2020-11-25 12:50:40 +00:00
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"""Prime order of finite field underlying secp256k1 (2^256 - 2^32 - 977)"""
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P = 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC2F
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"""Finite field underlying secp256k1"""
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F = FiniteField(P)
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"""Elliptic curve secp256k1: y^2 = x^3 + 7"""
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C = EllipticCurve([F(0), F(7)])
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"""Base point of secp256k1"""
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G = C.lift_x(0x79BE667EF9DCBBAC55A06295CE870B07029BFCDB2DCE28D959F2815B16F81798)
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2021-10-20 14:14:13 +00:00
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if int(G[1]) & 1:
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# G.y is even
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G = -G
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2020-11-25 12:50:40 +00:00
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"""Prime order of secp256k1"""
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N = C.order()
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"""Finite field of scalars of secp256k1"""
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Z = FiniteField(N)
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""" Beta value of secp256k1 non-trivial endomorphism: lambda * (x, y) = (beta * x, y)"""
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BETA = F(2)^((P-1)/3)
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""" Lambda value of secp256k1 non-trivial endomorphism: lambda * (x, y) = (beta * x, y)"""
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LAMBDA = Z(3)^((N-1)/3)
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assert is_prime(P)
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assert is_prime(N)
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assert BETA != F(1)
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assert BETA^3 == F(1)
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2020-11-25 13:12:27 +00:00
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assert BETA^2 + BETA + 1 == 0
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2020-11-25 12:50:40 +00:00
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assert LAMBDA != Z(1)
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assert LAMBDA^3 == Z(1)
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2020-11-25 13:12:27 +00:00
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assert LAMBDA^2 + LAMBDA + 1 == 0
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assert Integer(LAMBDA)*G == C(BETA*G[0], G[1])
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