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- # https://eprint.iacr.org/2021/060.pdf
- from hashlib import sha256
- t = 3 # Threshold
- n = 5 # Participants
- # secp256k1
- p = 2^256-2^32-977
- q = 0xfffffffffffffffffffffffffffffffebaaedce6af48a03bbfd25e8cd0364141
- Fp = GF(p)
- Fq = GF(q)
- Ep = EllipticCurve(Fp, [0, 7])
- Ep.set_order(q)
- # Base point
- g = Ep([
- 0x79be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798,
- 0x483ada7726a3c4655da4fbfc0e1108a8fd17b448a68554199c47d08ffb10d4b8,
- ])
- # Key Generation
- # ==============
- xi = []
- Xi = []
- Xi_proofs = []
- for i in range(n):
- x_i = Fq.random_element()
- X_i = g * x_i
- xi.append(x_i)
- Xi.append(X_i)
- # Schnorr proof of knowledge
- k = Fq.random_element()
- R = k * g
- hasher = sha256()
- hasher.update(str(X_i.xy()))
- hasher.update(str(R.xy()))
- e = Fq(int(hasher.hexdigest(), 16))
- s = k + e * x_i
- Xi_proofs.append((R, s))
- # Verifier computes: e = hash(X || r), s*g == R+e*X
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