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321 lines
11 KiB
321 lines
11 KiB
"""
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Multilayer Linkable Spontaneous Anonymous Group (MLSAG)
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Optimized versions with incremental hashing.
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Both Simple and Full Monero tx types are supported.
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See https://eprint.iacr.org/2015/1098.pdf for details.
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Also explained in From Zero to Monero section 3.3 and 5.
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----------
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Please note, that the MLSAG code is written in a generic manner,
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where it is designed for multiple public keys (aka inputs). In another
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words, MLSAG should be used to sign multiple inputs, but that is currently
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not the case of Monero, where the inputs are signed one by one.
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So the public keys matrix has always two rows (one for public keys,
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one for commitments), although the algorithm is designed for `n` rows.
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This has one unfortunate effect where `rows` is always equal to 2 and
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dsRows always to 1, but the algorithm is still written as the numbers
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are arbitrary. That's why there are loops such as `for i in range(dsRows)`
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where it is run only once currently.
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----------
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Also note, that the matrix of public keys is indexed by columns first.
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This is because the code was ported from the official Monero client,
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which is written in C++ and where it does have some memory advantages.
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For ring size = 3 and one input the matrix M will look like this:
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|------------------------|------------------------|------------------------|
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| public key 0 | public key 1 | public key 2 |
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| cmt 0 - pseudo_out cmt | cmt 1 - pseudo_out cmt | cmt 2 - pseudo_out cmt |
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and `sk` is equal to:
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|--------------|-----------------------------------------------------|
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| private key* | input secret key's mask - pseudo_out's mask (alpha) |
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* corresponding to one of the public keys (`index` denotes which one)
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----------
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Mostly ported from official Monero client, but also inspired by Mininero.
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Author: Dusan Klinec, ph4r05, 2018
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"""
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from apps.monero.xmr import crypto
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def generate_mlsag_full(
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message, pubs, in_sk, out_sk_mask, out_pk_commitments, kLRki, index, txn_fee_key
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):
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cols = len(pubs)
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if cols == 0:
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raise ValueError("Empty pubs")
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rows = len(pubs[0])
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if rows == 0:
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raise ValueError("Empty pub row")
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for i in range(cols):
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if len(pubs[i]) != rows:
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raise ValueError("pub is not rectangular")
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if len(in_sk) != rows:
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raise ValueError("Bad inSk size")
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if len(out_sk_mask) != len(out_pk_commitments):
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raise ValueError("Bad outsk/putpk size")
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sk = _key_vector(rows + 1)
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M = _key_matrix(rows + 1, cols)
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for i in range(rows + 1):
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sk[i] = crypto.sc_0()
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for i in range(cols):
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M[i][rows] = crypto.identity()
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for j in range(rows):
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M[i][j] = crypto.decodepoint(pubs[i][j].dest)
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M[i][rows] = crypto.point_add(
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M[i][rows], crypto.decodepoint(pubs[i][j].commitment)
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)
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sk[rows] = crypto.sc_0()
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for j in range(rows):
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sk[j] = in_sk[j].dest
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sk[rows] = crypto.sc_add(sk[rows], in_sk[j].mask) # add masks in last row
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for i in range(cols):
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for j in range(len(out_pk_commitments)):
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M[i][rows] = crypto.point_sub(
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M[i][rows], crypto.decodepoint(out_pk_commitments[j])
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) # subtract output Ci's in last row
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# Subtract txn fee output in last row
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M[i][rows] = crypto.point_sub(M[i][rows], txn_fee_key)
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for j in range(len(out_pk_commitments)):
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sk[rows] = crypto.sc_sub(
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sk[rows], out_sk_mask[j]
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) # subtract output masks in last row
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return generate_mlsag(message, M, sk, kLRki, index, rows)
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def generate_mlsag_simple(message, pubs, in_sk, a, cout, kLRki, index):
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"""
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MLSAG for RctType.Simple
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:param message: the full message to be signed (actually its hash)
