mirror of
https://github.com/trezor/trezor-firmware.git
synced 2024-11-22 07:28:10 +00:00
use curve25519-donna from floodyberry
This commit is contained in:
Pavol Rusnak
parent
bede439a62
commit
0abc61f672
4
Makefile
4
Makefile
@ -46,7 +46,7 @@ SRCS += sha2.c
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SRCS += sha3.c
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SRCS += aescrypt.c aeskey.c aestab.c aes_modes.c
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SRCS += ed25519-donna/ed25519.c
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SRCS += curve25519-donna/curve25519-donna.c
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SRCS += curve25519-donna/curve25519.c
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OBJS = $(SRCS:.c=.o)
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@ -62,7 +62,7 @@ tests: tests.o $(OBJS)
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$(CC) tests.o $(OBJS) $(TESTLIBS) -o tests
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test_speed: test_speed.o $(OBJS)
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$(CC) test_speed.o $(OBJS) $(TESTLIBS) -o test_speed
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$(CC) test_speed.o $(OBJS) -o test_speed
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test-openssl: test-openssl.o $(OBJS)
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$(CC) test-openssl.o $(OBJS) $(TESTSSLLIBS) -o test-openssl
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6
bip32.c
6
bip32.c
@ -37,7 +37,7 @@
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#include "secp256k1.h"
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#include "nist256p1.h"
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#include "ed25519.h"
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#include "curve25519-donna.h"
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#include "curve25519.h"
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#if USE_ETHEREUM
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#include "sha3.h"
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#endif
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@ -400,7 +400,7 @@ void hdnode_fill_public_key(HDNode *node)
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ed25519_publickey(node->private_key, node->public_key + 1);
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} else if (node->curve == &curve25519_info) {
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node->public_key[0] = 1;
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curve25519_publickey(node->public_key + 1, node->private_key);
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curve25519_donna_basepoint(node->public_key + 1, node->private_key);
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} else {
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ecdsa_get_public_key33(node->curve->params, node->private_key, node->public_key);
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}
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@ -466,7 +466,7 @@ int hdnode_get_shared_key(const HDNode *node, const uint8_t *peer_public_key, ui
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if (peer_public_key[0] != 0x40) {
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return 1; // Curve25519 public key should start with 0x40 byte.
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}
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curve25519_scalarmult(session_key + 1, node->private_key, peer_public_key + 1);
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curve25519_donna(session_key + 1, node->private_key, peer_public_key + 1);
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*result_size = 33;
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return 0;
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} else {
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107
curve25519-donna/README.md
Normal file
107
curve25519-donna/README.md
Normal file
@ -0,0 +1,107 @@
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[curve25519](http://cr.yp.to/ecdh.html) is an elliptic curve, developed by
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[Dan Bernstein](http://cr.yp.to/djb.html), for fast
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[Diffie-Hellman](http://en.wikipedia.org/wiki/Diffie-Hellman) key agreement.
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DJB's [original implementation](http://cr.yp.to/ecdh.html) was written in a
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language of his own devising called [qhasm](http://cr.yp.to/qhasm.html).
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The original qhasm source isn't available, only the x86 32-bit assembly output.
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This project provides performant, portable 32-bit & 64-bit implementations.
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All implementations are of course constant time in regard to secret data.
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#### Performance
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Compilers versions are gcc 4.6.3, icc 13.1.1, clang 3.4-1~exp1.
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Counts are in thousands of cycles.
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Note that SSE2 performance may be less impressive on AMD & older CPUs with slower SSE ops!
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##### E5200 @ 2.5ghz, march=core2
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<table>
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<thead><tr><th>Version</th><th>gcc</th><th>icc</th><th>clang</th></tr></thead>
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<tbody>
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<tr><td>64-bit SSE2 </td><td> 278k</td><td> 265k</td><td> 302k</td></tr>
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<tr><td>64-bit </td><td> 273k</td><td> 271k</td><td> 377k</td></tr>
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<tr><td>32-bit SSE2 </td><td> 304k</td><td> 289k</td><td> 317k</td></tr>
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<tr><td>32-bit </td><td> 1417k</td><td> 845k</td><td> 981k</td></tr>
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</tbody>
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</table>
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##### E3-1270 @ 3.4ghz, march=corei7-avx
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<table>
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<thead><tr><th>Version</th><th>gcc</th><th>icc</th><th>clang</th></tr></thead>
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<tbody>
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<tr><td>64-bit </td><td> 201k</td><td> 192k</td><td> 233k</td></tr>
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<tr><td>64-bit SSE2 </td><td> 201k</td><td> 201k</td><td> 261k</td></tr>
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<tr><td>32-bit SSE2 </td><td> 238k</td><td> 225k</td><td> 250k</td></tr>
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<tr><td>32-bit </td><td> 1293k</td><td> 822k</td><td> 848k</td></tr>
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</tbody>
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</table>
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#### Compilation
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No configuration is needed.
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##### 32-bit
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gcc curve25519.c -m32 -O3 -c
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##### 64-bit
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gcc curve25519.c -m64 -O3 -c
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##### SSE2
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gcc curve25519.c -m32 -O3 -c -DCURVE25519_SSE2 -msse2
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gcc curve25519.c -m64 -O3 -c -DCURVE25519_SSE2
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clang, icc, and msvc are also supported
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##### Named Versions
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Define CURVE25519_SUFFIX to append a suffix to public functions, e.g.
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`-DCURVE25519_SUFFIX=_sse2` to create curve25519_donna_sse2 and
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curve25519_donna_basepoint_sse2.
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#### Usage
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To use the code, link against `curve25519.o` and:
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#include "curve25519.h"
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To generate a private/secret key, generate 32 cryptographically random bytes:
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curve25519_key sk;
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randombytes(sk, sizeof(curve25519_key));
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Manual clamping is not needed, and it is actually not possible to use unclamped
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keys due to the code taking advantage of the clamped bits internally.
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To generate the public key from the private/secret key:
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curve25519_key pk;
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curve25519_donna_basepoint(pk, sk);
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To generate a shared key with your private/secret key and someone elses public key:
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curve25519_key shared;
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curve25519_donna(shared, mysk, yourpk);
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And hash `shared` with a cryptographic hash before using, or e.g. pass `shared` through
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HSalsa20/HChacha as NaCl does.
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#### Testing
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Fuzzing against a reference implemenation is now available. See [fuzz/README](fuzz/README.md).
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Building `curve25519.c` and linking with `test.c` will run basic sanity tests and benchmark curve25519_donna.
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#### Papers
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[djb's curve25519 paper](http://cr.yp.to/ecdh/curve25519-20060209.pdf)
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#### License
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Public Domain, or MIT
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466
curve25519-donna/curve25519-donna-32bit.h
Normal file
466
curve25519-donna/curve25519-donna-32bit.h
Normal file
@ -0,0 +1,466 @@
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typedef uint32_t bignum25519[10];
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static const uint32_t reduce_mask_26 = (1 << 26) - 1;
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static const uint32_t reduce_mask_25 = (1 << 25) - 1;
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/* out = in */
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DONNA_INLINE static void
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curve25519_copy(bignum25519 out, const bignum25519 in) {
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out[0] = in[0];
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out[1] = in[1];
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out[2] = in[2];
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out[3] = in[3];
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out[4] = in[4];
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out[5] = in[5];
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out[6] = in[6];
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out[7] = in[7];
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out[8] = in[8];
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out[9] = in[9];
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}
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/* out = a + b */
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DONNA_INLINE static void
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curve25519_add(bignum25519 out, const bignum25519 a, const bignum25519 b) {
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out[0] = a[0] + b[0];
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out[1] = a[1] + b[1];
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out[2] = a[2] + b[2];
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out[3] = a[3] + b[3];
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out[4] = a[4] + b[4];
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out[5] = a[5] + b[5];
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out[6] = a[6] + b[6];
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out[7] = a[7] + b[7];
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out[8] = a[8] + b[8];
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out[9] = a[9] + b[9];
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}
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/* out = a - b */
