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87 lines
2.1 KiB
87 lines
2.1 KiB
# Implementation of: https://sci-hub.se/10.1109/iccke.2013.6682844
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# more details at: https://arnaucube.com/blog/blind-signatures-ec.html#the-scheme
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# A Go implementation of this schema can be found at: https://github.com/arnaucube/go-blindsecp256k1
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from hashlib import sha256
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def hash(m):
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h_output = sha256(str(m).encode('utf-8'))
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return int(h_output.hexdigest(), 16)
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class User:
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def __init__(self, F, G):
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self.F = F # Z_q
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self.G = G # elliptic curve generator
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def blind_msg(self, m, R_):
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self.a = self.F.random_element()
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self.b = self.F.random_element()
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self.R = self.a * R_ + self.b * self.G
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m_ = self.F(self.a)^(-1) * self.F(self.R.xy()[0]) * self.F(hash(m))
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return m_
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def unblind_sig(self, s_):
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s = self.a * s_ + self.b
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return (self.R, s)
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class Signer:
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def __init__(self, F, G):
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self.F = F # Z_q
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self.G = G # elliptic curve generator
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# gen Signer's key pair
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self.d = self.F.random_element()
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self.Q = self.G * self.d
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def new_request_params(self):
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self.k = self.F.random_element()
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R_ = self.G * self.k
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return R_
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def blind_sign(self, m_):
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return self.d * m_ + self.k
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def verify(G, Q, sig, m):
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(R, s) = sig
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return s*G == R + (Fq(R.xy()[0]) * Fq(hash(m))) * Q
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# ethereum elliptic curve
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p = 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC2F # base field
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a = 0
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b = 7
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F = GF(p) # base field
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E = EllipticCurve(F, [a,b])
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GX = 0x79BE667EF9DCBBAC55A06295CE870B07029BFCDB2DCE28D959F2815B16F81798
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GY = 0x483ADA7726A3C4655DA4FBFC0E1108A8FD17B448A68554199C47D08FFB10D4B8
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g = E(GX,GY)
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n = 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141
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q = g.order() # order of Fp
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assert is_prime(p)
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assert is_prime(q)
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Fq = GF(q) # scalar field
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# protocol flow:
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user = User(Fq, g)
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signer = Signer(Fq, g)
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R_ = signer.new_request_params()
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m = 12345 # user's message
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m_ = user.blind_msg(m, R_)
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s_ = signer.blind_sign(m_)
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sig = user.unblind_sig(s_)
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v = verify(g, signer.Q, sig, m)
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print(v)
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assert v
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