def add_mixed_hmv(
pt1, pt2: Optimized_Point3D[Optimized_Field]
) -> Optimized_Point3D[Optimized_Field]:
x1, y1, z1 = pt1
x2, y2, z2 = pt2
assert z2 == FQ2.one()
T1 = z1 * z1
T2 = T1 * z1
T1 = T1 * x2
T2 = T2 * y2
T1 = T1 - x1
T2 = T2 - y1
if T1 == FQ2.zero():
if T2 == FQ2.zero():
return double(pt1)
return inf
z3 = z1 * T1
T3 = T1 * T1
T4 = T3 * T1
T3 = T3 * x1
T1 = 2 * T3
x3 = T2 * T2
x3 = x3 - T1
x3 = x3 - T4
T3 = T3 - x3
T3 = T3 * T2
T4 = T4 * y1
y3 = T3 - T4
return (x3, y3, z3)
def normalize(
pt: Optimized_Point3D[Optimized_Field],
) -> Optimized_Point3D[Optimized_Field]:
x1, y1, z1 = pt
z = z1.inv()
z2 = z * z
x3 = x1 * z2
y3 = y1 * z2 * z
return (x3, y3, FQ2.one())
def _try_sqrt_in_fp2(a: FQ2) -> FQ2:
a1 = a**P_MINUS3_OVER4
alpha = a1 * a1 * a
x0 = a1 * a
if alpha == FQ2([-1, 0]):
return FQ2((x0.coeffs[1], x0.coeffs[0]))
alpha = alpha + FQ2.one()
alpha = alpha**P_MINUS1_OVER2
return alpha * x0
def pubkey_to_g2(pub: Pubkey) -> G2Point:
g2 = (
FQ2([big_endian_to_int(pub[:32]),
big_endian_to_int(pub[32:64])]),
FQ2([big_endian_to_int(pub[64:96]),
big_endian_to_int(pub[96:])]),
FQ2.one(),
)
assert is_valid_g2_point(g2)
return g2
def map_to_g2(raw_hash: FQ2) -> G2Point:
one = FQ2.one()
x = raw_hash
while True:
y = x * x * x + b2
y = sqrt(y)
if y is not None:
break
x += one
h = multiply((x, y, one), COFACTOR_G2)
assert is_on_curve(h, b2)
return h
def signature_to_G2(signature: Signature) -> G2Point:
g2 = (
FQ2([
big_endian_to_int(signature[:32]),
big_endian_to_int(signature[32:64])
]),
FQ2([
big_endian_to_int(signature[64:96]),
big_endian_to_int(signature[96:])
]),
FQ2.one(),
)
assert is_g2_on_curve(g2)
return g2
def _normalize(p1) -> Optimized_Point3D[Optimized_Field]:
x, y = normalize(p1)
return (x, y, FQ2.one())
def sign(msg: Message, priv: PrivateKey) -> Signature:
x, y = normalize(multiply(hash_to_g2(msg), priv))
g2 = (x, y, FQ2.one())
return G2_to_signature(g2)
from py_ecc.optimized_bn128 import FQ2, b2 as B
from py_ecc.typing import Optimized_Field, Optimized_Point3D
inf = (FQ2.zero(), FQ2.one(), FQ2.zero())
def double(
pt: Optimized_Point3D[Optimized_Field],
) -> Optimized_Point3D[Optimized_Field]:
x, y, z = pt
A = x * x
B = y * y
C = B * B
t = x + B
D = 2 * (t * t - A - C)
E = 3 * A
F = E * E
x3 = F - 2 * D
y3 = E * (D - x3) - 8 * C
z3 = 2 * z * y
return (x3, y3, z3)
def add(
pt1, pt2: Optimized_Point3D[Optimized_Field]
) -> Optimized_Point3D[Optimized_Field]:
x1, y1, z1 = pt1
x2, y2, z2 = pt2
Z1Z1 = z1 * z1
Z2Z2 = z2 * z2
U1 = x1 * Z2Z2
def priv_to_pub(priv: PrivateKey) -> Pubkey:
x, y = normalize(multiply(G2, priv))
g2 = (x, y, FQ2.one())
return g2_to_pubkey(g2)
def _normalize(p1):
x, y = normalize(p1)
return (x, y, FQ2.one())