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DONNA_INLINE static void
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curve25519_sub(bignum25519 out, const bignum25519 a, const bignum25519 b) {
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uint32_t c;
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out[0] = 0x7ffffda + a[0] - b[0] ; c = (out[0] >> 26); out[0] &= reduce_mask_26;
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out[1] = 0x3fffffe + a[1] - b[1] + c; c = (out[1] >> 25); out[1] &= reduce_mask_25;
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out[2] = 0x7fffffe + a[2] - b[2] + c; c = (out[2] >> 26); out[2] &= reduce_mask_26;
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out[3] = 0x3fffffe + a[3] - b[3] + c; c = (out[3] >> 25); out[3] &= reduce_mask_25;
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out[4] = 0x7fffffe + a[4] - b[4] + c; c = (out[4] >> 26); out[4] &= reduce_mask_26;
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out[5] = 0x3fffffe + a[5] - b[5] + c; c = (out[5] >> 25); out[5] &= reduce_mask_25;
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out[6] = 0x7fffffe + a[6] - b[6] + c; c = (out[6] >> 26); out[6] &= reduce_mask_26;
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out[7] = 0x3fffffe + a[7] - b[7] + c; c = (out[7] >> 25); out[7] &= reduce_mask_25;
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out[8] = 0x7fffffe + a[8] - b[8] + c; c = (out[8] >> 26); out[8] &= reduce_mask_26;
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out[9] = 0x3fffffe + a[9] - b[9] + c; c = (out[9] >> 25); out[9] &= reduce_mask_25;
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out[0] += 19 * c;
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}
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/* out = in * scalar */
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DONNA_INLINE static void
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curve25519_scalar_product(bignum25519 out, const bignum25519 in, const uint32_t scalar) {
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uint64_t a;
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uint32_t c;
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a = mul32x32_64(in[0], scalar); out[0] = (uint32_t)a & reduce_mask_26; c = (uint32_t)(a >> 26);
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a = mul32x32_64(in[1], scalar) + c; out[1] = (uint32_t)a & reduce_mask_25; c = (uint32_t)(a >> 25);
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a = mul32x32_64(in[2], scalar) + c; out[2] = (uint32_t)a & reduce_mask_26; c = (uint32_t)(a >> 26);
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a = mul32x32_64(in[3], scalar) + c; out[3] = (uint32_t)a & reduce_mask_25; c = (uint32_t)(a >> 25);
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a = mul32x32_64(in[4], scalar) + c; out[4] = (uint32_t)a & reduce_mask_26; c = (uint32_t)(a >> 26);
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a = mul32x32_64(in[5], scalar) + c; out[5] = (uint32_t)a & reduce_mask_25; c = (uint32_t)(a >> 25);
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a = mul32x32_64(in[6], scalar) + c; out[6] = (uint32_t)a & reduce_mask_26; c = (uint32_t)(a >> 26);
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a = mul32x32_64(in[7], scalar) + c; out[7] = (uint32_t)a & reduce_mask_25; c = (uint32_t)(a >> 25);
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a = mul32x32_64(in[8], scalar) + c; out[8] = (uint32_t)a & reduce_mask_26; c = (uint32_t)(a >> 26);
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a = mul32x32_64(in[9], scalar) + c; out[9] = (uint32_t)a & reduce_mask_25; c = (uint32_t)(a >> 25);
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out[0] += c * 19;
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}
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/* out = a * b */
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DONNA_INLINE static void
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curve25519_mul(bignum25519 out, const bignum25519 a, const bignum25519 b) {
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uint32_t r0,r1,r2,r3,r4,r5,r6,r7,r8,r9;
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uint32_t s0,s1,s2,s3,s4,s5,s6,s7,s8,s9;
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uint64_t m0,m1,m2,m3,m4,m5,m6,m7,m8,m9,c;
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uint32_t p;
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r0 = b[0];
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r1 = b[1];
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r2 = b[2];
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r3 = b[3];
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r4 = b[4];
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r5 = b[5];
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r6 = b[6];
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r7 = b[7];
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r8 = b[8];
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r9 = b[9];
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s0 = a[0];
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s1 = a[1];
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s2 = a[2];
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s3 = a[3];
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s4 = a[4];
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s5 = a[5];
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s6 = a[6];
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s7 = a[7];
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s8 = a[8];
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s9 = a[9];
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m1 = mul32x32_64(r0, s1) + mul32x32_64(r1, s0);
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m3 = mul32x32_64(r0, s3) + mul32x32_64(r1, s2) + mul32x32_64(r2, s1) + mul32x32_64(r3, s0);
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m5 = mul32x32_64(r0, s5) + mul32x32_64(r1, s4) + mul32x32_64(r2, s3) + mul32x32_64(r3, s2) + mul32x32_64(r4, s1) + mul32x32_64(r5, s0);
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m7 = mul32x32_64(r0, s7) + mul32x32_64(r1, s6) + mul32x32_64(r2, s5) + mul32x32_64(r3, s4) + mul32x32_64(r4, s3) + mul32x32_64(r5, s2) + mul32x32_64(r6, s1) + mul32x32_64(r7, s0);
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m9 = mul32x32_64(r0, s9) + mul32x32_64(r1, s8) + mul32x32_64(r2, s7) + mul32x32_64(r3, s6) + mul32x32_64(r4, s5) + mul32x32_64(r5, s4) + mul32x32_64(r6, s3) + mul32x32_64(r7, s2) + mul32x32_64(r8, s1) + mul32x32_64(r9, s0);
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r1 *= 2;
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r3 *= 2;
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r5 *= 2;
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r7 *= 2;
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m0 = mul32x32_64(r0, s0);
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m2 = mul32x32_64(r0, s2) + mul32x32_64(r1, s1) + mul32x32_64(r2, s0);
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m4 = mul32x32_64(r0, s4) + mul32x32_64(r1, s3) + mul32x32_64(r2, s2) + mul32x32_64(r3, s1) + mul32x32_64(r4, s0);
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m6 = mul32x32_64(r0, s6) + mul32x32_64(r1, s5) + mul32x32_64(r2, s4) + mul32x32_64(r3, s3) + mul32x32_64(r4, s2) + mul32x32_64(r5, s1) + mul32x32_64(r6, s0);
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m8 = mul32x32_64(r0, s8) + mul32x32_64(r1, s7) + mul32x32_64(r2, s6) + mul32x32_64(r3, s5) + mul32x32_64(r4, s4) + mul32x32_64(r5, s3) + mul32x32_64(r6, s2) + mul32x32_64(r7, s1) + mul32x32_64(r8, s0);
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r1 *= 19;
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r2 *= 19;
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r3 = (r3 / 2) * 19;
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r4 *= 19;
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r5 = (r5 / 2) * 19;
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r6 *= 19;
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r7 = (r7 / 2) * 19;
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r8 *= 19;
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r9 *= 19;
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m1 += (mul32x32_64(r9, s2) + mul32x32_64(r8, s3) + mul32x32_64(r7, s4) + mul32x32_64(r6, s5) + mul32x32_64(r5, s6) + mul32x32_64(r4, s7) + mul32x32_64(r3, s8) + mul32x32_64(r2, s9));
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m3 += (mul32x32_64(r9, s4) + mul32x32_64(r8, s5) + mul32x32_64(r7, s6) + mul32x32_64(r6, s7) + mul32x32_64(r5, s8) + mul32x32_64(r4, s9));
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m5 += (mul32x32_64(r9, s6) + mul32x32_64(r8, s7) + mul32x32_64(r7, s8) + mul32x32_64(r6, s9));
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m7 += (mul32x32_64(r9, s8) + mul32x32_64(r8, s9));
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r3 *= 2;
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r5 *= 2;
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r7 *= 2;
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r9 *= 2;
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m0 += (mul32x32_64(r9, s1) + mul32x32_64(r8, s2) + mul32x32_64(r7, s3) + mul32x32_64(r6, s4) + mul32x32_64(r5, s5) + mul32x32_64(r4, s6) + mul32x32_64(r3, s7) + mul32x32_64(r2, s8) + mul32x32_64(r1, s9));
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m2 += (mul32x32_64(r9, s3) + mul32x32_64(r8, s4) + mul32x32_64(r7, s5) + mul32x32_64(r6, s6) + mul32x32_64(r5, s7) + mul32x32_64(r4, s8) + mul32x32_64(r3, s9));
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m4 += (mul32x32_64(r9, s5) + mul32x32_64(r8, s6) + mul32x32_64(r7, s7) + mul32x32_64(r6, s8) + mul32x32_64(r5, s9));
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m6 += (mul32x32_64(r9, s7) + mul32x32_64(r8, s8) + mul32x32_64(r7, s9));
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m8 += (mul32x32_64(r9, s9));
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r0 = (uint32_t)m0 & reduce_mask_26; c = (m0 >> 26);
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m1 += c; r1 = (uint32_t)m1 & reduce_mask_25; c = (m1 >> 25);
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m2 += c; r2 = (uint32_t)m2 & reduce_mask_26; c = (m2 >> 26);
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m3 += c; r3 = (uint32_t)m3 & reduce_mask_25; c = (m3 >> 25);
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m4 += c; r4 = (uint32_t)m4 & reduce_mask_26; c = (m4 >> 26);
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m5 += c; r5 = (uint32_t)m5 & reduce_mask_25; c = (m5 >> 25);
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m6 += c; r6 = (uint32_t)m6 & reduce_mask_26; c = (m6 >> 26);
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m7 += c; r7 = (uint32_t)m7 & reduce_mask_25; c = (m7 >> 25);
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m8 += c; r8 = (uint32_t)m8 & reduce_mask_26; c = (m8 >> 26);
|
||||
m9 += c; r9 = (uint32_t)m9 & reduce_mask_25; p = (uint32_t)(m9 >> 25);
|
||||
m0 = r0 + mul32x32_64(p,19); r0 = (uint32_t)m0 & reduce_mask_26; p = (uint32_t)(m0 >> 26);
|
||||
r1 += p;
|
||||
|
||||
out[0] = r0;
|
||||
out[1] = r1;
|
||||
out[2] = r2;
|
||||
out[3] = r3;
|
||||
out[4] = r4;
|
||||
out[5] = r5;
|
||||
out[6] = r6;
|
||||
out[7] = r7;
|
||||
out[8] = r8;
|
||||
out[9] = r9;
|
||||
}
|
||||
|
||||
/* out = in * in */
|
||||
DONNA_INLINE static void
|
||||
curve25519_square(bignum25519 out, const bignum25519 in) {
|
||||
uint32_t r0,r1,r2,r3,r4,r5,r6,r7,r8,r9;
|
||||
uint32_t d6,d7,d8,d9;
|
||||
uint64_t m0,m1,m2,m3,m4,m5,m6,m7,m8,m9,c;
|
||||
uint32_t p;
|
||||
|
||||
r0 = in[0];
|
||||
r1 = in[1];
|
||||
r2 = in[2];
|
||||
r3 = in[3];
|
||||
r4 = in[4];
|
||||
r5 = in[5];
|
||||
r6 = in[6];
|
||||
r7 = in[7];
|
||||
r8 = in[8];
|
||||
r9 = in[9];
|
||||
|
||||
|
||||
m0 = mul32x32_64(r0, r0);
|
||||
r0 *= 2;
|
||||
m1 = mul32x32_64(r0, r1);
|
||||
m2 = mul32x32_64(r0, r2) + mul32x32_64(r1, r1 * 2);
|
||||
r1 *= 2;
|
||||
m3 = mul32x32_64(r0, r3) + mul32x32_64(r1, r2 );
|
||||
m4 = mul32x32_64(r0, r4) + mul32x32_64(r1, r3 * 2) + mul32x32_64(r2, r2);
|
||||
r2 *= 2;
|
||||
m5 = mul32x32_64(r0, r5) + mul32x32_64(r1, r4 ) + mul32x32_64(r2, r3);
|
||||
m6 = mul32x32_64(r0, r6) + mul32x32_64(r1, r5 * 2) + mul32x32_64(r2, r4) + mul32x32_64(r3, r3 * 2);
|
||||
r3 *= 2;
|
||||
m7 = mul32x32_64(r0, r7) + mul32x32_64(r1, r6 ) + mul32x32_64(r2, r5) + mul32x32_64(r3, r4 );
|
||||
m8 = mul32x32_64(r0, r8) + mul32x32_64(r1, r7 * 2) + mul32x32_64(r2, r6) + mul32x32_64(r3, r5 * 2) + mul32x32_64(r4, r4 );
|
||||
m9 = mul32x32_64(r0, r9) + mul32x32_64(r1, r8 ) + mul32x32_64(r2, r7) + mul32x32_64(r3, r6 ) + mul32x32_64(r4, r5 * 2);
|
||||
|
||||
d6 = r6 * 19;
|
||||
d7 = r7 * 2 * 19;
|
||||
d8 = r8 * 19;
|
||||
d9 = r9 * 2 * 19;
|
||||
|
||||
m0 += (mul32x32_64(d9, r1 ) + mul32x32_64(d8, r2 ) + mul32x32_64(d7, r3 ) + mul32x32_64(d6, r4 * 2) + mul32x32_64(r5, r5 * 2 * 19));
|
||||
m1 += (mul32x32_64(d9, r2 / 2) + mul32x32_64(d8, r3 ) + mul32x32_64(d7, r4 ) + mul32x32_64(d6, r5 * 2));
|
||||
m2 += (mul32x32_64(d9, r3 ) + mul32x32_64(d8, r4 * 2) + mul32x32_64(d7, r5 * 2) + mul32x32_64(d6, r6 ));
|
||||
m3 += (mul32x32_64(d9, r4 ) + mul32x32_64(d8, r5 * 2) + mul32x32_64(d7, r6 ));
|
||||
m4 += (mul32x32_64(d9, r5 * 2) + mul32x32_64(d8, r6 * 2) + mul32x32_64(d7, r7 ));
|
||||
m5 += (mul32x32_64(d9, r6 ) + mul32x32_64(d8, r7 * 2));
