,11 +169,11 @@ def test_segwit_non_segwit_segwit_inputs(client): ) assert ( signatures[2].hex() - == "30450221008aa7c6ea2b017701145c8b062e05c35259d271ea3009229776b9ef6e17a823da022004a11059927dcc21ff3f0e9441e36e91b4e0db879d102ea6a26f84a8a5d6d35c" + == "3045022100f2d398ac6bc702cfa4f7eb3d2579a233f1d7c920c45a14329a741db6c24fde8f02203b1f6aed5671eece8ba5b5c05ec0330a43c0914b8ff606945cb8cf9e164ec88f" ) assert ( serialized_tx.hex() - == "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" + == "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" ) @@ -195,10 +195,7 @@ def test_non_segwit_segwit_non_segwit_inputs(client): script_type=messages.InputScriptType.SPENDWITNESS, ) inp3 = messages.TxInputType( - address_n=parse_path("44'/1'/1'/0/0"), - amount=1, - prev_hash=TXHASH_2bac7a, - prev_index=0, + address_n=parse_path("44'/1'/1'/0/0"), prev_hash=TXHASH_2bac7a, prev_index=0, ) out1 = messages.TxOutputType( address="tb1q54un3q39sf7e7tlfq99d6ezys7qgc62a6rxllc", From 5209804fc384ad2c206ac6890760095226302cec Mon Sep 17 00:00:00 2001 From: matejcik Date: Tue, 26 May 2020 15:37:06 +0200 Subject: [PATCH 22/24] core: relax path checks on GetPublicKey (cherry picked from commit 554d8949f5660f994a5273dbf0a0cfb17b7951db) --- core/src/apps/bitcoin/get_public_key.py | 42 ++----------------- tests/device_tests/test_msg_getpublickey.py | 2 +- .../test_msg_getpublickey_curve.py | 2 +- 3 files changed, 6 insertions(+), 40 deletions(-) diff --git a/core/src/apps/bitcoin/get_public_key.py b/core/src/apps/bitcoin/get_public_key.py index 1cd98d5fad..2b007d59f9 100644 --- a/core/src/apps/bitcoin/get_public_key.py +++ b/core/src/apps/bitcoin/get_public_key.py @@ -3,50 +3,16 @@ from trezor.messages import InputScriptType from trezor.messages.HDNodeType import HDNodeType from trezor.messages.PublicKey import PublicKey -from apps.common import HARDENED, coins, layout, seed - -from .keychain import get_keychain_for_coin - - -async def get_keychain_for_curve(ctx: wire.Context, curve_name: str) -> seed.Keychain: - """Set up a keychain for SLIP-13 and SLIP-17 namespaces with a specified curve.""" - namespaces = [ - (curve_name, [13 | HARDENED]), - (curve_name, [17 | HARDENED]), - ] - return await seed.get_keychain(ctx, namespaces) +from apps.common import coins, layout, seed async def get_public_key(ctx, msg): coin_name = msg.coin_name or "Bitcoin" script_type = msg.script_type or InputScriptType.SPENDADDRESS + coin = coins.by_name(coin_name) + curve_name = msg.ecdsa_curve_name or coin.curve_name - if msg.ecdsa_curve_name is not None: - # If a curve name is provided, disallow coin-specific features. - if ( - msg.coin_name is not None - or msg.script_type is not InputScriptType.SPENDADDRESS - ): - raise wire.DataError( - "Cannot use coin_name or script_type with ecdsa_curve_name" - ) - - coin = coins.by_name("Bitcoin") - # only allow SLIP-13/17 namespaces - keychain = await get_keychain_for_curve(ctx, msg.ecdsa_curve_name) - - elif ( - coin_name == "Bitcoin" - and script_type is InputScriptType.SPENDADDRESS - and msg.address_n == [HARDENED] - ): - # allow extracting PSBT master fingerprinty by calling GetPublicKey(m/0') - coin = coins.by_name("Bitcoin") - keychain = await seed.get_keychain(ctx, [("secp256k1", [HARDENED])]) - - else: - # select curve and namespaces based on the requested coin properties - keychain, coin = await get_keychain_for_coin(ctx, msg.coin_name) + keychain = await