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_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 prove_range_mem(amount, last_mask=None):
"""
Memory optimized range proof.
Gives C, and mask such that \sumCi = C
c.f. http:#eprint.iacr.org/2015/1098 section 5.1
Ci is a commitment to either 0 or 2^i, i=0,...,63
thus this proves that "amount" is in [0, 2^ATOMS]
mask is a such that C = aG + bH, and b = amount
:param amount:
:param last_mask: ai[ATOMS-1] will be computed as \sum_{i=0}^{ATOMS-2} a_i - last_mask
:param use_asnl: use ASNL, used before Borromean
:return: sumCi, mask, RangeSig.
sumCi is Pedersen commitment on the amount value. sumCi = aG + amount*H
mask is "a" from the Pedersent commitment above.
"""
res = bytearray(32 * (64 + 64 + 64 + 1))
mv = memoryview(res)
gc.collect()
def as0(mv, x, i):
crypto.encodeint_into(x, mv[32 * i:])
def as1(mv, x, i):
crypto.encodeint_into(x, mv[32 * 64 + 32 * i:])
def aci(mv, x, i):
crypto.encodepoint_into(x, mv[32 * 64 * 2 + 32 + 32 * i:])
n = 64
bb = d2b(amount, n) # gives binary form of bb in "digits" binary digits
ai = key_zero_vector(n)
a = crypto.sc_0()
C = crypto.identity()
alpha = key_zero_vector(n)
c_H = crypto.gen_H()
kck = crypto.get_keccak() # ee computation
# First pass, generates: ai, alpha, Ci, ee, s1
for ii in range(n):
ai[ii] = crypto.random_scalar()
if last_mask is not None and ii == 64 - 1:
ai[ii] = crypto.sc_sub(last_mask, a)
a = crypto.sc_add(
a, ai[ii]
) # creating the total mask since you have to pass this to receiver...
alpha[ii] = crypto.random_scalar()
L = crypto.scalarmult_base(alpha[ii])
if bb[ii] == 0:
Ctmp = crypto.scalarmult_base(ai[ii])
else:
Ctmp = crypto.point_add(crypto.scalarmult_base(ai[ii]), c_H)
C = crypto.point_add(C, Ctmp)
aci(mv, Ctmp, ii)
if bb[ii] == 0:
si = crypto.random_scalar()
c = crypto.hash_to_scalar(crypto.encodepoint(L))
L = crypto.add_keys2(si, c, crypto.point_sub(Ctmp, c_H))
kck.update(crypto.encodepoint(L))
as1(mv, si, ii)
else:
kck.update(crypto.encodepoint(L))
c_H = crypto.point_double(c_H)
# Compute ee, memory cleanup
ee = crypto.sc_reduce32(crypto.decodeint(kck.digest()))
crypto.encodeint_into(ee, mv[64 * 32 * 2:])
del kck
gc.collect()
# Second phase computes: s0, s1
c_H = crypto.gen_H()
for jj in range(n):
if not bb[jj]:
s0 = crypto.sc_mulsub(ai[jj], ee, alpha[jj])
else:
s0 = crypto.random_scalar()
Ctmp = crypto.decodepoint(
mv[32 * 64 * 2 + 32 + 32 * jj:32 * 64 * 2 + 32 + 32 * jj + 32])
LL = crypto.add_keys2(s0, ee, Ctmp)
cc = crypto.hash_to_scalar(crypto.encodepoint(LL))
si = crypto.sc_mulsub(ai[jj], cc, alpha[jj])
as1(mv, si, jj)
as0(mv, s0, jj)
c_H = crypto.point_double(c_H)
gc.collect()
return C, a, res
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(tmp3, mvbuff[buff_off:buff_off + 32])
buff_off += 32
tmp3 = crypto.hash_to_ec(crypto.encodepoint(pubs[i]))
tmp2 = crypto.scalarmult(tmp3, k)
crypto.encodepoint_into(tmp2, mvbuff[buff_off:buff_off + 32])
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(tmp2, mvbuff[buff_off:buff_off + 32])
buff_off += 32
tmp3 = crypto.hash_to_ec(crypto.encodepoint(tmp3))
tmp2 = crypto.ge_double_scalarmult_precomp_vartime(
sig[i][1], tmp3, sig[i][0], image_pre)
crypto.encodepoint_into(tmp2, mvbuff[buff_off:buff_off + 32])
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