|
||||
m6 += (mul32x32_64(d9, r7 * 2) + mul32x32_64(d8, r8 ));
|
||||
m7 += (mul32x32_64(d9, r8 ));
|
||||
m8 += (mul32x32_64(d9, r9 ));
|
||||
|
||||
r0 = (uint32_t)m0 & reduce_mask_26; c = (m0 >> 26);
|
||||
m1 += c; r1 = (uint32_t)m1 & reduce_mask_25; c = (m1 >> 25);
|
||||
m2 += c; r2 = (uint32_t)m2 & reduce_mask_26; c = (m2 >> 26);
|
||||
m3 += c; r3 = (uint32_t)m3 & reduce_mask_25; c = (m3 >> 25);
|
||||
m4 += c; r4 = (uint32_t)m4 & reduce_mask_26; c = (m4 >> 26);
|
||||
m5 += c; r5 = (uint32_t)m5 & reduce_mask_25; c = (m5 >> 25);
|
||||
m6 += c; r6 = (uint32_t)m6 & reduce_mask_26; c = (m6 >> 26);
|
||||
m7 += c; r7 = (uint32_t)m7 & reduce_mask_25; c = (m7 >> 25);
|
||||
m8 += c; r8 = (uint32_t)m8 & reduce_mask_26; c = (m8 >> 26);
|
||||
m9 += c; r9 = (uint32_t)m9 & reduce_mask_25; p = (uint32_t)(m9 >> 25);
|
||||
m0 = r0 + mul32x32_64(p,19); r0 = (uint32_t)m0 & reduce_mask_26; p = (uint32_t)(m0 >> 26);
|
||||
r1 += p;
|
||||
|
||||
out[0] = r0;
|
||||
out[1] = r1;
|
||||
out[2] = r2;
|
||||
out[3] = r3;
|
||||
out[4] = r4;
|
||||
out[5] = r5;
|
||||
out[6] = r6;
|
||||
out[7] = r7;
|
||||
out[8] = r8;
|
||||
out[9] = r9;
|
||||
}
|
||||
|
||||
/* out = in^(2 * count) */
|
||||
static void
|
||||
curve25519_square_times(bignum25519 out, const bignum25519 in, int count) {
|
||||
uint32_t r0,r1,r2,r3,r4,r5,r6,r7,r8,r9;
|
||||
uint32_t d6,d7,d8,d9;
|
||||
uint64_t m0,m1,m2,m3,m4,m5,m6,m7,m8,m9,c;
|
||||
uint32_t p;
|
||||
|
||||
r0 = in[0];
|
||||
r1 = in[1];
|
||||
r2 = in[2];
|
||||
r3 = in[3];
|
||||
r4 = in[4];
|
||||
r5 = in[5];
|
||||
r6 = in[6];
|
||||
r7 = in[7];
|
||||
r8 = in[8];
|
||||
r9 = in[9];
|
||||
|
||||
do {
|
||||
m0 = mul32x32_64(r0, r0);
|
||||
r0 *= 2;
|
||||
m1 = mul32x32_64(r0, r1);
|
||||
m2 = mul32x32_64(r0, r2) + mul32x32_64(r1, r1 * 2);
|
||||
r1 *= 2;
|
||||
m3 = mul32x32_64(r0, r3) + mul32x32_64(r1, r2 );
|
||||
m4 = mul32x32_64(r0, r4) + mul32x32_64(r1, r3 * 2) + mul32x32_64(r2, r2);
|
||||
r2 *= 2;
|
||||
m5 = mul32x32_64(r0, r5) + mul32x32_64(r1, r4 ) + mul32x32_64(r2, r3);
|
||||
m6 = mul32x32_64(r0, r6) + mul32x32_64(r1, r5 * 2) + mul32x32_64(r2, r4) + mul32x32_64(r3, r3 * 2);
|
||||
r3 *= 2;
|
||||
m7 = mul32x32_64(r0, r7) + mul32x32_64(r1, r6 ) + mul32x32_64(r2, r5) + mul32x32_64(r3, r4 );
|
||||
m8 = mul32x32_64(r0, r8) + mul32x32_64(r1, r7 * 2) + mul32x32_64(r2, r6) + mul32x32_64(r3, r5 * 2) + mul32x32_64(r4, r4 );
|
||||
m9 = mul32x32_64(r0, r9) + mul32x32_64(r1, r8 ) + mul32x32_64(r2, r7) + mul32x32_64(r3, r6 ) + mul32x32_64(r4, r5 * 2);
|
||||
|
||||
d6 = r6 * 19;
|
||||
d7 = r7 * 2 * 19;
|
||||
d8 = r8 * 19;
|
||||
d9 = r9 * 2 * 19;
|
||||
|
||||
m0 += (mul32x32_64(d9, r1 ) + mul32x32_64(d8, r2 ) + mul32x32_64(d7, r3 ) + mul32x32_64(d6, r4 * 2) + mul32x32_64(r5, r5 * 2 * 19));
|
||||
m1 += (mul32x32_64(d9, r2 / 2) + mul32x32_64(d8, r3 ) + mul32x32_64(d7, r4 ) + mul32x32_64(d6, r5 * 2));
|
||||
m2 += (mul32x32_64(d9, r3 ) + mul32x32_64(d8, r4 * 2) + mul32x32_64(d7, r5 * 2) + mul32x32_64(d6, r6 ));
|
||||
m3 += (mul32x32_64(d9, r4 ) + mul32x32_64(d8, r5 * 2) + mul32x32_64(d7, r6 ));
|
||||
m4 += (mul32x32_64(d9, r5 * 2) + mul32x32_64(d8, r6 * 2) + mul32x32_64(d7, r7 ));
|
||||
m5 += (mul32x32_64(d9, r6 ) + mul32x32_64(d8, r7 * 2));
|
||||
m6 += (mul32x32_64(d9, r7 * 2) + mul32x32_64(d8, r8 ));
|
||||
m7 += (mul32x32_64(d9, r8 ));
|
||||
m8 += (mul32x32_64(d9, r9 ));
|
||||
|
||||
r0 = (uint32_t)m0 & reduce_mask_26; c = (m0 >> 26);
|
||||
m1 += c; r1 = (uint32_t)m1 & reduce_mask_25; c = (m1 >> 25);
|
||||
m2 += c; r2 = (uint32_t)m2 & reduce_mask_26; c = (m2 >> 26);
|
||||
m3 += c; r3 = (uint32_t)m3 & reduce_mask_25; c = (m3 >> 25);
|
||||
m4 += c; r4 = (uint32_t)m4 & reduce_mask_26; c = (m4 >> 26);
|
||||
m5 += c; r5 = (uint32_t)m5 & reduce_mask_25; c = (m5 >> 25);
|
||||
m6 += c; r6 = (uint32_t)m6 & reduce_mask_26; c = (m6 >> 26);
|
||||
m7 += c; r7 = (uint32_t)m7 & reduce_mask_25; c = (m7 >> 25);
|
||||
m8 += c; r8 = (uint32_t)m8 & reduce_mask_26; c = (m8 >> 26);
|
||||
m9 += c; r9 = (uint32_t)m9 & reduce_mask_25; p = (uint32_t)(m9 >> 25);
|
||||
m0 = r0 + mul32x32_64(p,19); r0 = (uint32_t)m0 & reduce_mask_26; p = (uint32_t)(m0 >> 26);
|
||||
r1 += p;
|
||||
} while (--count);
|
||||
|
||||
out[0] = r0;
|
||||
out[1] = r1;
|
||||
out[2] = r2;
|
||||
out[3] = r3;
|
||||
out[4] = r4;
|
||||
out[5] = r5;
|
||||
out[6] = r6;
|
||||
out[7] = r7;
|
||||
out[8] = r8;
|
||||
out[9] = r9;
|
||||
}
|
||||
|
||||
|
||||
/* Take a little-endian, 32-byte number and expand it into polynomial form */
|
||||
static void
|
||||
curve25519_expand(bignum25519 out, const unsigned char in[32]) {
|
||||
static const union { uint8_t b[2]; uint16_t s; } endian_check = {{1,0}};
|
||||
uint32_t x0,x1,x2,x3,x4,x5,x6,x7;
|
||||
|
||||
if (endian_check.s == 1) {
|
||||
x0 = *(uint32_t *)(in + 0);
|
||||
x1 = *(uint32_t *)(in + 4);
|
||||
x2 = *(uint32_t *)(in + 8);
|
||||
x3 = *(uint32_t *)(in + 12);
|
||||
x4 = *(uint32_t *)(in + 16);
|
||||
x5 = *(uint32_t *)(in + 20);
|
||||
x6 = *(uint32_t *)(in + 24);
|
||||
x7 = *(uint32_t *)(in + 28);
|
||||
} else {
|
||||
#define F(s) \
|
||||
((((uint32_t)in[s + 0]) ) | \
|
||||
(((uint32_t)in[s + 1]) << 8) | \
|
||||
(((uint32_t)in[s + 2]) << 16) | \
|
||||
(((uint32_t)in[s + 3]) << 24))
|
||||
x0 = F(0);
|
||||
x1 = F(4);
|
||||
x2 = F(8);
|
||||
x3 = F(12);
|
||||
x4 = F(16);
|
||||
x5 = F(20);
|
||||
x6 = F(24);
|
||||
x7 = F(28);
|
||||
#undef F
|
||||
}
|
||||
|
||||
out[0] = ( x0 ) & reduce_mask_26;
|
||||
out[1] = ((((uint64_t)x1 << 32) | x0) >> 26) & reduce_mask_25;
|
||||
out[2] = ((((uint64_t)x2 << 32) | x1) >> 19) & reduce_mask_26;
|
||||
out[3] = ((((uint64_t)x3 << 32) | x2) >> 13) & reduce_mask_25;
|
||||
out[4] = (( x3) >> 6) & reduce_mask_26;
|
||||
out[5] = ( x4 ) & reduce_mask_25;
|
||||
out[6] = ((((uint64_t)x5 << 32) | x4) >> 25) & reduce_mask_26;
|
||||
out[7] = ((((uint64_t)x6 << 32) | x5) >> 19) & reduce_mask_25;
|
||||
out[8] = ((((uint64_t)x7 << 32) | x6) >> 12) & reduce_mask_26;
|
||||
out[9] = (( x7) >> 6) & reduce_mask_25; /* ignore the top bit */
|
||||
}
|
||||
|
||||
/* Take a fully reduced polynomial form number and contract it into a little-endian, 32-byte array */
|
||||
static void
|
||||
curve25519_contract(unsigned char out[32], const bignum25519 in) {
|
||||
bignum25519 f;
|
||||
curve25519_copy(f, in);
|
||||
|
||||
#define carry_pass() \
|
||||
f[1] += f[0] >> 26; f[0] &= reduce_mask_26; \
|
||||
f[2] += f[1] >> 25; f[1] &= reduce_mask_25; \
|
||||
f[3] += f[2] >> 26; f[2] &= reduce_mask_26; \
|
||||
f[4] += f[3] >> 25; f[3] &= reduce_mask_25; \
|
||||
f[5] += f[4] >> 26; f[4] &= reduce_mask_26; \
|
||||
f[6] += f[5] >> 25; f[5] &= reduce_mask_25; \
|
||||
f[7] += f[6] >> 26; f[6] &= reduce_mask_26; \
|
||||
f[8] += f[7] >> 25; f[7] &= reduce_mask_25; \
|
||||
f[9] += f[8] >> 26; f[8] &= reduce_mask_26;
|
||||
|
||||
#define carry_pass_full() \
|
||||
carry_pass() \
|
||||
f[0] += 19 * (f[9] >> 25); f[9] &= reduce_mask_25;
|
||||
|
||||
#define carry_pass_final() \
|
||||
carry_pass() \
|
||||
f[9] &= reduce_mask_25;
|
||||
|
||||
carry_pass_full()
|
||||
carry_pass_full()
|
||||
|
||||
/* now t is between 0 and 2^255-1, properly carried. */
|
||||
/* case 1: between 0 and 2^255-20. case 2: between 2^255-19 and 2^255-1. */
|
||||
f[0] += 19;
|
||||
carry_pass_full()
|
||||
|
||||
/* now between 19 and 2^255-1 in both cases, and offset by 19. */
|
||||
f[0] += (1 << 26) - 19;
|
||||
f[1] += (1 << 25) - 1;
|
||||
f[2] += (1 << 26) - 1;
|
||||
f[3] += (1 << 25) - 1;
|
||||
f[4] += (1 << 26) - 1;
|
||||
f[5] += (1 << 25) - 1;
|
||||
f[6] += (1 << 26) - 1;
|
||||
f[7] += (1 << 25) - 1;
|
||||
f[8] += (1 << 26) - 1;
|
||||
f[9] += (1 << 25) - 1;
|
||||
|
||||
/* now between 2^255 and 2^256-20, and offset by 2^255. */
|
||||
carry_pass_final()
|
||||
|
||||
#undef carry_pass
|
||||
#undef carry_full
|
||||
#undef carry_final
|
||||
|
||||
f[1] <<= 2;
|
||||
f[2] <<= 3;
|
||||
f[3] <<= 5;
|
||||
f[4] <<= 6;
|
||||
f[6] <<= 1;
|
||||
f[7] <<= 3;
|
||||
f[8] <<= 4;
|
||||
f[9] <<= 6;
|
||||
|
||||
#define F(i, s) \
|
||||
out[s+0] |= (unsigned char )(f[i] & 0xff); \
|
||||
out[s+1] = (unsigned char )((f[i] >> 8) & 0xff); \
|
||||
out[s+2] = (unsigned char )((f[i] >> 16) & 0xff); \
|
||||
out[s+3] = (unsigned char )((f[i] >> 24) & 0xff);
|
||||
|
||||
out[0] = 0;
|
||||
out[16] = 0;
|
||||
F(0,0);
|
||||
F(1,3);
|
||||
F(2,6);
|
||||
F(3,9);
|
||||
F(4,12);
|
||||
F(5,16);
|
||||
F(6,19);
|
||||
F(7,22);
|
||||
F(8,25);
|
||||
F(9,28);
|
||||
#undef F
|
||||
}
|
||||
|
||||
/*
|
||||
* Swap the contents of [qx] and [qpx] iff @swap is non-zero
|
||||
*/
|
||||
DONNA_INLINE static void
|
||||
curve25519_swap_conditional(bignum25519 x, bignum25519 qpx, uint32_t iswap) {
|
||||
const uint32_t swap = (uint32_t)(-(int32_t)iswap);
|
||||
uint32_t x0,x1,x2,x3,x4,x5,x6,x7,x8,x9;
|
||||
|
||||
x0 = swap & (x[0] ^ qpx[0]); x[0] ^= x0; qpx[0] ^= x0;
|
||||
x1 = swap & (x[1] ^ qpx[1]); x[1] ^= x1; qpx[1] ^= x1;
|
||||
x2 = swap & (x[2] ^ qpx[2]); x[2] ^= x2; qpx[2] ^= x2;
|
||||
x3 = swap & (x[3] ^ qpx[3]); x[3] ^= x3; qpx[3] ^= x3;
|
||||
x4 = swap & (x[4] ^ qpx[4]); x[4] ^= x4; qpx[4] ^= x4;
|
||||
x5 = swap & (x[5] ^ qpx[5]); x[5] ^= x5; qpx[5] ^= x5;
|
||||
x6 = swap & (x[6] ^ qpx[6]); x[6] ^= x6; qpx[6] ^= x6;
|
||||
x7 = swap & (x[7] ^ qpx[7]); x[7] ^= x7; qpx[7] ^= x7;
|
||||
x8 = swap & (x[8] ^ qpx[8]); x[8] ^= x8; qpx[8] ^= x8;
|
||||
x9 = swap & (x[9] ^ qpx[9]); x[9] ^= x9; qpx[9] ^= x9;
|
||||
}
|
||||
|
||||
345
curve25519-donna/curve25519-donna-64bit.h
Normal file
345
curve25519-donna/curve25519-donna-64bit.h
Normal file
@ -0,0 +1,345 @@
|
||||
typedef uint64_t bignum25519[5];
|
||||
|
||||
static const uint64_t reduce_mask_51 = ((uint64_t)1 << 51) - 1;
|
||||
static const uint64_t reduce_mask_52 = ((uint64_t)1 << 52) - 1;
|
||||
|
||||
/* out = in */
|
||||
DONNA_INLINE static void
|
||||
curve25519_copy(bignum25519 out, const bignum25519 in) {
|
||||
out[0] = in[0];
|
||||
out[1] = in[1];
|
||||
out[2] = in[2];
|
||||
out[3] = in[3];
|
||||
out[4] = in[4];
|
||||
}
|
||||
|
||||
/* out = a + b */
|
||||
DONNA_INLINE static void
|
||||
curve25519_add(bignum25519 out, const bignum25519 a, const bignum25519 b) {
|
||||
out[0] = a[0] + b[0];
|
||||
out[1] = a[1] + b[1];
|
||||
out[2] = a[2] + b[2];
|
||||
out[3] = a[3] + b[3];
|
||||
out[4] = a[4] + b[4];
|
||||
}
|
||||
|
||||
static const uint64_t two54m152 = (((uint64_t)1) << 54) - 152;
|
||||
static const uint64_t two54m8 = (((uint64_t)1) << 54) - 8;
|
||||
|
||||
/* out = a - b */
|
||||
DONNA_INLINE static void
|
||||
curve25519_sub(bignum25519 out, const bignum25519 a, const bignum25519 b) {
|
||||
out[0] = a[0] + two54m152 - b[0];
|
||||
out[1] = a[1] + two54m8 - b[1];
|
||||
out[2] = a[2] + two54m8 - b[2];
|
||||
out[3] = a[3] + two54m8 - b[3];
|
||||
out[4] = a[4] + two54m8 - b[4];
|
||||
}
|
||||
|
||||
|
||||
/* out = (in * scalar) */
|
||||
DONNA_INLINE static void
|
||||
curve25519_scalar_product(bignum25519 out, const bignum25519 in, const uint64_t scalar) {
|
||||
uint128_t a;
|
||||
uint64_t c;
|
||||
|
||||
#if defined(HAVE_NATIVE_UINT128)
|
||||
a = ((uint128_t) in[0]) * scalar; out[0] = (uint64_t)a & reduce_mask_51; c = (uint64_t)(a >> 51);
|
||||
a = ((uint128_t) in[1]) * scalar + c; out[1] = (uint64_t)a & reduce_mask_51; c = (uint64_t)(a >> 51);
|
||||
a = ((uint128_t) in[2]) * scalar + c; out[2] = (uint64_t)a & reduce_mask_51; c = (uint64_t)(a >> 51);
|
||||
a = ((uint128_t) in[3]) * scalar + c; out[3] = (uint64_t)a & reduce_mask_51; c = (uint64_t)(a >> 51);
|
||||
a = ((uint128_t) in[4]) * scalar + c; out[4] = (uint64_t)a & reduce_mask_51; c = (uint64_t)(a >> 51);
|
||||
out[0] += c * 19;
|
||||
#else
|
||||
mul64x64_128(a, in[0], scalar) out[0] = lo128(a) & reduce_mask_51; shr128(c, a, 51);
|
||||
mul64x64_128(a, in[1], scalar) add128_64(a, c) out[1] = lo128(a) & reduce_mask_51; shr128(c, a, 51);
|
||||
mul64x64_128(a, in[2], scalar) add128_64(a, c) out[2] = lo128(a) & reduce_mask_51; shr128(c, a, 51);
|
||||
mul64x64_128(a, in[3], scalar) add128_64(a, c) out[3] = lo128(a) & reduce_mask_51; shr128(c, a, 51);
|
||||
mul64x64_128(a, in[4], scalar) add128_64(a, c) out[4] = lo128(a) & reduce_mask_51; shr128(c, a, 51);
|
||||
out[0] += c * 19;
|
||||
#endif
|
||||
}
|
||||
|
||||
/* out = a * b */
|
||||
DONNA_INLINE static void
|
||||
curve25519_mul(bignum25519 out, const bignum25519 a, const bignum25519 b) {
|
||||
#if !defined(HAVE_NATIVE_UINT128)
|
||||
uint128_t mul;
|
||||
#endif
|
||||
uint128_t t[5];
|
||||
uint64_t r0,r1,r2,r3,r4,s0,s1,s2,s3,s4,c;
|
||||
|
||||
r0 = b[0];
|
||||
r1 = b[1];
|
||||
r2 = b[2];
|
||||
r3 = b[3];
|
||||
r4 = b[4];
|
||||
|
||||
s0 = a[0];
|
||||
s1 = a[1];
|
||||
s2 = a[2];
|
||||
s3 = a[3];
|
||||
s4 = a[4];
|
||||
|
||||
#if defined(HAVE_NATIVE_UINT128)
|
||||
t[0] = ((uint128_t) r0) * s0;
|
||||
t[1] = ((uint128_t) r0) * s1 + ((uint128_t) r1) * s0;
|
||||
t[2] = ((uint128_t) r0) * s2 + ((uint128_t) r2) * s0 + ((uint128_t) r1) * s1;
|
||||
t[3] = ((uint128_t) r0) * s3 + ((uint128_t) r3) * s0 + ((uint128_t) r1) * s2 + ((uint128_t) r2) * s1;
|
||||
t[4] = ((uint128_t) r0) * s4 + ((uint128_t) r4) * s0 + ((uint128_t) r3) * s1 + ((uint128_t) r1) * s3 + ((uint128_t) r2) * s2;
|
||||
#else
|
||||
mul64x64_128(t[0], r0, s0)
|
||||
mul64x64_128(t[1], r0, s1) mul64x64_128(mul, r1, s0) add128(t[1], mul)
|
||||
mul64x64_128(t[2], r0, s2) mul64x64_128(mul, r2, s0) add128(t[2], mul) mul64x64_128(mul, r1, s1) add128(t[2], mul)
|
||||
mul64x64_128(t[3], r0, s3) mul64x64_128(mul, r3, s0) add128(t[3], mul) mul64x64_128(mul, r1, s2) add128(t[3], mul) mul64x64_128(mul, r2, s1) add128(t[3], mul)
