from __future__ import absolute_import
from optimized_field_elements import (
FQ2,
FQ12,
field_modulus,
FQ,
)
curve_order = 21888242871839275222246405745257275088548364400416034343698204186575808495617
NullPoint = (FQ(0), FQ(0), FQ(0))
NullPoint2 = (FQ2([0, 0]), FQ2([0, 0]), FQ2([0, 0]))
# Curve order should be prime
assert pow(2, curve_order, curve_order) == 2
# Curve order should be a factor of field_modulus**12 - 1
assert (field_modulus**12 - 1) % curve_order == 0
# Curve is y**2 = x**3 + 3
b = FQ(3)
# Twisted curve over FQ**2
b2 = FQ2([3, 0]) / FQ2([9, 1])
# Extension curve over FQ**12; same b value as over FQ
b12 = FQ12([3] + [0] * 11)
# Generator for curve over FQ
G = (FQ(1), FQ(2), FQ(1))
# Generator for twisted curve over FQ2
G2 = (
FQ2([
10857046999023057135944570762232829481370756359578518086990519993285655852781,
from bn128_field_elements import field_modulus, FQ
from optimized_field_elements import FQ2, FQ12
# from bn128_field_elements import FQ2, FQ12
curve_order = 21888242871839275222246405745257275088548364400416034343698204186575808495617
# Curve order should be prime
assert pow(2, curve_order, curve_order) == 2
# Curve order should be a factor of field_modulus**12 - 1
assert (field_modulus ** 12 - 1) % curve_order == 0
# Curve is y**2 = x**3 + 3
b = FQ(3)
# Twisted curve over FQ**2
b2 = FQ2([3, 0]) / FQ2([0, 1])
# Extension curve over FQ**12; same b value as over FQ
b12 = FQ12([3] + [0] * 11)
# Generator for curve over FQ
G1 = (FQ(1), FQ(2), FQ(1))
# Generator for twisted curve over FQ2
G2 = (FQ2([16260673061341949275257563295988632869519996389676903622179081103440260644990, 11559732032986387107991004021392285783925812861821192530917403151452391805634]),
FQ2([15530828784031078730107954109694902500959150953518636601196686752670329677317, 4082367875863433681332203403145435568316851327593401208105741076214120093531]), FQ2.one())
# Check that a point is on the curve defined by y**2 == x**3 + b
def is_on_curve(pt, b):
if pt is None:
return True
x, y, z = pt
return y**2 * z - x**3 == b * z**3