def generate_key_image(public_key: bytes, secret_key: Sc25519) -> Ge25519:
"""
Key image: secret_key * H_p(pub_key)
"""
point = crypto.hash_to_point(public_key)
point2 = crypto.scalarmult(point, secret_key)
return point2
def generate_mlsag(message, pk, xx, kLRki, index, dsRows):
"""
Multilayered Spontaneous Anonymous Group Signatures (MLSAG signatures)
:param message: the full message to be signed (actually its hash)
:param pk: matrix of public keys and commitments
:param xx: input secret array composed of a private key and commitment mask
:param kLRki: used only in multisig, currently not implemented
:param index: specifies corresponding public key to the `xx`'s private key in the `pk` array
:param dsRows: separates pubkeys from commitment
:return MgSig
"""
from apps.monero.xmr.serialize_messages.tx_full import MgSig
rows, cols = gen_mlsag_assert(pk, xx, kLRki, index, dsRows)
rv = MgSig()
c, L, R, Hi = 0, None, None, None
# calculates the "first" c, key images and random scalars alpha
c_old, Ip, alpha = generate_first_c_and_key_images(message, rv, pk, xx,
kLRki, index, dsRows,
rows, cols)
i = (index + 1) % cols
if i == 0:
rv.cc = c_old
tmp_buff = bytearray(32)
while i != index:
rv.ss[i] = _generate_random_vector(rows)
hasher = _hasher_message(message)
for j in range(dsRows):
# L = rv.ss[i][j] * G + c_old * pk[i][j]
L = crypto.add_keys2(rv.ss[i][j], c_old, pk[i][j])
Hi = crypto.hash_to_point(crypto.encodepoint(pk[i][j]))
# R = rv.ss[i][j] * H(pk[i][j]) + c_old * Ip[j]
R = crypto.add_keys3(rv.ss[i][j], Hi, c_old, rv.II[j])
_hash_point(hasher, pk[i][j], tmp_buff)
_hash_point(hasher, L, tmp_buff)
_hash_point(hasher, R, tmp_buff)
for j in range(dsRows, rows):
# again, omitting R here as discussed above
L = crypto.add_keys2(rv.ss[i][j], c_old, pk[i][j])
_hash_point(hasher, pk[i][j], tmp_buff)
_hash_point(hasher, L, tmp_buff)
c = crypto.decodeint(hasher.digest())
c_old = c
i = (i + 1) % cols
if i == 0:
rv.cc = c_old
for j in range(rows):
rv.ss[index][j] = crypto.sc_mulsub(c, xx[j], alpha[j])
return rv
def generate_key_image(public_key, secret_key):
"""
Key image: secret_key * H_p(pub_key)
"""
point = crypto.hash_to_point(public_key)
point2 = crypto.scalarmult(point, secret_key)
return point2
def test_hash_to_point(self):
data = unhexlify(
b"42f6835bf83114a1f5f6076fe79bdfa0bd67c74b88f127d54572d3910dd09201"
)
res = crypto.hash_to_point(data)
res_p = crypto.encodepoint(res)
self.assertEqual(
res_p,
unhexlify(
b"54863a0464c008acc99cffb179bc6cf34eb1bbdf6c29f7a070a7c6376ae30ab5"
),
)
def check_ring_singature(prefix_hash, image, pubs, sig):
"""
Checks ring signature generated with generate_ring_signature
:param prefix_hash:
:param image:
:param pubs:
:param sig:
:return:
"""
from apps.monero.xmr.common import memcpy
image_unp = crypto.ge_frombytes_vartime(image)
image_pre = crypto.ge_dsm_precomp(image_unp)
buff_off = len(prefix_hash)
buff = bytearray(buff_off + 2 * 32 * len(pubs))
memcpy(buff, 0, prefix_hash, 0, buff_off)
mvbuff = memoryview(buff)
sum = crypto.sc_0()
for i in range(len(pubs)):
if crypto.sc_check(sig[i][0]) != 0 or crypto.sc_check(sig[i][1]) != 0:
return False
tmp3 = crypto.ge_frombytes_vartime(pubs[i])
tmp2 = crypto.ge_double_scalarmult_base_vartime(sig[i][0], tmp3, sig[i][1])
crypto.encodepoint_into(mvbuff[buff_off : buff_off + 32], tmp2)
buff_off += 32
tmp3 = crypto.hash_to_point(crypto.encodepoint(pubs[i]))
tmp2 = crypto.ge_double_scalarmult_precomp_vartime(
sig[i][1], tmp3, sig[i][0], image_pre
)
crypto.encodepoint_into(mvbuff[buff_off : buff_off + 32], tmp2)
buff_off += 32
sum = crypto.sc_add(sum, sig[i][0])
h = crypto.hash_to_scalar(buff)
h = crypto.sc_sub(h, sum)
return crypto.sc_isnonzero(h) == 0
def generate_ring_signature(
prefix_hash: bytes,
image: Ge25519,
pubs: list[Ge25519],
sec: Sc25519,
sec_idx: int,
test: bool = False,
) -> Sig:
"""
Generates ring signature with key image.