|
||||
mul64x64_128(t[4], r0, s4) mul64x64_128(mul, r4, s0) add128(t[4], mul) mul64x64_128(mul, r3, s1) add128(t[4], mul) mul64x64_128(mul, r1, s3) add128(t[4], mul) mul64x64_128(mul, r2, s2) add128(t[4], mul)
|
||||
#endif
|
||||
|
||||
r1 *= 19;
|
||||
r2 *= 19;
|
||||
r3 *= 19;
|
||||
r4 *= 19;
|
||||
|
||||
#if defined(HAVE_NATIVE_UINT128)
|
||||
t[0] += ((uint128_t) r4) * s1 + ((uint128_t) r1) * s4 + ((uint128_t) r2) * s3 + ((uint128_t) r3) * s2;
|
||||
t[1] += ((uint128_t) r4) * s2 + ((uint128_t) r2) * s4 + ((uint128_t) r3) * s3;
|
||||
t[2] += ((uint128_t) r4) * s3 + ((uint128_t) r3) * s4;
|
||||
t[3] += ((uint128_t) r4) * s4;
|
||||
#else
|
||||
mul64x64_128(mul, r4, s1) add128(t[0], mul) mul64x64_128(mul, r1, s4) add128(t[0], mul) mul64x64_128(mul, r2, s3) add128(t[0], mul) mul64x64_128(mul, r3, s2) add128(t[0], mul)
|
||||
mul64x64_128(mul, r4, s2) add128(t[1], mul) mul64x64_128(mul, r2, s4) add128(t[1], mul) mul64x64_128(mul, r3, s3) add128(t[1], mul)
|
||||
mul64x64_128(mul, r4, s3) add128(t[2], mul) mul64x64_128(mul, r3, s4) add128(t[2], mul)
|
||||
mul64x64_128(mul, r4, s4) add128(t[3], mul)
|
||||
#endif
|
||||
|
||||
r0 = lo128(t[0]) & reduce_mask_51; shr128(c, t[0], 51);
|
||||
add128_64(t[1], c) r1 = lo128(t[1]) & reduce_mask_51; shr128(c, t[1], 51);
|
||||
add128_64(t[2], c) r2 = lo128(t[2]) & reduce_mask_51; shr128(c, t[2], 51);
|
||||
add128_64(t[3], c) r3 = lo128(t[3]) & reduce_mask_51; shr128(c, t[3], 51);
|
||||
add128_64(t[4], c) r4 = lo128(t[4]) & reduce_mask_51; shr128(c, t[4], 51);
|
||||
r0 += c * 19; c = r0 >> 51; r0 = r0 & reduce_mask_51;
|
||||
r1 += c;
|
||||
|
||||
out[0] = r0;
|
||||
out[1] = r1;
|
||||
out[2] = r2;
|
||||
out[3] = r3;
|
||||
out[4] = r4;
|
||||
}
|
||||
|
||||
/* out = in^(2 * count) */
|
||||
DONNA_INLINE static void
|
||||
curve25519_square_times(bignum25519 out, const bignum25519 in, uint64_t count) {
|
||||
#if !defined(HAVE_NATIVE_UINT128)
|
||||
uint128_t mul;
|
||||
#endif
|
||||
uint128_t t[5];
|
||||
uint64_t r0,r1,r2,r3,r4,c;
|
||||
uint64_t d0,d1,d2,d4,d419;
|
||||
|
||||
r0 = in[0];
|
||||
r1 = in[1];
|
||||
r2 = in[2];
|
||||
r3 = in[3];
|
||||
r4 = in[4];
|
||||
|
||||
do {
|
||||
d0 = r0 * 2;
|
||||
d1 = r1 * 2;
|
||||
d2 = r2 * 2 * 19;
|
||||
d419 = r4 * 19;
|
||||
d4 = d419 * 2;
|
||||
|
||||
#if defined(HAVE_NATIVE_UINT128)
|
||||
t[0] = ((uint128_t) r0) * r0 + ((uint128_t) d4) * r1 + (((uint128_t) d2) * (r3 ));
|
||||
t[1] = ((uint128_t) d0) * r1 + ((uint128_t) d4) * r2 + (((uint128_t) r3) * (r3 * 19));
|
||||
t[2] = ((uint128_t) d0) * r2 + ((uint128_t) r1) * r1 + (((uint128_t) d4) * (r3 ));
|
||||
t[3] = ((uint128_t) d0) * r3 + ((uint128_t) d1) * r2 + (((uint128_t) r4) * (d419 ));
|
||||
t[4] = ((uint128_t) d0) * r4 + ((uint128_t) d1) * r3 + (((uint128_t) r2) * (r2 ));
|
||||
#else
|
||||
mul64x64_128(t[0], r0, r0) mul64x64_128(mul, d4, r1) add128(t[0], mul) mul64x64_128(mul, d2, r3) add128(t[0], mul)
|
||||
mul64x64_128(t[1], d0, r1) mul64x64_128(mul, d4, r2) add128(t[1], mul) mul64x64_128(mul, r3, r3 * 19) add128(t[1], mul)
|
||||
mul64x64_128(t[2], d0, r2) mul64x64_128(mul, r1, r1) add128(t[2], mul) mul64x64_128(mul, d4, r3) add128(t[2], mul)
|
||||
mul64x64_128(t[3], d0, r3) mul64x64_128(mul, d1, r2) add128(t[3], mul) mul64x64_128(mul, r4, d419) add128(t[3], mul)
|
||||
mul64x64_128(t[4], d0, r4) mul64x64_128(mul, d1, r3) add128(t[4], mul) mul64x64_128(mul, r2, r2) add128(t[4], mul)
|
||||
#endif
|
||||
|
||||
r0 = lo128(t[0]) & reduce_mask_51; shr128(c, t[0], 51);
|
||||
add128_64(t[1], c) r1 = lo128(t[1]) & reduce_mask_51; shr128(c, t[1], 51);
|
||||
add128_64(t[2], c) r2 = lo128(t[2]) & reduce_mask_51; shr128(c, t[2], 51);
|
||||
add128_64(t[3], c) r3 = lo128(t[3]) & reduce_mask_51; shr128(c, t[3], 51);
|
||||
add128_64(t[4], c) r4 = lo128(t[4]) & reduce_mask_51; shr128(c, t[4], 51);
|
||||
r0 += c * 19; c = r0 >> 51; r0 = r0 & reduce_mask_51;
|
||||
r1 += c;
|
||||
} while(--count);
|
||||
|
||||
out[0] = r0;
|
||||
out[1] = r1;
|
||||
out[2] = r2;
|
||||
out[3] = r3;
|
||||
out[4] = r4;
|
||||
}
|
||||
|
||||
DONNA_INLINE static void
|
||||
curve25519_square(bignum25519 out, const bignum25519 in) {
|
||||
#if !defined(HAVE_NATIVE_UINT128)
|
||||
uint128_t mul;
|
||||
#endif
|
||||
uint128_t t[5];
|
||||
uint64_t r0,r1,r2,r3,r4,c;
|
||||
uint64_t d0,d1,d2,d4,d419;
|
||||
|
||||
r0 = in[0];
|
||||
r1 = in[1];
|
||||
r2 = in[2];
|
||||
r3 = in[3];
|
||||
r4 = in[4];
|
||||
|
||||
d0 = r0 * 2;
|
||||
d1 = r1 * 2;
|
||||
d2 = r2 * 2 * 19;
|
||||
d419 = r4 * 19;
|
||||
d4 = d419 * 2;
|
||||
|
||||
#if defined(HAVE_NATIVE_UINT128)
|
||||
t[0] = ((uint128_t) r0) * r0 + ((uint128_t) d4) * r1 + (((uint128_t) d2) * (r3 ));
|
||||
t[1] = ((uint128_t) d0) * r1 + ((uint128_t) d4) * r2 + (((uint128_t) r3) * (r3 * 19));
|
||||
t[2] = ((uint128_t) d0) * r2 + ((uint128_t) r1) * r1 + (((uint128_t) d4) * (r3 ));
|
||||
t[3] = ((uint128_t) d0) * r3 + ((uint128_t) d1) * r2 + (((uint128_t) r4) * (d419 ));
|
||||
t[4] = ((uint128_t) d0) * r4 + ((uint128_t) d1) * r3 + (((uint128_t) r2) * (r2 ));
|
||||
#else
|
||||
mul64x64_128(t[0], r0, r0) mul64x64_128(mul, d4, r1) add128(t[0], mul) mul64x64_128(mul, d2, r3) add128(t[0], mul)
|
||||
mul64x64_128(t[1], d0, r1) mul64x64_128(mul, d4, r2) add128(t[1], mul) mul64x64_128(mul, r3, r3 * 19) add128(t[1], mul)
|
||||
mul64x64_128(t[2], d0, r2) mul64x64_128(mul, r1, r1) add128(t[2], mul) mul64x64_128(mul, d4, r3) add128(t[2], mul)
|
||||
mul64x64_128(t[3], d0, r3) mul64x64_128(mul, d1, r2) add128(t[3], mul) mul64x64_128(mul, r4, d419) add128(t[3], mul)
|
||||
mul64x64_128(t[4], d0, r4) mul64x64_128(mul, d1, r3) add128(t[4], mul) mul64x64_128(mul, r2, r2) add128(t[4], mul)
|
||||
#endif
|
||||
|
||||
r0 = lo128(t[0]) & reduce_mask_51; shr128(c, t[0], 51);
|
||||
add128_64(t[1], c) r1 = lo128(t[1]) & reduce_mask_51; shr128(c, t[1], 51);
|
||||
add128_64(t[2], c) r2 = lo128(t[2]) & reduce_mask_51; shr128(c, t[2], 51);
|
||||
add128_64(t[3], c) r3 = lo128(t[3]) & reduce_mask_51; shr128(c, t[3], 51);
|
||||
add128_64(t[4], c) r4 = lo128(t[4]) & reduce_mask_51; shr128(c, t[4], 51);
|
||||
r0 += c * 19; c = r0 >> 51; r0 = r0 & reduce_mask_51;
|
||||
r1 += c;
|
||||
|
||||
out[0] = r0;
|
||||
out[1] = r1;
|
||||
out[2] = r2;
|
||||
out[3] = r3;
|
||||
out[4] = r4;
|
||||
}
|
||||
|
||||
|
||||
/* Take a little-endian, 32-byte number and expand it into polynomial form */
|
||||
DONNA_INLINE static void
|
||||
curve25519_expand(bignum25519 out, const unsigned char *in) {
|
||||
static const union { uint8_t b[2]; uint16_t s; } endian_check = {{1,0}};
|
||||
uint64_t x0,x1,x2,x3;
|
||||
|
||||
if (endian_check.s == 1) {
|
||||
x0 = *(uint64_t *)(in + 0);
|
||||
x1 = *(uint64_t *)(in + 8);
|
||||
x2 = *(uint64_t *)(in + 16);
|
||||
x3 = *(uint64_t *)(in + 24);
|
||||
} else {
|
||||
#define F(s) \
|
||||
((((uint64_t)in[s + 0]) ) | \
|
||||
(((uint64_t)in[s + 1]) << 8) | \
|
||||
(((uint64_t)in[s + 2]) << 16) | \
|
||||
(((uint64_t)in[s + 3]) << 24) | \
|
||||
(((uint64_t)in[s + 4]) << 32) | \
|
||||
(((uint64_t)in[s + 5]) << 40) | \
|
||||
(((uint64_t)in[s + 6]) << 48) | \
|
||||
(((uint64_t)in[s + 7]) << 56))
|
||||
|
||||
x0 = F(0);
|
||||
x1 = F(8);
|
||||
x2 = F(16);
|
||||
x3 = F(24);
|
||||
}
|
||||
|
||||
out[0] = x0 & reduce_mask_51; x0 = (x0 >> 51) | (x1 << 13);
|
||||
out[1] = x0 & reduce_mask_51; x1 = (x1 >> 38) | (x2 << 26);
|
||||
out[2] = x1 & reduce_mask_51; x2 = (x2 >> 25) | (x3 << 39);
|
||||
out[3] = x2 & reduce_mask_51; x3 = (x3 >> 12);
|
||||
out[4] = x3 & reduce_mask_51; /* ignore the top bit */
|
||||
}
|
||||
|
||||
/* Take a fully reduced polynomial form number and contract it into a
|
||||
* little-endian, 32-byte array
|
||||
*/
|
||||
DONNA_INLINE static void
|
||||
curve25519_contract(unsigned char *out, const bignum25519 input) {
|
||||
uint64_t t[5];
|
||||
uint64_t f, i;
|
||||
|
||||
t[0] = input[0];
|
||||
t[1] = input[1];
|
||||
t[2] = input[2];
|
||||
t[3] = input[3];
|
||||
t[4] = input[4];
|
||||
|
||||
#define curve25519_contract_carry() \
|
||||
t[1] += t[0] >> 51; t[0] &= reduce_mask_51; \
|
||||
t[2] += t[1] >> 51; t[1] &= reduce_mask_51; \
|
||||
t[3] += t[2] >> 51; t[2] &= reduce_mask_51; \
|
||||
t[4] += t[3] >> 51; t[3] &= reduce_mask_51;
|
||||
|
||||
#define curve25519_contract_carry_full() curve25519_contract_carry() \
|
||||
t[0] += 19 * (t[4] >> 51); t[4] &= reduce_mask_51;
|
||||
|
||||
#define curve25519_contract_carry_final() curve25519_contract_carry() \
|
||||
t[4] &= reduce_mask_51;
|
||||
|
||||
curve25519_contract_carry_full()
|
||||
curve25519_contract_carry_full()
|
||||
|
||||
/* now t is between 0 and 2^255-1, properly carried. */
|
||||
/* case 1: between 0 and 2^255-20. case 2: between 2^255-19 and 2^255-1. */
|
||||
t[0] += 19;
|
||||
curve25519_contract_carry_full()
|
||||
|
||||
/* now between 19 and 2^255-1 in both cases, and offset by 19. */
|
||||
t[0] += 0x8000000000000 - 19;
|
||||
t[1] += 0x8000000000000 - 1;
|
||||
t[2] += 0x8000000000000 - 1;
|
||||
t[3] += 0x8000000000000 - 1;
|
||||
t[4] += 0x8000000000000 - 1;
|
||||
|
||||
/* now between 2^255 and 2^256-20, and offset by 2^255. */
|
||||
curve25519_contract_carry_final()
|
||||
|
||||
#define write51full(n,shift) \
|
||||
f = ((t[n] >> shift) | (t[n+1] << (51 - shift))); \
|
||||
for (i = 0; i < 8; i++, f >>= 8) *out++ = (unsigned char)f;
|
||||
#define write51(n) write51full(n,13*n)
|
||||
|
||||
write51(0)
|
||||
write51(1)
|
||||
write51(2)
|
||||
write51(3)
|
||||
|
||||
#undef curve25519_contract_carry
|
||||
#undef curve25519_contract_carry_full
|
||||
#undef curve25519_contract_carry_final
|
||||
#undef write51full
|
||||
#undef write51
|
||||
}
|
||||
|
||||
/*
|
||||
* Swap the contents of [qx] and [qpx] iff @swap is non-zero
|
||||
*/
|
||||
DONNA_INLINE static void
|
||||
curve25519_swap_conditional(bignum25519 x, bignum25519 qpx, uint64_t iswap) {
|
||||
const uint64_t swap = (uint64_t)(-(int64_t)iswap);
|
||||
uint64_t x0,x1,x2,x3,x4;
|
||||
|
||||
x0 = swap & (x[0] ^ qpx[0]); x[0] ^= x0; qpx[0] ^= x0;
|
||||
x1 = swap & (x[1] ^ qpx[1]); x[1] ^= x1; qpx[1] ^= x1;
|
||||
x2 = swap & (x[2] ^ qpx[2]); x[2] ^= x2; qpx[2] ^= x2;
|
||||
x3 = swap & (x[3] ^ qpx[3]); x[3] ^= x3; qpx[3] ^= x3;
|
||||
x4 = swap & (x[4] ^ qpx[4]); x[4] ^= x4; qpx[4] ^= x4;
|
||||
|
||||
}
|
||||
|
||||
43
curve25519-donna/curve25519-donna-common.h
Normal file
43
curve25519-donna/curve25519-donna-common.h
Normal file
@ -0,0 +1,43 @@
|
||||
/*
|
||||
* In: b = 2^5 - 2^0
|
||||
* Out: b = 2^250 - 2^0
|
||||
*/
|
||||
static void
|
||||
curve25519_pow_two5mtwo0_two250mtwo0(bignum25519 b) {
|
||||
bignum25519 ALIGN(16) t0,c;
|
||||
|
||||
/* 2^5 - 2^0 */ /* b */
|
||||
/* 2^10 - 2^5 */ curve25519_square_times(t0, b, 5);
|
||||
/* 2^10 - 2^0 */ curve25519_mul(b, t0, b);
|
||||
/* 2^20 - 2^10 */ curve25519_square_times(t0, b, 10);
|
||||
/* 2^20 - 2^0 */ curve25519_mul(c, t0, b);
|
||||
/* 2^40 - 2^20 */ curve25519_square_times(t0, c, 20);
|
||||
/* 2^40 - 2^0 */ curve25519_mul(t0, t0, c);
|
||||
/* 2^50 - 2^10 */ curve25519_square_times(t0, t0, 10);
|
||||
/* 2^50 - 2^0 */ curve25519_mul(b, t0, b);
|
||||
/* 2^100 - 2^50 */ curve25519_square_times(t0, b, 50);
|
||||
/* 2^100 - 2^0 */ curve25519_mul(c, t0, b);
|
||||
/* 2^200 - 2^100 */ curve25519_square_times(t0, c, 100);
|
||||
/* 2^200 - 2^0 */ curve25519_mul(t0, t0, c);
|
||||
/* 2^250 - 2^50 */ curve25519_square_times(t0, t0, 50);
|
||||
/* 2^250 - 2^0 */ curve25519_mul(b, t0, b);
|
||||
}
|
||||
|
||||
/*
|
||||
* z^(p - 2) = z(2^255 - 21)
|
||||
*/
|
||||
static void
|
||||
curve25519_recip(bignum25519 out, const bignum25519 z) {
|
||||
bignum25519 ALIGN(16) a,t0,b;
|
||||
|
||||
/* 2 */ curve25519_square(a, z); /* a = 2 */
|
||||
/* 8 */ curve25519_square_times(t0, a, 2);
|
||||
/* 9 */ curve25519_mul(b, t0, z); /* b = 9 */
|
||||
/* 11 */ curve25519_mul(a, b, a); /* a = 11 */
|
||||
/* 22 */ curve25519_square(t0, a);
|
||||
/* 2^5 - 2^0 = 31 */ curve25519_mul(b, t0, b);
|
||||
/* 2^250 - 2^0 */ curve25519_pow_two5mtwo0_two250mtwo0(b);
|
||||
/* 2^255 - 2^5 */ curve25519_square_times(b, b, 5);
|
||||
/* 2^255 - 21 */ curve25519_mul(out, b, a);
|
||||
}
|
||||
|
||||
103
curve25519-donna/curve25519-donna-portable-identify.h
Normal file
103
curve25519-donna/curve25519-donna-portable-identify.h
Normal file
@ -0,0 +1,103 @@
|
||||
/* os */
|
||||
#if defined(_WIN32) || defined(_WIN64) || defined(__TOS_WIN__) || defined(__WINDOWS__)
|
||||
#define OS_WINDOWS
|
||||
#elif defined(sun) || defined(__sun) || defined(__SVR4) || defined(__svr4__)
|
||||
#define OS_SOLARIS
|
||||
#else
|
||||
#include <sys/param.h> /* need this to define BSD */
|
||||
#define OS_NIX
|
||||
#if defined(__linux__)
|
||||
#define OS_LINUX
|
||||
#elif defined(BSD)
|
||||
#define OS_BSD
|
||||
#if defined(MACOS_X) || (defined(__APPLE__) & defined(__MACH__))
|
||||
#define OS_OSX
|
||||
#elif defined(macintosh) || defined(Macintosh)
|
||||
#define OS_MAC
|
||||
#elif defined(__OpenBSD__)
|
||||
#define OS_OPENBSD
|
||||
#endif
|
||||
#endif
|
||||
#endif
|
||||
|
||||
|
||||
/* compiler */
|
||||
#if defined(_MSC_VER)
|
||||
#define COMPILER_MSVC
|
||||
#endif
|
||||
#if defined(__ICC)
|
||||
#define COMPILER_INTEL
|
||||
#endif
|
||||
#if defined(__GNUC__)
|
||||
#if (__GNUC__ >= 3)
|
||||
#define COMPILER_GCC ((__GNUC__ * 10000) + (__GNUC_MINOR__ * 100) + (__GNUC_PATCHLEVEL__))
|
||||
#else
|
||||
#define COMPILER_GCC ((__GNUC__ * 10000) + (__GNUC_MINOR__ * 100) )
|
||||
#endif
|
||||
#endif
|
||||
#if defined(__PATHCC__)
|
||||
#define COMPILER_PATHCC
|
||||
#endif
|
||||
#if defined(__clang__)