seed.get_keychain(ctx, [(curve_name, [])]) node = keychain.derive(msg.address_n) diff --git a/tests/device_tests/test_msg_getpublickey.py b/tests/device_tests/test_msg_getpublickey.py index c23277b1ba..2286dda41b 100644 --- a/tests/device_tests/test_msg_getpublickey.py +++ b/tests/device_tests/test_msg_getpublickey.py @@ -116,7 +116,7 @@ def test_get_public_node(client, coin_name, xpub_magic, path, xpub): assert bip32.serialize(res.node, xpub_magic) == xpub -@pytest.mark.skip_t1 +@pytest.mark.xfail(reason="Currently path validation on get_public_node is disabled.") @pytest.mark.parametrize("coin_name, path", VECTORS_INVALID) def test_invalid_path(client, coin_name, path): with pytest.raises(TrezorFailure, match="Forbidden key path"): diff --git a/tests/device_tests/test_msg_getpublickey_curve.py b/tests/device_tests/test_msg_getpublickey_curve.py index 4f2f1594e7..3b034c6963 100644 --- a/tests/device_tests/test_msg_getpublickey_curve.py +++ b/tests/device_tests/test_msg_getpublickey_curve.py @@ -65,7 +65,7 @@ def test_ed25519_public(client): btc.get_public_node(client, PATH_PUBLIC, ecdsa_curve_name="ed25519") -@pytest.mark.skip_t1 +@pytest.mark.xfail(reason="Currently path validation on get_public_node is disabled.") def test_coin_and_curve(client): with pytest.raises( TrezorFailure, match="Cannot use coin_name or script_type with ecdsa_curve_name" From 81553df02f2a21f821e6f50297aa92b5a7e456a3 Mon Sep 17 00:00:00 2001 From: Tomas Susanka Date: Mon, 25 May 2020 18:43:31 +0000 Subject: [PATCH 23/24] legacy: add ToS dialog to recovery (cherry picked from commit 28b22cef224b25975a81821cf705afababb49dd5) --- legacy/firmware/recovery.c | 3 ++- 1 file changed, 2 insertions(+), 1 deletion(-) diff --git a/legacy/firmware/recovery.c b/legacy/firmware/recovery.c index b1f4db8037..38fa2e9fea 100644 --- a/legacy/firmware/recovery.c +++ b/legacy/firmware/recovery.c @@ -482,7 +482,8 @@ void recovery_init(uint32_t _word_count, bool passphrase_protection, if (!dry_run) { layoutDialogSwipe(&bmp_icon_question, _("Cancel"), _("Confirm"), NULL, _("Do you really want to"), _("recover the device?"), - NULL, NULL, NULL, NULL); + NULL, _("By continuing you"), _("agree to trezor.io/tos"), + NULL); if (!protectButton(ButtonRequestType_ButtonRequest_ProtectCall, false)) { fsm_sendFailure(FailureType_Failure_ActionCancelled, NULL); layoutHome(); From c6b2580cd245ee924507f45e9675f857a3d78768 Mon Sep 17 00:00:00 2001 From: Pavol Rusnak Date: Mon, 1 Jun 2020 23:39:17 +0200 Subject: [PATCH 24/24] ci/Dockerfile: set PIPENV_CACHE_DIR (cherry picked from commit ae2d5813f0de74502aa6d75a535479b396af4523) --- ci/Dockerfile | 5 +++-- 1 file changed, 3 insertions(+), 2 deletions(-) diff --git a/ci/Dockerfile b/ci/Dockerfile index 39ccb05a98..454e99c949 100644 --- a/ci/Dockerfile +++ b/ci/Dockerfile @@ -118,8 +118,6 @@ ENV PYTHON=python3 # use zipfile module to extract files world-readable RUN ${PYTHON} -m zipfile -e "protoc-${PROTOBUF_VERSION}-linux-x86_64.zip" /usr/local && chmod 755 /usr/local/bin/protoc -ENV WORKON_HOME=/tmp/.venvs - # download monero tests binary ENV TREZOR_MONERO_TESTS_SHA256SUM=5b35342c79eb91265f5f427224016a52994fff32c8ea078de5d502b37d3022d6 @@ -134,6 +132,9 @@ RUN if [ "${FULLDEPS_TESTING}" = "1" ]; then \ # install python dependencies +ENV WORKON_HOME=/tmp/.venvs +ENV PIPENV_CACHE_DIR=/tmp/.pipenv-cache + RUN ${PYTHON} -m pip install pipenv RUN ${PYTHON} --version