void crypto_ops::generate_ring_signature()
"""
from trezor.utils import memcpy
if test:
t = crypto.scalarmult_base(sec)
if not crypto.point_eq(t, pubs[sec_idx]):
raise ValueError("Invalid sec key")
k_i = monero.generate_key_image(crypto.encodepoint(pubs[sec_idx]), sec)
if not crypto.point_eq(k_i, image):
raise ValueError("Key image invalid")
for k in pubs:
crypto.check_ed25519point(k)
buff_off = len(prefix_hash)
buff = bytearray(buff_off + 2 * 32 * len(pubs))
memcpy(buff, 0, prefix_hash, 0, buff_off)
mvbuff = memoryview(buff)
sum = crypto.sc_0()
k = crypto.sc_0()
sig = []
for _ in range(len(pubs)):
sig.append([crypto.sc_0(), crypto.sc_0()]) # c, r
for i in range(len(pubs)):
if i == sec_idx:
k = crypto.random_scalar()
tmp3 = crypto.scalarmult_base(k)
crypto.encodepoint_into(mvbuff[buff_off:buff_off + 32], tmp3)
buff_off += 32
tmp3 = crypto.hash_to_point(crypto.encodepoint(pubs[i]))
tmp2 = crypto.scalarmult(tmp3, k)
crypto.encodepoint_into(mvbuff[buff_off:buff_off + 32], tmp2)
buff_off += 32
else:
sig[i] = [crypto.random_scalar(), crypto.random_scalar()]
tmp3 = pubs[i]
tmp2 = crypto.ge25519_double_scalarmult_base_vartime(
sig[i][0], tmp3, sig[i][1])
crypto.encodepoint_into(mvbuff[buff_off:buff_off + 32], tmp2)
buff_off += 32
tmp3 = crypto.hash_to_point(crypto.encodepoint(tmp3))
tmp2 = crypto.ge25519_double_scalarmult_vartime2(
sig[i][1], tmp3, sig[i][0], image)
crypto.encodepoint_into(mvbuff[buff_off:buff_off + 32], tmp2)
buff_off += 32
sum = crypto.sc_add(sum, sig[i][0])
h = crypto.hash_to_scalar(buff)
sig[sec_idx][0] = crypto.sc_sub(h, sum)
sig[sec_idx][1] = crypto.sc_mulsub(sig[sec_idx][0], sec, k)
return sig
def generate_ring_signature(prefix_hash, image, pubs, sec, sec_idx, test=False):
"""
Generates ring signature with key image.
