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)
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