|
||||
#define COMPILER_CLANG ((__clang_major__ * 10000) + (__clang_minor__ * 100) + (__clang_patchlevel__))
|
||||
#endif
|
||||
|
||||
|
||||
|
||||
/* cpu */
|
||||
#if defined(__amd64__) || defined(__amd64) || defined(__x86_64__ ) || defined(_M_X64)
|
||||
#define CPU_X86_64
|
||||
#elif defined(__i586__) || defined(__i686__) || (defined(_M_IX86) && (_M_IX86 >= 500))
|
||||
#define CPU_X86 500
|
||||
#elif defined(__i486__) || (defined(_M_IX86) && (_M_IX86 >= 400))
|
||||
#define CPU_X86 400
|
||||
#elif defined(__i386__) || (defined(_M_IX86) && (_M_IX86 >= 300)) || defined(__X86__) || defined(_X86_) || defined(__I86__)
|
||||
#define CPU_X86 300
|
||||
#elif defined(__ia64__) || defined(_IA64) || defined(__IA64__) || defined(_M_IA64) || defined(__ia64)
|
||||
#define CPU_IA64
|
||||
#endif
|
||||
|
||||
#if defined(__sparc__) || defined(__sparc) || defined(__sparcv9)
|
||||
#define CPU_SPARC
|
||||
#if defined(__sparcv9)
|
||||
#define CPU_SPARC64
|
||||
#endif
|
||||
#endif
|
||||
|
||||
#if defined(powerpc) || defined(__PPC__) || defined(__ppc__) || defined(_ARCH_PPC) || defined(__powerpc__) || defined(__powerpc) || defined(POWERPC) || defined(_M_PPC)
|
||||
#define CPU_PPC
|
||||
#if defined(_ARCH_PWR7)
|
||||
#define CPU_POWER7
|
||||
#elif defined(__64BIT__)
|
||||
#define CPU_PPC64
|
||||
#else
|
||||
#define CPU_PPC32
|
||||
#endif
|
||||
#endif
|
||||
|
||||
#if defined(__hppa__) || defined(__hppa)
|
||||
#define CPU_HPPA
|
||||
#endif
|
||||
|
||||
#if defined(__alpha__) || defined(__alpha) || defined(_M_ALPHA)
|
||||
#define CPU_ALPHA
|
||||
#endif
|
||||
|
||||
/* 64 bit cpu */
|
||||
#if defined(CPU_X86_64) || defined(CPU_IA64) || defined(CPU_SPARC64) || defined(__64BIT__) || defined(__LP64__) || defined(_LP64) || (defined(_MIPS_SZLONG) && (_MIPS_SZLONG == 64))
|
||||
#define CPU_64BITS
|
||||
#endif
|
||||
|
||||
#if defined(COMPILER_MSVC)
|
||||
typedef signed char int8_t;
|
||||
typedef unsigned char uint8_t;
|
||||
typedef signed short int16_t;
|
||||
typedef unsigned short uint16_t;
|
||||
typedef signed int int32_t;
|
||||
typedef unsigned int uint32_t;
|
||||
typedef signed __int64 int64_t;
|
||||
typedef unsigned __int64 uint64_t;
|
||||
#else
|
||||
#include <stdint.h>
|
||||
#endif
|
||||
|
||||
92
curve25519-donna/curve25519-donna-portable.h
Normal file
92
curve25519-donna/curve25519-donna-portable.h
Normal file
@ -0,0 +1,92 @@
|
||||
#include "curve25519-donna-portable-identify.h"
|
||||
|
||||
#define mul32x32_64(a,b) (((uint64_t)(a))*(b))
|
||||
|
||||
/* platform */
|
||||
#if defined(COMPILER_MSVC)
|
||||
#include <intrin.h>
|
||||
#if !defined(_DEBUG)
|
||||
#undef mul32x32_64
|
||||
#define mul32x32_64(a,b) __emulu(a,b)
|
||||
#endif
|
||||
#undef inline
|
||||
#define inline __forceinline
|
||||
#define DONNA_INLINE __forceinline
|
||||
#define DONNA_NOINLINE __declspec(noinline)
|
||||
#define ALIGN(x) __declspec(align(x))
|
||||
#define ROTL32(a,b) _rotl(a,b)
|
||||
#define ROTR32(a,b) _rotr(a,b)
|
||||
#else
|
||||
#include <sys/param.h>
|
||||
#define DONNA_INLINE inline __attribute__((always_inline))
|
||||
#define DONNA_NOINLINE __attribute__((noinline))
|
||||
#define ALIGN(x) __attribute__((aligned(x)))
|
||||
#define ROTL32(a,b) (((a) << (b)) | ((a) >> (32 - b)))
|
||||
#define ROTR32(a,b) (((a) >> (b)) | ((a) << (32 - b)))
|
||||
#endif
|
||||
|
||||
/* uint128_t */
|
||||
#if defined(CPU_64BITS) && !defined(ED25519_FORCE_32BIT)
|
||||
#if defined(COMPILER_CLANG) && (COMPILER_CLANG >= 30100)
|
||||
#define HAVE_NATIVE_UINT128
|
||||
typedef unsigned __int128 uint128_t;
|
||||
#elif defined(COMPILER_MSVC)
|
||||
#define HAVE_UINT128
|
||||
typedef struct uint128_t {
|
||||
uint64_t lo, hi;
|
||||
} uint128_t;
|
||||
#define mul64x64_128(out,a,b) out.lo = _umul128(a,b,&out.hi);
|
||||
#define shr128_pair(out,hi,lo,shift) out = __shiftright128(lo, hi, shift);
|
||||
#define shl128_pair(out,hi,lo,shift) out = __shiftleft128(lo, hi, shift);
|
||||
#define shr128(out,in,shift) shr128_pair(out, in.hi, in.lo, shift)
|
||||
#define shl128(out,in,shift) shl128_pair(out, in.hi, in.lo, shift)
|
||||
#define add128(a,b) { uint64_t p = a.lo; a.lo += b.lo; a.hi += b.hi + (a.lo < p); }
|
||||
#define add128_64(a,b) { uint64_t p = a.lo; a.lo += b; a.hi += (a.lo < p); }
|
||||
#define lo128(a) (a.lo)
|
||||
#define hi128(a) (a.hi)
|
||||
#elif defined(COMPILER_GCC) && !defined(HAVE_NATIVE_UINT128)
|
||||
#if defined(__SIZEOF_INT128__)
|
||||
#define HAVE_NATIVE_UINT128
|
||||
typedef unsigned __int128 uint128_t;
|
||||
#elif (COMPILER_GCC >= 40400)
|
||||
#define HAVE_NATIVE_UINT128
|
||||
typedef unsigned uint128_t __attribute__((mode(TI)));
|
||||
#elif defined(CPU_X86_64)
|
||||
#define HAVE_UINT128
|
||||
typedef struct uint128_t {
|
||||
uint64_t lo, hi;
|
||||
} uint128_t;
|
||||
#define mul64x64_128(out,a,b) __asm__ ("mulq %3" : "=a" (out.lo), "=d" (out.hi) : "a" (a), "rm" (b));
|
||||
#define shr128_pair(out,hi,lo,shift) __asm__ ("shrdq %2,%1,%0" : "+r" (lo) : "r" (hi), "J" (shift)); out = lo;
|
||||
#define shl128_pair(out,hi,lo,shift) __asm__ ("shldq %2,%1,%0" : "+r" (hi) : "r" (lo), "J" (shift)); out = hi;
|
||||
#define shr128(out,in,shift) shr128_pair(out,in.hi, in.lo, shift)
|
||||
#define shl128(out,in,shift) shl128_pair(out,in.hi, in.lo, shift)
|
||||
#define add128(a,b) __asm__ ("addq %4,%2; adcq %5,%3" : "=r" (a.hi), "=r" (a.lo) : "1" (a.lo), "0" (a.hi), "rm" (b.lo), "rm" (b.hi) : "cc");
|
||||
#define add128_64(a,b) __asm__ ("addq %4,%2; adcq $0,%3" : "=r" (a.hi), "=r" (a.lo) : "1" (a.lo), "0" (a.hi), "rm" (b) : "cc");
|
||||
#define lo128(a) (a.lo)
|
||||
#define hi128(a) (a.hi)
|
||||
#endif
|
||||
#endif
|
||||
|
||||
#if defined(HAVE_NATIVE_UINT128)
|
||||
#define HAVE_UINT128
|
||||
#define mul64x64_128(out,a,b) out = (uint128_t)a * b;
|
||||
#define shr128_pair(out,hi,lo,shift) out = (uint64_t)((((uint128_t)hi << 64) | lo) >> (shift));
|
||||
#define shl128_pair(out,hi,lo,shift) out = (uint64_t)(((((uint128_t)hi << 64) | lo) << (shift)) >> 64);
|
||||
#define shr128(out,in,shift) out = (uint64_t)(in >> (shift));
|
||||
#define shl128(out,in,shift) out = (uint64_t)((in << shift) >> 64);
|
||||
#define add128(a,b) a += b;
|
||||
#define add128_64(a,b) a += (uint64_t)b;
|
||||
#define lo128(a) ((uint64_t)a)
|
||||
#define hi128(a) ((uint64_t)(a >> 64))
|
||||
#endif
|
||||
|
||||
#if !defined(HAVE_UINT128)
|
||||
#error Need a uint128_t implementation!
|
||||
#endif
|
||||
#endif
|
||||
|
||||
#include <stdlib.h>
|
||||
#include <string.h>
|
||||
|
||||
|
||||
66
curve25519-donna/curve25519-donna-scalarmult-base.h
Normal file
66
curve25519-donna/curve25519-donna-scalarmult-base.h
Normal file
@ -0,0 +1,66 @@
|
||||
/* Calculates nQ where Q is the x-coordinate of a point on the curve
|
||||
*
|
||||
* mypublic: the packed little endian x coordinate of the resulting curve point
|
||||
* n: a little endian, 32-byte number
|
||||
* basepoint: a packed little endian point of the curve
|
||||
*/
|
||||
|
||||
static void
|
||||
curve25519_scalarmult_donna(curve25519_key mypublic, const curve25519_key n, const curve25519_key basepoint) {
|
||||
bignum25519 nqpqx = {1}, nqpqz = {0}, nqz = {1}, nqx;
|
||||
bignum25519 q, qx, qpqx, qqx, zzz, zmone;
|
||||
size_t bit, lastbit;
|
||||
int32_t i;
|
||||
|
||||
curve25519_expand(q, basepoint);
|
||||
curve25519_copy(nqx, q);
|
||||
|
||||
/* bit 255 is always 0, and bit 254 is always 1, so skip bit 255 and
|
||||
start pre-swapped on bit 254 */
|
||||
lastbit = 1;
|
||||
|
||||
/* we are doing bits 254..3 in the loop, but are swapping in bits 253..2 */
|
||||
for (i = 253; i >= 2; i--) {
|
||||
curve25519_add(qx, nqx, nqz);
|
||||
curve25519_sub(nqz, nqx, nqz);
|
||||
curve25519_add(qpqx, nqpqx, nqpqz);
|
||||
curve25519_sub(nqpqz, nqpqx, nqpqz);
|
||||
curve25519_mul(nqpqx, qpqx, nqz);
|
||||
curve25519_mul(nqpqz, qx, nqpqz);
|
||||
curve25519_add(qqx, nqpqx, nqpqz);
|
||||
curve25519_sub(nqpqz, nqpqx, nqpqz);
|
||||
curve25519_square(nqpqz, nqpqz);
|
||||
curve25519_square(nqpqx, qqx);
|
||||
curve25519_mul(nqpqz, nqpqz, q);
|
||||
curve25519_square(qx, qx);
|
||||
curve25519_square(nqz, nqz);
|
||||
curve25519_mul(nqx, qx, nqz);
|
||||
curve25519_sub(nqz, qx, nqz);
|
||||
curve25519_scalar_product(zzz, nqz, 121665);
|
||||
curve25519_add(zzz, zzz, qx);
|
||||
curve25519_mul(nqz, nqz, zzz);
|
||||
|
||||
bit = (n[i/8] >> (i & 7)) & 1;
|
||||
curve25519_swap_conditional(nqx, nqpqx, bit ^ lastbit);
|
||||
curve25519_swap_conditional(nqz, nqpqz, bit ^ lastbit);
|
||||
lastbit = bit;
|
||||
}
|
||||
|
||||
/* the final 3 bits are always zero, so we only need to double */
|
||||
for (i = 0; i < 3; i++) {
|
||||
curve25519_add(qx, nqx, nqz);
|
||||
curve25519_sub(nqz, nqx, nqz);
|
||||
curve25519_square(qx, qx);
|
||||
curve25519_square(nqz, nqz);
|
||||
curve25519_mul(nqx, qx, nqz);
|
||||
curve25519_sub(nqz, qx, nqz);
|
||||
curve25519_scalar_product(zzz, nqz, 121665);
|
||||
curve25519_add(zzz, zzz, qx);
|
||||
curve25519_mul(nqz, nqz, zzz);
|
||||
}
|
||||
|
||||
curve25519_recip(zmone, nqz);
|
||||
curve25519_mul(nqz, nqx, zmone);
|
||||
curve25519_contract(mypublic, nqz);
|
||||
}
|
||||
|
||||
65
curve25519-donna/curve25519-donna-scalarmult-sse2.h
Normal file
65
curve25519-donna/curve25519-donna-scalarmult-sse2.h
Normal file
@ -0,0 +1,65 @@
|
||||
|
||||
/* Calculates nQ where Q is the x-coordinate of a point on the curve
|
||||
*
|
||||
* mypublic: the packed little endian x coordinate of the resulting curve point
|
||||
* n: a little endian, 32-byte number
|
||||
* basepoint: a packed little endian point of the curve
|
||||
*/
|
||||
static void
|
||||
curve25519_scalarmult_donna(curve25519_key mypublic, const curve25519_key n, const curve25519_key basepoint) {
|
||||
bignum25519 ALIGN(16) nqx = {1}, nqpqz = {1}, nqz = {0}, nqpqx, zmone;
|
||||
packed32bignum25519 qx, qz, pqz, pqx;
|
||||
packed64bignum25519 nq, sq, sqscalar, prime, primex, primez, nqpq;
|
||||
bignum25519mulprecomp preq;
|
||||
size_t bit, lastbit, i;
|
||||
|
||||
curve25519_expand(nqpqx, basepoint);
|
||||
curve25519_mul_precompute(&preq, nqpqx);
|
||||
|
||||
/* do bits 254..3 */
|
||||
for (i = 254, lastbit = 0; i >= 3; i--) {
|
||||
bit = (n[i/8] >> (i & 7)) & 1;
|
||||
curve25519_swap_conditional(nqx, nqpqx, bit ^ lastbit);
|
||||
curve25519_swap_conditional(nqz, nqpqz, bit ^ lastbit);
|
||||
lastbit = bit;
|
||||
|
||||
curve25519_tangle32(qx, nqx, nqpqx); /* qx = [nqx,nqpqx] */
|
||||
curve25519_tangle32(qz, nqz, nqpqz); /* qz = [nqz,nqpqz] */
|
||||
|
||||
curve25519_add_packed32(pqx, qx, qz); /* pqx = [nqx+nqz,nqpqx+nqpqz] */
|
||||
curve25519_sub_packed32(pqz, qx, qz); /* pqz = [nqx-nqz,nqpqx-nqpqz] */
|
||||
|
||||
curve25519_make_nqpq(primex, primez, pqx, pqz); /* primex = [nqx+nqz,nqpqx+nqpqz], primez = [nqpqx-nqpqz,nqx-nqz] */
|
||||
curve25519_mul_packed64(prime, primex, primez); /* prime = [nqx+nqz,nqpqx+nqpqz] * [nqpqx-nqpqz,nqx-nqz] */
|
||||
curve25519_addsub_packed64(prime); /* prime = [prime.x+prime.z,prime.x-prime.z] */
|
||||
curve25519_square_packed64(nqpq, prime); /* nqpq = prime^2 */
|
||||
curve25519_untangle64(nqpqx, nqpqz, nqpq);
|
||||
curve25519_mul_precomputed(nqpqz, nqpqz, &preq); /* nqpqz = nqpqz * q */
|
||||
|
||||
/* (((sq.x-sq.z)*121665)+sq.x) * (sq.x-sq.z) is equivalent to (sq.x*121666-sq.z*121665) * (sq.x-sq.z) */
|
||||
curve25519_make_nq(nq, pqx, pqz); /* nq = [nqx+nqz,nqx-nqz] */
|
||||
curve25519_square_packed64(sq, nq); /* sq = nq^2 */
|
||||
curve25519_121665_packed64(sqscalar, sq); /* sqscalar = sq * [121666,121665] */
|
||||
curve25519_final_nq(nq, sq, sqscalar); /* nq = [sq.x,sqscalar.x-sqscalar.z] * [sq.z,sq.x-sq.z] */
|
||||
curve25519_untangle64(nqx, nqz, nq);
|
||||
};
|
||||
|
||||
/* it's possible to get rid of this swap with the swap in the above loop
|
||||
at the bottom instead of the top, but compilers seem to optimize better this way */
|
||||
curve25519_swap_conditional(nqx, nqpqx, bit);
|
||||
curve25519_swap_conditional(nqz, nqpqz, bit);
|
||||
|
||||
/* do bits 2..0 */
|
||||
for (i = 0; i < 3; i++) {
|
||||
curve25519_compute_nq(nq, nqx, nqz);
|
||||
curve25519_square_packed64(sq, nq); /* sq = nq^2 */
|
||||
curve25519_121665_packed64(sqscalar, sq); /* sqscalar = sq * [121666,121665] */
|
||||
curve25519_final_nq(nq, sq, sqscalar); /* nq = [sq.x,sqscalar.x-sqscalar.z] * [sq.z,sq.x-sq.z] */
|
||||
curve25519_untangle64(nqx, nqz, nq);
|
||||
}
|
||||
|
||||
curve25519_recip(zmone, nqz);
|
||||
curve25519_mul(nqz, nqx, zmone);
|
||||
curve25519_contract(mypublic, nqz);
|
||||
}
|
||||
|
||||
1009
curve25519-donna/curve25519-donna-sse2.h
Normal file
1009
curve25519-donna/curve25519-donna-sse2.h
Normal file
File diff suppressed because it is too large
Load Diff
@ -1,863 +0,0 @@
|
||||
/* Copyright 2008, Google Inc.
|
||||
* All rights reserved.
|
||||
*
|
||||
* Redistribution and use in source and binary forms, with or without
|
||||
* modification, are permitted provided that the following conditions are
|
||||
* met:
|
||||
*
|
||||
* * Redistributions of source code must retain the above copyright
|
||||
* notice, this list of conditions and the following disclaimer.
|
||||
* * Redistributions in binary form must reproduce the above
|
||||
* copyright notice, this list of conditions and the following disclaimer
|
||||
* in the documentation and/or other materials provided with the
|
||||
* distribution.
|
||||
* * Neither the name of Google Inc. nor the names of its
|
||||
* contributors may be used to endorse or promote products derived from
|
||||
* this software without specific prior written permission.