void crypto_ops::generate_ring_signature()
:param prefix_hash:
:param image:
:param pubs:
:param sec:
:param sec_idx:
:param test:
:return:
"""
from apps.monero.xmr.common import memcpy
if test:
from apps.monero.xmr import monero
t = crypto.scalarmult_base(sec)
if not crypto.point_eq(t, pubs[sec_idx]):
raise ValueError("Invalid sec key")
k_i = monero.generate_key_image(crypto.encodepoint(pubs[sec_idx]), sec)
if not crypto.point_eq(k_i, image):
raise ValueError("Key image invalid")
for k in pubs:
crypto.ge_frombytes_vartime_check(k)
image_unp = crypto.ge_frombytes_vartime(image)
image_pre = crypto.ge_dsm_precomp(image_unp)
buff_off = len(prefix_hash)
buff = bytearray(buff_off + 2 * 32 * len(pubs))
memcpy(buff, 0, prefix_hash, 0, buff_off)
mvbuff = memoryview(buff)
sum = crypto.sc_0()
k = crypto.sc_0()
sig = []
for i in range(len(pubs)):
sig.append([crypto.sc_0(), crypto.sc_0()]) # c, r
for i in range(len(pubs)):
if i == sec_idx:
k = crypto.random_scalar()
tmp3 = crypto.scalarmult_base(k)
crypto.encodepoint_into(mvbuff[buff_off : buff_off + 32], tmp3)
buff_off += 32
tmp3 = crypto.hash_to_point(crypto.encodepoint(pubs[i]))
tmp2 = crypto.scalarmult(tmp3, k)
crypto.encodepoint_into(mvbuff[buff_off : buff_off + 32], tmp2)
buff_off += 32
else:
sig[i] = [crypto.random_scalar(), crypto.random_scalar()]
tmp3 = crypto.ge_frombytes_vartime(pubs[i])
tmp2 = crypto.ge_double_scalarmult_base_vartime(sig[i][0], tmp3, sig[i][1])
crypto.encodepoint_into(mvbuff[buff_off : buff_off + 32], tmp2)
buff_off += 32
tmp3 = crypto.hash_to_point(crypto.encodepoint(tmp3))
tmp2 = crypto.ge_double_scalarmult_precomp_vartime(
sig[i][1], tmp3, sig[i][0], image_pre
)
crypto.encodepoint_into(mvbuff[buff_off : buff_off + 32], tmp2)
buff_off += 32
sum = crypto.sc_add(sum, sig[i][0])
h = crypto.hash_to_scalar(buff)
sig[sec_idx][0] = crypto.sc_sub(h, sum)
sig[sec_idx][1] = crypto.sc_mulsub(sig[sec_idx][0], sec, k)
return sig
def generate_first_c_and_key_images(message, rv, pk, xx, kLRki, index, dsRows,
rows, cols):
"""
MLSAG computation - the part with secret keys
:param message: the full message to be signed (actually its hash)
:param rv: MgSig
:param pk: matrix of public keys and commitments
:param xx: input secret array composed of a private key and commitment mask
:param kLRki: used only in multisig, currently not implemented
:param index: specifies corresponding public key to the `xx`'s private key in the `pk` array
:param dsRows: row number where the pubkeys "end" (and commitments follow)
:param rows: total number of rows
:param cols: size of ring
"""
Ip = _key_vector(dsRows)
rv.II = _key_vector(dsRows)
alpha = _key_vector(rows)
rv.ss = _key_matrix(rows, cols)
tmp_buff = bytearray(32)
hasher = _hasher_message(message)
for i in range(dsRows):
# this is somewhat extra as compared to the Ring Confidential Tx paper
# see footnote in From Zero to Monero section 3.3
hasher.update(crypto.encodepoint(pk[index][i]))
if kLRki:
raise NotImplementedError("Multisig not implemented")