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:param pubs: vector of MoneroRctKey; this forms the ring; point values in encoded form; (dest, mask) = (P, C)
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:param in_sk: CtKey; spending private key with input commitment mask (original); better_name: input_secret_key
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:param a: mask from the pseudo output commitment; better name: pseudo_out_alpha
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:param cout: pseudo output commitment; point, decoded; better name: pseudo_out_c
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:param kLRki: used only in multisig, currently not implemented
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:param index: specifies corresponding public key to the `in_sk` in the pubs array
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:return: MgSig
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"""
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# Monero signs inputs separately, so `rows` always equals 2 (pubkey, commitment)
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# and `dsRows` is always 1 (denotes where the pubkeys "end")
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rows = 2
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dsRows = 1
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cols = len(pubs)
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if cols == 0:
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raise ValueError("Empty pubs")
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sk = _key_vector(rows)
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M = _key_matrix(rows, cols)
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sk[0] = in_sk.dest
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sk[1] = crypto.sc_sub(in_sk.mask, a)
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for i in range(cols):
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M[i][0] = crypto.decodepoint(pubs[i].dest)
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M[i][1] = crypto.point_sub(crypto.decodepoint(pubs[i].commitment), cout)
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return generate_mlsag(message, M, sk, kLRki, index, dsRows)
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def gen_mlsag_assert(pk, xx, kLRki, index, dsRows):
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"""
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Conditions check
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"""
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cols = len(pk)
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if cols <= 1:
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raise ValueError("Cols == 1")
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if index >= cols:
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raise ValueError("Index out of range")
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rows = len(pk[0])
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if rows == 0:
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raise ValueError("Empty pk")
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for i in range(cols):
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if len(pk[i]) != rows:
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raise ValueError("pk is not rectangular")
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if len(xx) != rows:
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raise ValueError("Bad xx size")
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if dsRows > rows:
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raise ValueError("Bad dsRows size")
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if kLRki and dsRows != 1:
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raise ValueError("Multisig requires exactly 1 dsRows")
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if kLRki:
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raise NotImplementedError("Multisig not implemented")
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return rows, cols
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def generate_first_c_and_key_images(
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message, rv, pk, xx, kLRki, index, dsRows, rows, cols
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):
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"""
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MLSAG computation - the part with secret keys
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:param message: the full message to be signed (actually its hash)
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:param rv: MgSig
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:param pk: matrix of public keys and commitments
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:param xx: input secret array composed of a private key and commitment mask
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:param kLRki: used only in multisig, currently not implemented
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:param index: specifies corresponding public key to the `xx`'s private key in the `pk` array
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:param dsRows: row number where the pubkeys "end" (and commitments follow)
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:param rows: total number of rows
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:param cols: size of ring
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"""
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Ip = _key_vector(dsRows)
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rv.II = _key_vector(dsRows)
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alpha = _key_vector(rows)
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rv.ss = _key_matrix(rows, cols)
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tmp_buff = bytearray(32)
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hasher = _hasher_message(message)
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for i in range(dsRows):
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# this is somewhat extra as compared to the Ring Confidential Tx paper
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# see footnote in From Zero to Monero section 3.3
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hasher.update(crypto.encodepoint(pk[index][i]))
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if kLRki:
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raise NotImplementedError("Multisig not implemented")
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# alpha[i] = kLRki.k
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# rv.II[i] = kLRki.ki
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# hash_point(hasher, kLRki.L, tmp_buff)
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# hash_point(hasher, kLRki.R, tmp_buff)
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else:
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Hi = crypto.hash_to_point(crypto.encodepoint(pk[index][i]))
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alpha[i] = crypto.random_scalar()
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# L = alpha_i * G
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aGi = crypto.scalarmult_base(alpha[i])
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# Ri = alpha_i * H(P_i)
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aHPi = crypto.scalarmult(Hi, alpha[i])
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# key image
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rv.II[i] = crypto.scalarmult(Hi, xx[i])
