mirror of
https://github.com/jb55/nostril.git
synced 2024-11-24 17:09:07 -05:00
40 lines
1023 B
Python
40 lines
1023 B
Python
|
"""Prime order of finite field underlying secp256k1 (2^256 - 2^32 - 977)"""
|
||
|
|
P = 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC2F
|
||
|
|
|
||
|
|
"""Finite field underlying secp256k1"""
|
||
|
|
F = FiniteField(P)
|
||
|
|
|
||
|
|
"""Elliptic curve secp256k1: y^2 = x^3 + 7"""
|
||
|
|
C = EllipticCurve([F(0), F(7)])
|
||
|
|
|
||
|
|
"""Base point of secp256k1"""
|
||
|
|
G = C.lift_x(0x79BE667EF9DCBBAC55A06295CE870B07029BFCDB2DCE28D959F2815B16F81798)
|
||
|
|
if int(G[1]) & 1:
|
||
|
|
# G.y is even
|
||
|
|
G = -G
|
||
|
|
|
||
|
|
"""Prime order of secp256k1"""
|
||
|
|
N = C.order()
|
||
|
|
|
||
|
|
"""Finite field of scalars of secp256k1"""
|
||
|
|
Z = FiniteField(N)
|
||
|
|
|
||
|
|
""" Beta value of secp256k1 non-trivial endomorphism: lambda * (x, y) = (beta * x, y)"""
|
||
|
|
BETA = F(2)^((P-1)/3)
|
||
|
|
|
||
|
|
""" Lambda value of secp256k1 non-trivial endomorphism: lambda * (x, y) = (beta * x, y)"""
|
||
|
|
LAMBDA = Z(3)^((N-1)/3)
|
||
|
|
|
||
|
|
assert is_prime(P)
|
||
|
|
assert is_prime(N)
|
||
|
|
|
||
|
|
assert BETA != F(1)
|
||
|
|
assert BETA^3 == F(1)
|
||
|
|
assert BETA^2 + BETA + 1 == 0
|
||
|
|
|
||
|
|
assert LAMBDA != Z(1)
|
||
|
|
assert LAMBDA^3 == Z(1)
|
||
|
|
assert LAMBDA^2 + LAMBDA + 1 == 0
|
||
|
|
|
||
|
|
assert Integer(LAMBDA)*G == C(BETA*G[0], G[1])
|