|
||||
*
|
||||
* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
|
||||
* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
|
||||
* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
|
||||
* A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
|
||||
* OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
|
||||
* SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
|
||||
* LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
|
||||
* DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
|
||||
* THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
|
||||
* (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
|
||||
* OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
|
||||
*
|
||||
* curve25519-donna: Curve25519 elliptic curve, public key function
|
||||
*
|
||||
* http://code.google.com/p/curve25519-donna/
|
||||
*
|
||||
* Adam Langley <agl@imperialviolet.org>
|
||||
*
|
||||
* Derived from public domain C code by Daniel J. Bernstein <djb@cr.yp.to>
|
||||
*
|
||||
* More information about curve25519 can be found here
|
||||
* http://cr.yp.to/ecdh.html
|
||||
*
|
||||
* djb's sample implementation of curve25519 is written in a special assembly
|
||||
* language called qhasm and uses the floating point registers.
|
||||
*
|
||||
* This is, almost, a clean room reimplementation from the curve25519 paper. It
|
||||
* uses many of the tricks described therein. Only the crecip function is taken
|
||||
* from the sample implementation. */
|
||||
|
||||
#include <string.h>
|
||||
|
||||
#include "curve25519-donna.h"
|
||||
|
||||
#ifdef _MSC_VER
|
||||
#define inline __inline
|
||||
#endif
|
||||
|
||||
typedef int32_t s32;
|
||||
typedef int64_t limb;
|
||||
|
||||
/* Field element representation:
|
||||
*
|
||||
* Field elements are written as an array of signed, 64-bit limbs, least
|
||||
* significant first. The value of the field element is:
|
||||
* x[0] + 2^26·x[1] + x^51·x[2] + 2^102·x[3] + ...
|
||||
*
|
||||
* i.e. the limbs are 26, 25, 26, 25, ... bits wide. */
|
||||
|
||||
/* Sum two numbers: output += in */
|
||||
static void fsum(limb *output, const limb *in) {
|
||||
unsigned i;
|
||||
for (i = 0; i < 10; i += 2) {
|
||||
output[0+i] = output[0+i] + in[0+i];
|
||||
output[1+i] = output[1+i] + in[1+i];
|
||||
}
|
||||
}
|
||||
|
||||
/* Find the difference of two numbers: output = in - output
|
||||
* (note the order of the arguments!). */
|
||||
static void fdifference(limb *output, const limb *in) {
|
||||
unsigned i;
|
||||
for (i = 0; i < 10; ++i) {
|
||||
output[i] = in[i] - output[i];
|
||||
}
|
||||
}
|
||||
|
||||
/* Multiply a number by a scalar: output = in * scalar */
|
||||
static void fscalar_product(limb *output, const limb *in, const limb scalar) {
|
||||
unsigned i;
|
||||
for (i = 0; i < 10; ++i) {
|
||||
output[i] = in[i] * scalar;
|
||||
}
|
||||
}
|
||||
|
||||
/* Multiply two numbers: output = in2 * in
|
||||
*
|
||||
* output must be distinct to both inputs. The inputs are reduced coefficient
|
||||
* form, the output is not.
|
||||
*
|
||||
* output[x] <= 14 * the largest product of the input limbs. */
|
||||
static void fproduct(limb *output, const limb *in2, const limb *in) {
|
||||
output[0] = ((limb) ((s32) in2[0])) * ((s32) in[0]);
|
||||
output[1] = ((limb) ((s32) in2[0])) * ((s32) in[1]) +
|
||||
((limb) ((s32) in2[1])) * ((s32) in[0]);
|
||||
output[2] = 2 * ((limb) ((s32) in2[1])) * ((s32) in[1]) +
|
||||
((limb) ((s32) in2[0])) * ((s32) in[2]) +
|
||||
((limb) ((s32) in2[2])) * ((s32) in[0]);
|
||||
output[3] = ((limb) ((s32) in2[1])) * ((s32) in[2]) +
|
||||
((limb) ((s32) in2[2])) * ((s32) in[1]) +
|
||||
((limb) ((s32) in2[0])) * ((s32) in[3]) +
|
||||
((limb) ((s32) in2[3])) * ((s32) in[0]);
|
||||
output[4] = ((limb) ((s32) in2[2])) * ((s32) in[2]) +
|
||||
2 * (((limb) ((s32) in2[1])) * ((s32) in[3]) +
|
||||
((limb) ((s32) in2[3])) * ((s32) in[1])) +
|
||||
((limb) ((s32) in2[0])) * ((s32) in[4]) +
|
||||
((limb) ((s32) in2[4])) * ((s32) in[0]);
|
||||
output[5] = ((limb) ((s32) in2[2])) * ((s32) in[3]) +
|
||||
((limb) ((s32) in2[3])) * ((s32) in[2]) +
|
||||
((limb) ((s32) in2[1])) * ((s32) in[4]) +
|
||||
((limb) ((s32) in2[4])) * ((s32) in[1]) +
|
||||
((limb) ((s32) in2[0])) * ((s32) in[5]) +
|
||||
((limb) ((s32) in2[5])) * ((s32) in[0]);
|
||||
output[6] = 2 * (((limb) ((s32) in2[3])) * ((s32) in[3]) +
|
||||
((limb) ((s32) in2[1])) * ((s32) in[5]) +
|
||||
((limb) ((s32) in2[5])) * ((s32) in[1])) +
|
||||
((limb) ((s32) in2[2])) * ((s32) in[4]) +
|
||||
((limb) ((s32) in2[4])) * ((s32) in[2]) +
|
||||
((limb) ((s32) in2[0])) * ((s32) in[6]) +
|
||||
((limb) ((s32) in2[6])) * ((s32) in[0]);
|
||||
output[7] = ((limb) ((s32) in2[3])) * ((s32) in[4]) +
|
||||
((limb) ((s32) in2[4])) * ((s32) in[3]) +
|
||||
((limb) ((s32) in2[2])) * ((s32) in[5]) +
|
||||
((limb) ((s32) in2[5])) * ((s32) in[2]) +
|
||||
((limb) ((s32) in2[1])) * ((s32) in[6]) +
|
||||
((limb) ((s32) in2[6])) * ((s32) in[1]) +
|
||||
((limb) ((s32) in2[0])) * ((s32) in[7]) +
|
||||
((limb) ((s32) in2[7])) * ((s32) in[0]);
|
||||
output[8] = ((limb) ((s32) in2[4])) * ((s32) in[4]) +
|
||||
2 * (((limb) ((s32) in2[3])) * ((s32) in[5]) +
|
||||
((limb) ((s32) in2[5])) * ((s32) in[3]) +
|
||||
((limb) ((s32) in2[1])) * ((s32) in[7]) +
|
||||
((limb) ((s32) in2[7])) * ((s32) in[1])) +
|
||||
((limb) ((s32) in2[2])) * ((s32) in[6]) +
|
||||
((limb) ((s32) in2[6])) * ((s32) in[2]) +
|
||||
((limb) ((s32) in2[0])) * ((s32) in[8]) +
|
||||
((limb) ((s32) in2[8])) * ((s32) in[0]);
|
||||
output[9] = ((limb) ((s32) in2[4])) * ((s32) in[5]) +
|
||||
((limb) ((s32) in2[5])) * ((s32) in[4]) +
|
||||
((limb) ((s32) in2[3])) * ((s32) in[6]) +
|
||||
((limb) ((s32) in2[6])) * ((s32) in[3]) +
|
||||
((limb) ((s32) in2[2])) * ((s32) in[7]) +
|
||||
((limb) ((s32) in2[7])) * ((s32) in[2]) +
|
||||
((limb) ((s32) in2[1])) * ((s32) in[8]) +
|
||||
((limb) ((s32) in2[8])) * ((s32) in[1]) +
|
||||
((limb) ((s32) in2[0])) * ((s32) in[9]) +
|
||||
((limb) ((s32) in2[9])) * ((s32) in[0]);
|
||||
output[10] = 2 * (((limb) ((s32) in2[5])) * ((s32) in[5]) +
|
||||
((limb) ((s32) in2[3])) * ((s32) in[7]) +
|
||||
((limb) ((s32) in2[7])) * ((s32) in[3]) +
|
||||
((limb) ((s32) in2[1])) * ((s32) in[9]) +
|
||||
((limb) ((s32) in2[9])) * ((s32) in[1])) +
|
||||
((limb) ((s32) in2[4])) * ((s32) in[6]) +
|
||||
((limb) ((s32) in2[6])) * ((s32) in[4]) +
|
||||
((limb) ((s32) in2[2])) * ((s32) in[8]) +
|
||||
((limb) ((s32) in2[8])) * ((s32) in[2]);
|
||||
output[11] = ((limb) ((s32) in2[5])) * ((s32) in[6]) +
|
||||
((limb) ((s32) in2[6])) * ((s32) in[5]) +
|
||||
((limb) ((s32) in2[4])) * ((s32) in[7]) +
|
||||
((limb) ((s32) in2[7])) * ((s32) in[4]) +
|
||||
((limb) ((s32) in2[3])) * ((s32) in[8]) +
|
||||
((limb) ((s32) in2[8])) * ((s32) in[3]) +
|
||||
((limb) ((s32) in2[2])) * ((s32) in[9]) +
|
||||
((limb) ((s32) in2[9])) * ((s32) in[2]);
|
||||
output[12] = ((limb) ((s32) in2[6])) * ((s32) in[6]) +
|
||||
2 * (((limb) ((s32) in2[5])) * ((s32) in[7]) +
|
||||
((limb) ((s32) in2[7])) * ((s32) in[5]) +
|
||||
((limb) ((s32) in2[3])) * ((s32) in[9]) +
|
||||
((limb) ((s32) in2[9])) * ((s32) in[3])) +
|
||||
((limb) ((s32) in2[4])) * ((s32) in[8]) +
|
||||
((limb) ((s32) in2[8])) * ((s32) in[4]);
|
||||
output[13] = ((limb) ((s32) in2[6])) * ((s32) in[7]) +
|
||||
((limb) ((s32) in2[7])) * ((s32) in[6]) +
|
||||
((limb) ((s32) in2[5])) * ((s32) in[8]) +
|
||||
((limb) ((s32) in2[8])) * ((s32) in[5]) +
|
||||
((limb) ((s32) in2[4])) * ((s32) in[9]) +
|
||||
((limb) ((s32) in2[9])) * ((s32) in[4]);
|
||||
output[14] = 2 * (((limb) ((s32) in2[7])) * ((s32) in[7]) +
|
||||
((limb) ((s32) in2[5])) * ((s32) in[9]) +
|
||||
((limb) ((s32) in2[9])) * ((s32) in[5])) +
|
||||
((limb) ((s32) in2[6])) * ((s32) in[8]) +
|
||||
((limb) ((s32) in2[8])) * ((s32) in[6]);
|
||||
output[15] = ((limb) ((s32) in2[7])) * ((s32) in[8]) +
|
||||
((limb) ((s32) in2[8])) * ((s32) in[7]) +
|
||||
((limb) ((s32) in2[6])) * ((s32) in[9]) +
|
||||
((limb) ((s32) in2[9])) * ((s32) in[6]);
|
||||
output[16] = ((limb) ((s32) in2[8])) * ((s32) in[8]) +
|
||||
2 * (((limb) ((s32) in2[7])) * ((s32) in[9]) +
|
||||
((limb) ((s32) in2[9])) * ((s32) in[7]));
|
||||
output[17] = ((limb) ((s32) in2[8])) * ((s32) in[9]) +
|
||||
((limb) ((s32) in2[9])) * ((s32) in[8]);
|
||||
output[18] = 2 * ((limb) ((s32) in2[9])) * ((s32) in[9]);
|
||||
}
|
||||
|
||||
/* Reduce a long form to a short form by taking the input mod 2^255 - 19.
|
||||
*
|
||||
* On entry: |output[i]| < 14*2^54
|
||||
* On exit: |output[0..8]| < 280*2^54 */
|
||||
static void freduce_degree(limb *output) {
|
||||
/* Each of these shifts and adds ends up multiplying the value by 19.
|
||||
*
|
||||
* For output[0..8], the absolute entry value is < 14*2^54 and we add, at
|
||||
* most, 19*14*2^54 thus, on exit, |output[0..8]| < 280*2^54. */
|
||||
output[8] += output[18] << 4;
|
||||
output[8] += output[18] << 1;
|
||||
output[8] += output[18];
|
||||
output[7] += output[17] << 4;
|
||||
output[7] += output[17] << 1;
|
||||
output[7] += output[17];
|
||||
output[6] += output[16] << 4;
|
||||
output[6] += output[16] << 1;
|
||||
output[6] += output[16];
|
||||
output[5] += output[15] << 4;
|
||||
output[5] += output[15] << 1;
|
||||
output[5] += output[15];
|
||||
output[4] += output[14] << 4;
|
||||
output[4] += output[14] << 1;
|
||||
output[4] += output[14];
|
||||
output[3] += output[13] << 4;
|
||||
output[3] += output[13] << 1;
|
||||
output[3] += output[13];
|
||||
output[2] += output[12] << 4;
|
||||
output[2] += output[12] << 1;
|
||||
output[2] += output[12];
|
||||
output[1] += output[11] << 4;
|
||||
output[1] += output[11] << 1;
|
||||
output[1] += output[11];
|
||||
output[0] += output[10] << 4;
|
||||
output[0] += output[10] << 1;
|
||||
output[0] += output[10];
|
||||
}
|
||||
|
||||
#if (-1 & 3) != 3
|
||||
#error "This code only works on a two's complement system"
|
||||
#endif
|
||||
|
||||
/* return v / 2^26, using only shifts and adds.
|
||||
*
|
||||
* On entry: v can take any value. */
|
||||
static inline limb
|
||||
div_by_2_26(const limb v)
|
||||
{
|
||||
/* High word of v; no shift needed. */
|
||||
const uint32_t highword = (uint32_t) (((uint64_t) v) >> 32);
|
||||
/* Set to all 1s if v was negative; else set to 0s. */
|
||||
const int32_t sign = ((int32_t) highword) >> 31;
|
||||
/* Set to 0x3ffffff if v was negative; else set to 0. */
|
||||
const int32_t roundoff = ((uint32_t) sign) >> 6;
|
||||
/* Should return v / (1<<26) */
|
||||
return (v + roundoff) >> 26;
|
||||
}
|
||||
|
||||
/* return v / (2^25), using only shifts and adds.
|
||||
*
|
||||
* On entry: v can take any value. */
|
||||
static inline limb
|
||||
div_by_2_25(const limb v)
|
||||
{
|
||||
/* High word of v; no shift needed*/
|
||||
const uint32_t highword = (uint32_t) (((uint64_t) v) >> 32);
|
||||
/* Set to all 1s if v was negative; else set to 0s. */
|
||||
const int32_t sign = ((int32_t) highword) >> 31;
|
||||
/* Set to 0x1ffffff if v was negative; else set to 0. */
|
||||
const int32_t roundoff = ((uint32_t) sign) >> 7;
|
||||
/* Should return v / (1<<25) */
|
||||
return (v + roundoff) >> 25;
|
||||
}
|
||||
|
||||
/* Reduce all coefficients of the short form input so that |x| < 2^26.
|
||||
*
|
||||
* On entry: |output[i]| < 280*2^54 */
|
||||
static void freduce_coefficients(limb *output) {
|
||||
unsigned i;
|
||||
|
||||
output[10] = 0;
|
||||
|
||||
for (i = 0; i < 10; i += 2) {
|
||||
limb over = div_by_2_26(output[i]);
|
||||
/* The entry condition (that |output[i]| < 280*2^54) means that over is, at
|
||||
* most, 280*2^28 in the first iteration of this loop. This is added to the
|
||||
* next limb and we can approximate the resulting bound of that limb by
|
||||
* 281*2^54. */
|
||||
output[i] -= over << 26;
|
||||
output[i+1] += over;
|
||||
|
||||
/* For the first iteration, |output[i+1]| < 281*2^54, thus |over| <
|
||||
* 281*2^29. When this is added to the next limb, the resulting bound can
|
||||
* be approximated as 281*2^54.
|
||||
*
|
||||
* For subsequent iterations of the loop, 281*2^54 remains a conservative
|
||||
* bound and no overflow occurs. */
|
||||
over = div_by_2_25(output[i+1]);
|
||||
output[i+1] -= over << 25;
|
||||
output[i+2] += over;
|
||||
}
|
||||
/* Now |output[10]| < 281*2^29 and all other coefficients are reduced. */
|
||||
output[0] += output[10] << 4;
|
||||
output[0] += output[10] << 1;
|
||||
output[0] += output[10];
|
||||
|
||||
output[10] = 0;
|
||||
|
||||
/* Now output[1..9] are reduced, and |output[0]| < 2^26 + 19*281*2^29
|
||||
* So |over| will be no more than 2^16. */
|
||||
{
|
||||
limb over = div_by_2_26(output[0]);
|
||||
output[0] -= over << 26;
|
||||
output[1] += over;
|
||||
}
|
||||
|
||||
/* Now output[0,2..9] are reduced, and |output[1]| < 2^25 + 2^16 < 2^26. The
|
||||
* bound on |output[1]| is sufficient to meet our needs. */
|
||||
}
|
||||
|
||||
/* A helpful wrapper around fproduct: output = in * in2.