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_hash_point(hasher, aGi, tmp_buff)
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_hash_point(hasher, aHPi, tmp_buff)
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Ip[i] = rv.II[i]
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for i in range(dsRows, rows):
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alpha[i] = crypto.random_scalar()
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# L = alpha_i * G
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aGi = crypto.scalarmult_base(alpha[i])
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# for some reasons we omit calculating R here, which seems
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# contrary to the paper, but it is in the Monero official client
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# see https://github.com/monero-project/monero/blob/636153b2050aa0642ba86842c69ac55a5d81618d/src/ringct/rctSigs.cpp#L191
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_hash_point(hasher, pk[index][i], tmp_buff)
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_hash_point(hasher, aGi, tmp_buff)
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# the first c
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c_old = hasher.digest()
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c_old = crypto.decodeint(c_old)
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return c_old, Ip, alpha
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def generate_mlsag(message, pk, xx, kLRki, index, dsRows):
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"""
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Multilayered Spontaneous Anonymous Group Signatures (MLSAG signatures)
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:param message: the full message to be signed (actually its hash)
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:param pk: matrix of public keys and commitments
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:param xx: input secret array composed of a private key and commitment mask
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:param kLRki: used only in multisig, currently not implemented
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:param index: specifies corresponding public key to the `xx`'s private key in the `pk` array
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:param dsRows: separates pubkeys from commitment
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:return MgSig
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"""
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from apps.monero.xmr.serialize_messages.tx_full import MgSig
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rows, cols = gen_mlsag_assert(pk, xx, kLRki, index, dsRows)
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rv = MgSig()
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c, L, R, Hi = 0, None, None, None
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# calculates the "first" c, key images and random scalars alpha
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c_old, Ip, alpha = generate_first_c_and_key_images(
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message, rv, pk, xx, kLRki, index, dsRows, rows, cols
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)
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i = (index + 1) % cols
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if i == 0:
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rv.cc = c_old
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tmp_buff = bytearray(32)
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while i != index:
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rv.ss[i] = _generate_random_vector(rows)
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hasher = _hasher_message(message)
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for j in range(dsRows):
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# L = rv.ss[i][j] * G + c_old * pk[i][j]
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L = crypto.add_keys2(rv.ss[i][j], c_old, pk[i][j])
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Hi = crypto.hash_to_point(crypto.encodepoint(pk[i][j]))
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# R = rv.ss[i][j] * H(pk[i][j]) + c_old * Ip[j]
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R = crypto.add_keys3(rv.ss[i][j], Hi, c_old, rv.II[j])
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_hash_point(hasher, pk[i][j], tmp_buff)
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_hash_point(hasher, L, tmp_buff)
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_hash_point(hasher, R, tmp_buff)
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for j in range(dsRows, rows):
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# again, omitting R here as discussed above
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L = crypto.add_keys2(rv.ss[i][j], c_old, pk[i][j])
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_hash_point(hasher, pk[i][j], tmp_buff)
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_hash_point(hasher, L, tmp_buff)
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c = crypto.decodeint(hasher.digest())
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c_old = c
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i = (i + 1) % cols
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if i == 0:
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rv.cc = c_old
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for j in range(rows):
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rv.ss[index][j] = crypto.sc_mulsub(c, xx[j], alpha[j])
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return rv
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def _key_vector(rows):
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return [None] * rows
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def _key_matrix(rows, cols):
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"""
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first index is columns (so slightly backward from math)
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"""
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rv = [None] * cols
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for i in range(0, cols):
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rv[i] = _key_vector(rows)
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return rv
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def _generate_random_vector(n):
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"""
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Generates vector of random scalars
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"""
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return [crypto.random_scalar() for _ in range(0, n)]
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def _hasher_message(message):
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"""
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Returns incremental hasher for MLSAG
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"""
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ctx = crypto.get_keccak()
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ctx.update(message)
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return ctx
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def _hash_point(hasher, point, tmp_buff):
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crypto.encodepoint_into(tmp_buff, point)
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hasher.update(tmp_buff)
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