# alpha[i] = kLRki.k
# rv.II[i] = kLRki.ki
# hash_point(hasher, kLRki.L, tmp_buff)
# hash_point(hasher, kLRki.R, tmp_buff)
else:
Hi = crypto.hash_to_point(crypto.encodepoint(pk[index][i]))
alpha[i] = crypto.random_scalar()
# L = alpha_i * G
aGi = crypto.scalarmult_base(alpha[i])
# Ri = alpha_i * H(P_i)
aHPi = crypto.scalarmult(Hi, alpha[i])
# key image
rv.II[i] = crypto.scalarmult(Hi, xx[i])
_hash_point(hasher, aGi, tmp_buff)
_hash_point(hasher, aHPi, tmp_buff)
Ip[i] = rv.II[i]
for i in range(dsRows, rows):
alpha[i] = crypto.random_scalar()
# L = alpha_i * G
aGi = crypto.scalarmult_base(alpha[i])
# for some reasons we omit calculating R here, which seems
# contrary to the paper, but it is in the Monero official client
# see https://github.com/monero-project/monero/blob/636153b2050aa0642ba86842c69ac55a5d81618d/src/ringct/rctSigs.cpp#L191
_hash_point(hasher, pk[index][i], tmp_buff)
_hash_point(hasher, aGi, tmp_buff)
# the first c
c_old = hasher.digest()
c_old = crypto.decodeint(c_old)
return c_old, Ip, alpha
def verify_clsag(self, msg, ss, sc1, sI, sD, pubs, C_offset):
n = len(pubs)
c = crypto.new_scalar()
D_8 = crypto.new_point()
tmp_bf = bytearray(32)
C_offset_bf = crypto.encodepoint(C_offset)
crypto.sc_copy(c, sc1)
crypto.point_mul8_into(D_8, sD)
hsh_P = crypto.get_keccak() # domain, I, D, P, C, C_offset
hsh_C = crypto.get_keccak() # domain, I, D, P, C, C_offset
hsh_P.update(mlsag._HASH_KEY_CLSAG_AGG_0)
hsh_C.update(mlsag._HASH_KEY_CLSAG_AGG_1)
def hsh_PC(x):
hsh_P.update(x)
hsh_C.update(x)
for x in pubs:
hsh_PC(x.dest)
for x in pubs:
hsh_PC(x.commitment)
hsh_PC(crypto.encodepoint_into(tmp_bf, sI))
hsh_PC(crypto.encodepoint_into(tmp_bf, sD))
hsh_PC(C_offset_bf)
mu_P = crypto.decodeint(hsh_P.digest())
mu_C = crypto.decodeint(hsh_C.digest())
c_to_hash = crypto.get_keccak(
) # domain, P, C, C_offset, message, L, R
c_to_hash.update(mlsag._HASH_KEY_CLSAG_ROUND)
for i in range(len(pubs)):
c_to_hash.update(pubs[i].dest)
for i in range(len(pubs)):
c_to_hash.update(pubs[i].commitment)
c_to_hash.update(C_offset_bf)
c_to_hash.update(msg)
c_p = crypto.new_scalar()
c_c = crypto.new_scalar()
L = crypto.new_point()
R = crypto.new_point()
tmp_pt = crypto.new_point()
i = 0
while i < n:
crypto.sc_mul_into(c_p, mu_P, c)
crypto.sc_mul_into(c_c, mu_C, c)
C_P = crypto.point_sub(
crypto.decodepoint_into(tmp_pt, pubs[i].commitment), C_offset)
crypto.add_keys2_into(
L, ss[i], c_p, crypto.decodepoint_into(tmp_pt, pubs[i].dest))
crypto.point_add_into(L, L,
crypto.scalarmult_into(tmp_pt, C_P, c_c))
HP = crypto.hash_to_point(pubs[i].dest)
crypto.add_keys3_into(R, ss[i], HP, c_p, sI)
crypto.point_add_into(R, R,
crypto.scalarmult_into(tmp_pt, D_8, c_c))
chasher = c_to_hash.copy()
chasher.update(crypto.encodepoint_into(tmp_bf, L))
chasher.update(crypto.encodepoint_into(tmp_bf, R))
crypto.decodeint_into(c, chasher.digest())
i += 1
res = crypto.sc_sub(c, sc1)
if not crypto.sc_eq(res, crypto.sc_0()):
raise ValueError("Signature error")