|
||||
*
|
||||
* On entry: |in[i]| < 2^27 and |in2[i]| < 2^27.
|
||||
*
|
||||
* output must be distinct to both inputs. The output is reduced degree
|
||||
* (indeed, one need only provide storage for 10 limbs) and |output[i]| < 2^26. */
|
||||
static void
|
||||
fmul(limb *output, const limb *in, const limb *in2) {
|
||||
limb t[19];
|
||||
fproduct(t, in, in2);
|
||||
/* |t[i]| < 14*2^54 */
|
||||
freduce_degree(t);
|
||||
freduce_coefficients(t);
|
||||
/* |t[i]| < 2^26 */
|
||||
memcpy(output, t, sizeof(limb) * 10);
|
||||
}
|
||||
|
||||
/* Square a number: output = in**2
|
||||
*
|
||||
* output must be distinct from the input. The inputs are reduced coefficient
|
||||
* form, the output is not.
|
||||
*
|
||||
* output[x] <= 14 * the largest product of the input limbs. */
|
||||
static void fsquare_inner(limb *output, const limb *in) {
|
||||
output[0] = ((limb) ((s32) in[0])) * ((s32) in[0]);
|
||||
output[1] = 2 * ((limb) ((s32) in[0])) * ((s32) in[1]);
|
||||
output[2] = 2 * (((limb) ((s32) in[1])) * ((s32) in[1]) +
|
||||
((limb) ((s32) in[0])) * ((s32) in[2]));
|
||||
output[3] = 2 * (((limb) ((s32) in[1])) * ((s32) in[2]) +
|
||||
((limb) ((s32) in[0])) * ((s32) in[3]));
|
||||
output[4] = ((limb) ((s32) in[2])) * ((s32) in[2]) +
|
||||
4 * ((limb) ((s32) in[1])) * ((s32) in[3]) +
|
||||
2 * ((limb) ((s32) in[0])) * ((s32) in[4]);
|
||||
output[5] = 2 * (((limb) ((s32) in[2])) * ((s32) in[3]) +
|
||||
((limb) ((s32) in[1])) * ((s32) in[4]) +
|
||||
((limb) ((s32) in[0])) * ((s32) in[5]));
|
||||
output[6] = 2 * (((limb) ((s32) in[3])) * ((s32) in[3]) +
|
||||
((limb) ((s32) in[2])) * ((s32) in[4]) +
|
||||
((limb) ((s32) in[0])) * ((s32) in[6]) +
|
||||
2 * ((limb) ((s32) in[1])) * ((s32) in[5]));
|
||||
output[7] = 2 * (((limb) ((s32) in[3])) * ((s32) in[4]) +
|
||||
((limb) ((s32) in[2])) * ((s32) in[5]) +
|
||||
((limb) ((s32) in[1])) * ((s32) in[6]) +
|
||||
((limb) ((s32) in[0])) * ((s32) in[7]));
|
||||
output[8] = ((limb) ((s32) in[4])) * ((s32) in[4]) +
|
||||
2 * (((limb) ((s32) in[2])) * ((s32) in[6]) +
|
||||
((limb) ((s32) in[0])) * ((s32) in[8]) +
|
||||
2 * (((limb) ((s32) in[1])) * ((s32) in[7]) +
|
||||
((limb) ((s32) in[3])) * ((s32) in[5])));
|
||||
output[9] = 2 * (((limb) ((s32) in[4])) * ((s32) in[5]) +
|
||||
((limb) ((s32) in[3])) * ((s32) in[6]) +
|
||||
((limb) ((s32) in[2])) * ((s32) in[7]) +
|
||||
((limb) ((s32) in[1])) * ((s32) in[8]) +
|
||||
((limb) ((s32) in[0])) * ((s32) in[9]));
|
||||
output[10] = 2 * (((limb) ((s32) in[5])) * ((s32) in[5]) +
|
||||
((limb) ((s32) in[4])) * ((s32) in[6]) +
|
||||
((limb) ((s32) in[2])) * ((s32) in[8]) +
|
||||
2 * (((limb) ((s32) in[3])) * ((s32) in[7]) +
|
||||
((limb) ((s32) in[1])) * ((s32) in[9])));
|
||||
output[11] = 2 * (((limb) ((s32) in[5])) * ((s32) in[6]) +
|
||||
((limb) ((s32) in[4])) * ((s32) in[7]) +
|
||||
((limb) ((s32) in[3])) * ((s32) in[8]) +
|
||||
((limb) ((s32) in[2])) * ((s32) in[9]));
|
||||
output[12] = ((limb) ((s32) in[6])) * ((s32) in[6]) +
|
||||
2 * (((limb) ((s32) in[4])) * ((s32) in[8]) +
|
||||
2 * (((limb) ((s32) in[5])) * ((s32) in[7]) +
|
||||
((limb) ((s32) in[3])) * ((s32) in[9])));
|
||||
output[13] = 2 * (((limb) ((s32) in[6])) * ((s32) in[7]) +
|
||||
((limb) ((s32) in[5])) * ((s32) in[8]) +
|
||||
((limb) ((s32) in[4])) * ((s32) in[9]));
|
||||
output[14] = 2 * (((limb) ((s32) in[7])) * ((s32) in[7]) +
|
||||
((limb) ((s32) in[6])) * ((s32) in[8]) +
|
||||
2 * ((limb) ((s32) in[5])) * ((s32) in[9]));
|
||||
output[15] = 2 * (((limb) ((s32) in[7])) * ((s32) in[8]) +
|
||||
((limb) ((s32) in[6])) * ((s32) in[9]));
|
||||
output[16] = ((limb) ((s32) in[8])) * ((s32) in[8]) +
|
||||
4 * ((limb) ((s32) in[7])) * ((s32) in[9]);
|
||||
output[17] = 2 * ((limb) ((s32) in[8])) * ((s32) in[9]);
|
||||
output[18] = 2 * ((limb) ((s32) in[9])) * ((s32) in[9]);
|
||||
}
|
||||
|
||||
/* fsquare sets output = in^2.
|
||||
*
|
||||
* On entry: The |in| argument is in reduced coefficients form and |in[i]| <
|
||||
* 2^27.
|
||||
*
|
||||
* On exit: The |output| argument is in reduced coefficients form (indeed, one
|
||||
* need only provide storage for 10 limbs) and |out[i]| < 2^26. */
|
||||
static void
|
||||
fsquare(limb *output, const limb *in) {
|
||||
limb t[19];
|
||||
fsquare_inner(t, in);
|
||||
/* |t[i]| < 14*2^54 because the largest product of two limbs will be <
|
||||
* 2^(27+27) and fsquare_inner adds together, at most, 14 of those
|
||||
* products. */
|
||||
freduce_degree(t);
|
||||
freduce_coefficients(t);
|
||||
/* |t[i]| < 2^26 */
|
||||
memcpy(output, t, sizeof(limb) * 10);
|
||||
}
|
||||
|
||||
/* Take a little-endian, 32-byte number and expand it into polynomial form */
|
||||
static void
|
||||
fexpand(limb *output, const u8 *input) {
|
||||
#define F(n,start,shift,mask) \
|
||||
output[n] = ((((limb) input[start + 0]) | \
|
||||
((limb) input[start + 1]) << 8 | \
|
||||
((limb) input[start + 2]) << 16 | \
|
||||
((limb) input[start + 3]) << 24) >> shift) & mask;
|
||||
F(0, 0, 0, 0x3ffffff);
|
||||
F(1, 3, 2, 0x1ffffff);
|
||||
F(2, 6, 3, 0x3ffffff);
|
||||
F(3, 9, 5, 0x1ffffff);
|
||||
F(4, 12, 6, 0x3ffffff);
|
||||
F(5, 16, 0, 0x1ffffff);
|
||||
F(6, 19, 1, 0x3ffffff);
|
||||
F(7, 22, 3, 0x1ffffff);
|
||||
F(8, 25, 4, 0x3ffffff);
|
||||
F(9, 28, 6, 0x1ffffff);
|
||||
#undef F
|
||||
}
|
||||
|
||||
#if (-32 >> 1) != -16
|
||||
#error "This code only works when >> does sign-extension on negative numbers"
|
||||
#endif
|
||||
|
||||
/* s32_eq returns 0xffffffff iff a == b and zero otherwise. */
|
||||
static s32 s32_eq(s32 a, s32 b) {
|
||||
a = ~(a ^ b);
|
||||
a &= a << 16;
|
||||
a &= a << 8;
|
||||
a &= a << 4;
|
||||
a &= a << 2;
|
||||
a &= a << 1;
|
||||
return a >> 31;
|
||||
}
|
||||
|
||||
/* s32_gte returns 0xffffffff if a >= b and zero otherwise, where a and b are
|
||||
* both non-negative. */
|
||||
static s32 s32_gte(s32 a, s32 b) {
|
||||
a -= b;
|
||||
/* a >= 0 iff a >= b. */
|
||||
return ~(a >> 31);
|
||||
}
|
||||
|
||||
/* Take a fully reduced polynomial form number and contract it into a
|
||||
* little-endian, 32-byte array.
|
||||
*
|
||||
* On entry: |input_limbs[i]| < 2^26 */
|
||||
static void
|
||||
fcontract(u8 *output, limb *input_limbs) {
|
||||
int i;
|
||||
int j;
|
||||
s32 input[10];
|
||||
|
||||
/* |input_limbs[i]| < 2^26, so it's valid to convert to an s32. */
|
||||
for (i = 0; i < 10; i++) {
|
||||
input[i] = input_limbs[i];
|
||||
}
|
||||
|
||||
for (j = 0; j < 2; ++j) {
|
||||
for (i = 0; i < 9; ++i) {
|
||||
if ((i & 1) == 1) {
|
||||
/* This calculation is a time-invariant way to make input[i]
|
||||
* non-negative by borrowing from the next-larger limb. */
|
||||
const s32 mask = input[i] >> 31;
|
||||
const s32 carry = -((input[i] & mask) >> 25);
|
||||
input[i] = input[i] + (carry << 25);
|
||||
input[i+1] = input[i+1] - carry;
|
||||
} else {
|
||||
const s32 mask = input[i] >> 31;
|
||||
const s32 carry = -((input[i] & mask) >> 26);
|
||||
input[i] = input[i] + (carry << 26);
|
||||
input[i+1] = input[i+1] - carry;
|
||||
}
|
||||
}
|
||||
|
||||
/* There's no greater limb for input[9] to borrow from, but we can multiply
|
||||
* by 19 and borrow from input[0], which is valid mod 2^255-19. */
|
||||
{
|
||||
const s32 mask = input[9] >> 31;
|
||||
const s32 carry = -((input[9] & mask) >> 25);
|
||||
input[9] = input[9] + (carry << 25);
|
||||
input[0] = input[0] - (carry * 19);
|
||||
}
|
||||
|
||||
/* After the first iteration, input[1..9] are non-negative and fit within
|
||||
* 25 or 26 bits, depending on position. However, input[0] may be
|
||||
* negative. */
|
||||
}
|
||||
|
||||
/* The first borrow-propagation pass above ended with every limb
|
||||
except (possibly) input[0] non-negative.
|
||||
|
||||
If input[0] was negative after the first pass, then it was because of a
|
||||
carry from input[9]. On entry, input[9] < 2^26 so the carry was, at most,
|
||||
one, since (2**26-1) >> 25 = 1. Thus input[0] >= -19.
|
||||
|
||||
In the second pass, each limb is decreased by at most one. Thus the second
|
||||
borrow-propagation pass could only have wrapped around to decrease
|
||||
input[0] again if the first pass left input[0] negative *and* input[1]
|
||||
through input[9] were all zero. In that case, input[1] is now 2^25 - 1,
|
||||
and this last borrow-propagation step will leave input[1] non-negative. */
|
||||
{
|
||||
const s32 mask = input[0] >> 31;
|
||||
const s32 carry = -((input[0] & mask) >> 26);
|
||||
input[0] = input[0] + (carry << 26);
|
||||
input[1] = input[1] - carry;
|
||||
}
|
||||
|
||||
/* All input[i] are now non-negative. However, there might be values between
|
||||
* 2^25 and 2^26 in a limb which is, nominally, 25 bits wide. */
|
||||
for (j = 0; j < 2; j++) {
|
||||
for (i = 0; i < 9; i++) {
|
||||
if ((i & 1) == 1) {
|
||||
const s32 carry = input[i] >> 25;
|
||||
input[i] &= 0x1ffffff;
|
||||
input[i+1] += carry;
|
||||
} else {
|
||||
const s32 carry = input[i] >> 26;
|
||||
input[i] &= 0x3ffffff;
|
||||
input[i+1] += carry;
|
||||
}
|
||||
}
|
||||
|
||||
{
|
||||
const s32 carry = input[9] >> 25;
|
||||
input[9] &= 0x1ffffff;
|
||||
input[0] += 19*carry;
|
||||
}
|
||||
}
|
||||
|
||||
/* If the first carry-chain pass, just above, ended up with a carry from
|
||||
* input[9], and that caused input[0] to be out-of-bounds, then input[0] was
|
||||
* < 2^26 + 2*19, because the carry was, at most, two.
|
||||
*
|
||||
* If the second pass carried from input[9] again then input[0] is < 2*19 and
|
||||
* the input[9] -> input[0] carry didn't push input[0] out of bounds. */
|
||||
|
||||
/* It still remains the case that input might be between 2^255-19 and 2^255.
|
||||
* In this case, input[1..9] must take their maximum value and input[0] must
|
||||
* be >= (2^255-19) & 0x3ffffff, which is 0x3ffffed. */
|
||||
s32 mask = s32_gte(input[0], 0x3ffffed);
|
||||
for (i = 1; i < 10; i++) {
|
||||
if ((i & 1) == 1) {
|
||||
mask &= s32_eq(input[i], 0x1ffffff);
|
||||
} else {
|
||||
mask &= s32_eq(input[i], 0x3ffffff);
|
||||
}
|
||||
}
|
||||
|
||||
/* mask is either 0xffffffff (if input >= 2^255-19) and zero otherwise. Thus
|
||||
* this conditionally subtracts 2^255-19. */
|
||||
input[0] -= mask & 0x3ffffed;
|
||||
|
||||
for (i = 1; i < 10; i++) {
|
||||
if ((i & 1) == 1) {
|
||||
input[i] -= mask & 0x1ffffff;
|
||||
} else {
|
||||
input[i] -= mask & 0x3ffffff;
|
||||
}
|
||||
}
|
||||
|
||||
input[1] <<= 2;
|
||||
input[2] <<= 3;
|
||||
input[3] <<= 5;
|
||||
input[4] <<= 6;
|
||||
input[6] <<= 1;
|
||||
input[7] <<= 3;
|
||||
input[8] <<= 4;
|
||||
input[9] <<= 6;
|
||||
#define F(i, s) \
|
||||
output[s+0] |= input[i] & 0xff; \
|
||||
output[s+1] = (input[i] >> 8) & 0xff; \
|
||||
output[s+2] = (input[i] >> 16) & 0xff; \
|
||||
output[s+3] = (input[i] >> 24) & 0xff;
|
||||
output[0] = 0;
|
||||
output[16] = 0;
|
||||
F(0,0);
|
||||
F(1,3);
|
||||
F(2,6);
|
||||
F(3,9);
|
||||
F(4,12);
|
||||
F(5,16);
|
||||
F(6,19);
|
||||
F(7,22);
|
||||
F(8,25);
|
||||
F(9,28);
|
||||
#undef F
|
||||
}
|
||||
|
||||
/* Input: Q, Q', Q-Q'
|
||||
* Output: 2Q, Q+Q'
|
||||
*
|
||||
* x2 z3: long form
|
||||
* x3 z3: long form
|
||||
* x z: short form, destroyed
|
||||
* xprime zprime: short form, destroyed
|
||||
* qmqp: short form, preserved
|
||||
*
|
||||
* On entry and exit, the absolute value of the limbs of all inputs and outputs
|
||||
* are < 2^26. */
|
||||
static void fmonty(limb *x2, limb *z2, /* output 2Q */
|
||||
limb *x3, limb *z3, /* output Q + Q' */
|
||||
limb *x, limb *z, /* input Q */
|
||||
limb *xprime, limb *zprime, /* input Q' */
|
||||
const limb *qmqp /* input Q - Q' */) {
|
||||
limb origx[10], origxprime[10], zzz[19], xx[19], zz[19], xxprime[19],
|
||||
zzprime[19], zzzprime[19], xxxprime[19];
|
||||
|
||||
memcpy(origx, x, 10 * sizeof(limb));
|
||||
fsum(x, z);
|
||||
/* |x[i]| < 2^27 */
|
||||
fdifference(z, origx); /* does x - z */
|
||||
/* |z[i]| < 2^27 */
|
||||
|
||||
memcpy(origxprime, xprime, sizeof(limb) * 10);
|
||||
fsum(xprime, zprime);
|
||||
/* |xprime[i]| < 2^27 */
|
||||
fdifference(zprime, origxprime);
|
||||
/* |zprime[i]| < 2^27 */
|
||||
fproduct(xxprime, xprime, z);
|
||||
/* |xxprime[i]| < 14*2^54: the largest product of two limbs will be <
|
||||
* 2^(27+27) and fproduct adds together, at most, 14 of those products.
