def map_to_g1(raw_hash: FQ) -> G1Point:
one = FQ.one()
x = raw_hash
while True:
y = x * x * x + b
y = sqrt(y)
if y is not None:
break
x += one
h = (x, y, FQ.one())
assert is_on_curve(h, b)
return h
def test_hash_to_point(BLSG2):
msg = b"\x00\x00\x00\x01"
_h = hash_to_g1(msg)
h = BLSG2.hashToPoint(msg)
assert FQ(h[0]) == _h[0]
assert FQ(h[1]) == _h[1]
import os
msg = os.urandom(256)
_h = hash_to_g1(msg)
h = BLSG2.hashToPoint(msg)
assert FQ(h[0]) == _h[0]
assert FQ(h[1]) == _h[1]
def test_sqrt(BLSG2):
def rand_fq() -> FQ:
from random import randint
return FQ(randint(1, field_modulus - 1))
aa = FQ(-1)
_, ok = BLSG2.sqrt(aa)
assert ok is False
a = rand_fq()
aa = a * a
a, ok = BLSG2.sqrt(aa)
assert ok is True
_a = FQ(a)
assert _a * _a == aa
def decompress_G1(p):
if p == 0:
return (FQ(1), FQ(1), FQ(0))
x = p % 2**255
y_mod_2 = p // 2**255
y = pow((x**3 + b.n) % field_modulus, (field_modulus+1)//4, field_modulus)
assert pow(y, 2, field_modulus) == (x**3 + b.n) % field_modulus
if y%2 != y_mod_2:
y = field_modulus - y
return (FQ(x), FQ(y), FQ(1))
def Fq(cls, n: IntOrFE) -> "FieldElement":
return FQ(n)
def hash_ORBLS(msg: bytes) -> FQ:
_msg = _hash(msg, b"")
return FQ(int.from_bytes(_msg, "big"))
def aggregate_pubs(pubs):
o = FQ(1), FQ(1), FQ(0)
for p in pubs:
o = add(o, decompress_G1(p))
return compress_G1(o)
def test_ec_pair_field_exceed_mod(f1):
FQ.fielf_modulus = 100
a = FQ(val=1)
f1.return_value = (a, a)
vec_c = [10] * 192
assert ec_pair(vec_c) == []
def test_ec_pair(f1, f2, f3, f4):
FQ.fielf_modulus = 100
a = FQ(val=1)
f1.return_value = (a, a)
vec_c = [0] * 192
assert ec_pair(vec_c) == [0] * 31 + [1]
def priv_to_pub(priv: PrivateKey) -> Pubkey:
x, y = normalize(multiply(G1, priv))
g1 = (x, y, FQ.one())
return G1_to_pubkey(g1)
def signature_to_g1(sig: Signature) -> G1Point:
a1 = big_endian_to_int(sig[:32])
a2 = big_endian_to_int(sig[32:])
g1 = (FQ(a1), FQ(a2), FQ(1))
assert is_valid_g1_point(g1)
return g1
def pubkey_to_G1(pubkey: Pubkey) -> G1Point:
a1 = big_endian_to_int(pubkey[:32])
a2 = big_endian_to_int(pubkey[32:])
g1 = (FQ(a1), FQ(a2), FQ(1))
assert is_g1_on_curve(g1)
return g1
def test_ec_add(f1, f2, f3):
FQ.fielf_modulus = 128
a = FQ(val=1)
f1.return_value = (a, a)
assert ec_add(VECTOR_A) == ([0] * 31 + [1]) * 2
def rand_fq() -> FQ:
from random import randint
return FQ(randint(1, field_modulus - 1))
def sign(msg: Message, priv: PrivateKey) -> Signature:
x, y = normalize(multiply(hash_to_g1(msg), priv))
g1 = (x, y, FQ.one())
return g1_to_signature(g1)