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