|
||||
* (Approximating that to 2^58 doesn't work out.) */
|
||||
fproduct(zzprime, x, zprime);
|
||||
/* |zzprime[i]| < 14*2^54 */
|
||||
freduce_degree(xxprime);
|
||||
freduce_coefficients(xxprime);
|
||||
/* |xxprime[i]| < 2^26 */
|
||||
freduce_degree(zzprime);
|
||||
freduce_coefficients(zzprime);
|
||||
/* |zzprime[i]| < 2^26 */
|
||||
memcpy(origxprime, xxprime, sizeof(limb) * 10);
|
||||
fsum(xxprime, zzprime);
|
||||
/* |xxprime[i]| < 2^27 */
|
||||
fdifference(zzprime, origxprime);
|
||||
/* |zzprime[i]| < 2^27 */
|
||||
fsquare(xxxprime, xxprime);
|
||||
/* |xxxprime[i]| < 2^26 */
|
||||
fsquare(zzzprime, zzprime);
|
||||
/* |zzzprime[i]| < 2^26 */
|
||||
fproduct(zzprime, zzzprime, qmqp);
|
||||
/* |zzprime[i]| < 14*2^52 */
|
||||
freduce_degree(zzprime);
|
||||
freduce_coefficients(zzprime);
|
||||
/* |zzprime[i]| < 2^26 */
|
||||
memcpy(x3, xxxprime, sizeof(limb) * 10);
|
||||
memcpy(z3, zzprime, sizeof(limb) * 10);
|
||||
|
||||
fsquare(xx, x);
|
||||
/* |xx[i]| < 2^26 */
|
||||
fsquare(zz, z);
|
||||
/* |zz[i]| < 2^26 */
|
||||
fproduct(x2, xx, zz);
|
||||
/* |x2[i]| < 14*2^52 */
|
||||
freduce_degree(x2);
|
||||
freduce_coefficients(x2);
|
||||
/* |x2[i]| < 2^26 */
|
||||
fdifference(zz, xx); // does zz = xx - zz
|
||||
/* |zz[i]| < 2^27 */
|
||||
memset(zzz + 10, 0, sizeof(limb) * 9);
|
||||
fscalar_product(zzz, zz, 121665);
|
||||
/* |zzz[i]| < 2^(27+17) */
|
||||
/* No need to call freduce_degree here:
|
||||
fscalar_product doesn't increase the degree of its input. */
|
||||
freduce_coefficients(zzz);
|
||||
/* |zzz[i]| < 2^26 */
|
||||
fsum(zzz, xx);
|
||||
/* |zzz[i]| < 2^27 */
|
||||
fproduct(z2, zz, zzz);
|
||||
/* |z2[i]| < 14*2^(26+27) */
|
||||
freduce_degree(z2);
|
||||
freduce_coefficients(z2);
|
||||
/* |z2|i| < 2^26 */
|
||||
}
|
||||
|
||||
/* Conditionally swap two reduced-form limb arrays if 'iswap' is 1, but leave
|
||||
* them unchanged if 'iswap' is 0. Runs in data-invariant time to avoid
|
||||
* side-channel attacks.
|
||||
*
|
||||
* NOTE that this function requires that 'iswap' be 1 or 0; other values give
|
||||
* wrong results. Also, the two limb arrays must be in reduced-coefficient,
|
||||
* reduced-degree form: the values in a[10..19] or b[10..19] aren't swapped,
|
||||
* and all all values in a[0..9],b[0..9] must have magnitude less than
|
||||
* INT32_MAX. */
|
||||
static void
|
||||
swap_conditional(limb a[19], limb b[19], limb iswap) {
|
||||
unsigned i;
|
||||
const s32 swap = (s32) -iswap;
|
||||
|
||||
for (i = 0; i < 10; ++i) {
|
||||
const s32 x = swap & ( ((s32)a[i]) ^ ((s32)b[i]) );
|
||||
a[i] = ((s32)a[i]) ^ x;
|
||||
b[i] = ((s32)b[i]) ^ x;
|
||||
}
|
||||
}
|
||||
|
||||
/* Calculates nQ where Q is the x-coordinate of a point on the curve
|
||||
*
|
||||
* resultx/resultz: the x coordinate of the resulting curve point (short form)
|
||||
* n: a little endian, 32-byte number
|
||||
* q: a point of the curve (short form) */
|
||||
static void
|
||||
cmult(limb *resultx, limb *resultz, const u8 *n, const limb *q) {
|
||||
limb a[19] = {0}, b[19] = {1}, c[19] = {1}, d[19] = {0};
|
||||
limb *nqpqx = a, *nqpqz = b, *nqx = c, *nqz = d, *t;
|
||||
limb e[19] = {0}, f[19] = {1}, g[19] = {0}, h[19] = {1};
|
||||
limb *nqpqx2 = e, *nqpqz2 = f, *nqx2 = g, *nqz2 = h;
|
||||
|
||||
unsigned i, j;
|
||||
|
||||
memcpy(nqpqx, q, sizeof(limb) * 10);
|
||||
|
||||
for (i = 0; i < 32; ++i) {
|
||||
u8 byte = n[31 - i];
|
||||
for (j = 0; j < 8; ++j) {
|
||||
const limb bit = byte >> 7;
|
||||
|
||||
swap_conditional(nqx, nqpqx, bit);
|
||||
swap_conditional(nqz, nqpqz, bit);
|
||||
fmonty(nqx2, nqz2,
|
||||
nqpqx2, nqpqz2,
|
||||
nqx, nqz,
|
||||
nqpqx, nqpqz,
|
||||
q);
|
||||
swap_conditional(nqx2, nqpqx2, bit);
|
||||
swap_conditional(nqz2, nqpqz2, bit);
|
||||
|
||||
t = nqx;
|
||||
nqx = nqx2;
|
||||
nqx2 = t;
|
||||
t = nqz;
|
||||
nqz = nqz2;
|
||||
nqz2 = t;
|
||||
t = nqpqx;
|
||||
nqpqx = nqpqx2;
|
||||
nqpqx2 = t;
|
||||
t = nqpqz;
|
||||
nqpqz = nqpqz2;
|
||||
nqpqz2 = t;
|
||||
|
||||
byte <<= 1;
|
||||
}
|
||||
}
|
||||
|
||||
memcpy(resultx, nqx, sizeof(limb) * 10);
|
||||
memcpy(resultz, nqz, sizeof(limb) * 10);
|
||||
}
|
||||
|
||||
// -----------------------------------------------------------------------------
|
||||
// Shamelessly copied from djb's code
|
||||
// -----------------------------------------------------------------------------
|
||||
static void
|
||||
crecip(limb *out, const limb *z) {
|
||||
limb z2[10];
|
||||
limb z9[10];
|
||||
limb z11[10];
|
||||
limb z2_5_0[10];
|
||||
limb z2_10_0[10];
|
||||
limb z2_20_0[10];
|
||||
limb z2_50_0[10];
|
||||
limb z2_100_0[10];
|
||||
limb t0[10];
|
||||
limb t1[10];
|
||||
int i;
|
||||
|
||||
/* 2 */ fsquare(z2,z);
|
||||
/* 4 */ fsquare(t1,z2);
|
||||
/* 8 */ fsquare(t0,t1);
|
||||
/* 9 */ fmul(z9,t0,z);
|
||||
/* 11 */ fmul(z11,z9,z2);
|
||||
/* 22 */ fsquare(t0,z11);
|
||||
/* 2^5 - 2^0 = 31 */ fmul(z2_5_0,t0,z9);
|
||||
|
||||
/* 2^6 - 2^1 */ fsquare(t0,z2_5_0);
|
||||
/* 2^7 - 2^2 */ fsquare(t1,t0);
|
||||
/* 2^8 - 2^3 */ fsquare(t0,t1);
|
||||
/* 2^9 - 2^4 */ fsquare(t1,t0);
|
||||
/* 2^10 - 2^5 */ fsquare(t0,t1);
|
||||
/* 2^10 - 2^0 */ fmul(z2_10_0,t0,z2_5_0);
|
||||
|
||||
/* 2^11 - 2^1 */ fsquare(t0,z2_10_0);
|
||||
/* 2^12 - 2^2 */ fsquare(t1,t0);
|
||||
/* 2^20 - 2^10 */ for (i = 2;i < 10;i += 2) { fsquare(t0,t1); fsquare(t1,t0); }
|
||||
/* 2^20 - 2^0 */ fmul(z2_20_0,t1,z2_10_0);
|
||||
|
||||
/* 2^21 - 2^1 */ fsquare(t0,z2_20_0);
|
||||
/* 2^22 - 2^2 */ fsquare(t1,t0);
|
||||
/* 2^40 - 2^20 */ for (i = 2;i < 20;i += 2) { fsquare(t0,t1); fsquare(t1,t0); }
|
||||
/* 2^40 - 2^0 */ fmul(t0,t1,z2_20_0);
|
||||
|
||||
/* 2^41 - 2^1 */ fsquare(t1,t0);
|
||||
/* 2^42 - 2^2 */ fsquare(t0,t1);
|
||||
/* 2^50 - 2^10 */ for (i = 2;i < 10;i += 2) { fsquare(t1,t0); fsquare(t0,t1); }
|
||||
/* 2^50 - 2^0 */ fmul(z2_50_0,t0,z2_10_0);
|
||||
|
||||
/* 2^51 - 2^1 */ fsquare(t0,z2_50_0);
|
||||
/* 2^52 - 2^2 */ fsquare(t1,t0);
|
||||
/* 2^100 - 2^50 */ for (i = 2;i < 50;i += 2) { fsquare(t0,t1); fsquare(t1,t0); }
|
||||
/* 2^100 - 2^0 */ fmul(z2_100_0,t1,z2_50_0);
|
||||
|
||||
/* 2^101 - 2^1 */ fsquare(t1,z2_100_0);
|
||||
/* 2^102 - 2^2 */ fsquare(t0,t1);
|
||||
/* 2^200 - 2^100 */ for (i = 2;i < 100;i += 2) { fsquare(t1,t0); fsquare(t0,t1); }
|
||||
/* 2^200 - 2^0 */ fmul(t1,t0,z2_100_0);
|
||||
|
||||
/* 2^201 - 2^1 */ fsquare(t0,t1);
|
||||
/* 2^202 - 2^2 */ fsquare(t1,t0);
|
||||
/* 2^250 - 2^50 */ for (i = 2;i < 50;i += 2) { fsquare(t0,t1); fsquare(t1,t0); }
|
||||
/* 2^250 - 2^0 */ fmul(t0,t1,z2_50_0);
|
||||
|
||||
/* 2^251 - 2^1 */ fsquare(t1,t0);
|
||||
/* 2^252 - 2^2 */ fsquare(t0,t1);
|
||||
/* 2^253 - 2^3 */ fsquare(t1,t0);
|
||||
/* 2^254 - 2^4 */ fsquare(t0,t1);
|
||||
/* 2^255 - 2^5 */ fsquare(t1,t0);
|
||||
/* 2^255 - 21 */ fmul(out,t1,z11);
|
||||
}
|
||||
|
||||
static const u8 curve25519_basepoint[32] = {9};
|
||||
|
||||
void curve25519_scalarmult(u8 *result, const u8 *secret, const u8 *basepoint) {
|
||||
limb bp[10], x[10], z[11], zmone[10];
|
||||
uint8_t e[32];
|
||||
int i;
|
||||
|
||||
for (i = 0; i < 32; ++i) e[i] = secret[i];
|
||||
e[0] &= 248;
|
||||
e[31] &= 127;
|
||||
e[31] |= 64;
|
||||
|
||||
fexpand(bp, basepoint);
|
||||
cmult(x, z, e, bp);
|
||||
crecip(zmone, z);
|
||||
fmul(z, x, zmone);
|
||||
fcontract(result, z);
|
||||
}
|
||||
|
||||
void curve25519_publickey(u8 *public, const u8 *secret) {
|
||||
curve25519_scalarmult(public, secret, curve25519_basepoint);
|
||||
}
|
||||
@ -1,11 +1,32 @@
|
||||
#ifndef CURVE25519_H
|
||||
#define CURVE25519_H
|
||||
#include "curve25519.h"
|
||||
#include "curve25519-donna-portable.h"
|
||||
|
||||
#include <stdint.h>
|
||||
#if defined(CURVE25519_SSE2)
|
||||
#else
|
||||
#if defined(HAVE_UINT128) && !defined(CURVE25519_FORCE_32BIT)
|
||||
#define CURVE25519_64BIT
|
||||
#else
|
||||
#define CURVE25519_32BIT
|
||||
#endif
|
||||
#endif
|
||||
|
||||
typedef uint8_t u8;
|
||||
#if !defined(CURVE25519_NO_INLINE_ASM)
|
||||
#endif
|
||||
|
||||
void curve25519_scalarmult(u8 *result, const u8 *secret, const u8 *basepoint);
|
||||
void curve25519_publickey(u8 *public, const u8 *secret);
|
||||
|
||||
#endif // CURVE25519_H
|
||||
#if defined(CURVE25519_SSE2)
|
||||
#include "curve25519-donna-sse2.h"
|
||||
#elif defined(CURVE25519_64BIT)
|
||||
#include "curve25519-donna-64bit.h"
|
||||
#else
|
||||
#include "curve25519-donna-32bit.h"
|
||||
#endif
|
||||
|
||||
#include "curve25519-donna-common.h"
|
||||
|
||||
#if defined(CURVE25519_SSE2)
|
||||
#include "curve25519-donna-scalarmult-sse2.h"
|
||||
#else
|
||||
#include "curve25519-donna-scalarmult-base.h"
|
||||
#endif
|
||||
|
||||
|
||||
27
curve25519-donna/curve25519.c
Normal file
27
curve25519-donna/curve25519.c
Normal file
@ -0,0 +1,27 @@
|
||||
#include "curve25519-donna.h"
|
||||
|
||||
#if !defined(CURVE25519_SUFFIX)
|
||||
#define CURVE25519_SUFFIX
|
||||
#endif
|
||||
|
||||
#define CURVE25519_FN3(fn,suffix) fn##suffix
|
||||
#define CURVE25519_FN2(fn,suffix) CURVE25519_FN3(fn,suffix)
|
||||
#define CURVE25519_FN(fn) CURVE25519_FN2(fn,CURVE25519_SUFFIX)
|
||||
|
||||
void
|
||||
CURVE25519_FN(curve25519_donna) (curve25519_key mypublic, const curve25519_key secret, const curve25519_key basepoint) {
|
||||
curve25519_key e;
|
||||
size_t i;
|
||||
|
||||
for (i = 0;i < 32;++i) e[i] = secret[i];
|
||||
e[0] &= 0xf8;
|
||||
e[31] &= 0x7f;
|
||||
e[31] |= 0x40;
|
||||
curve25519_scalarmult_donna(mypublic, e, basepoint);
|
||||
}
|
||||
|
||||
void
|
||||
CURVE25519_FN(curve25519_donna_basepoint) (curve25519_key mypublic, const curve25519_key secret) {
|
||||
static const curve25519_key basepoint = {9};
|
||||
CURVE25519_FN(curve25519_donna)(mypublic, secret, basepoint);
|
||||
}
|
||||
10
curve25519-donna/curve25519.h
Normal file
10
curve25519-donna/curve25519.h
Normal file
@ -0,0 +1,10 @@
|
||||
#ifndef CURVE25519_H
|
||||
#define CURVE25519_H
|
||||
|
||||
typedef unsigned char curve25519_key[32];
|
||||
|
||||
void curve25519_donna(curve25519_key mypublic, const curve25519_key secret, const curve25519_key basepoint);
|
||||
void curve25519_donna_basepoint(curve25519_key mypublic, const curve25519_key secret);
|
||||
|
||||
#endif /* CURVE25519_H */
|
||||
|
||||
@ -8,7 +8,7 @@
|
||||
#include "secp256k1.h"
|
||||
#include "nist256p1.h"
|
||||
#include "ed25519.h"
|
||||
#include "curve25519-donna.h"
|
||||
#include "curve25519.h"
|
||||
|
||||
static uint8_t msg[32];
|
||||
|
||||
@ -92,7 +92,7 @@ void bench_curve25519(void)
|
||||
|
||||
clock_t t = clock();
|
||||
for (int i = 0 ; i < 500; i++) {
|
||||
curve25519_scalarmult(result, secret, basepoint);
|
||||
curve25519_donna(result, secret, basepoint);
|
||||
}
|
||||
printf("Curve25519 multiplying speed: %0.2f mul/s\n", 500.0f / ((float)(clock() - t) / CLOCKS_PER_SEC));
|
||||
}
|
||||
|
||||
Loading…
Reference in New Issue
Block a user