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@@ -0,0 +1,41 @@
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+# https://eprint.iacr.org/2021/060.pdf
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+from hashlib import sha256
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+
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+t = 3 # Threshold
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+n = 5 # Participants
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+
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+# secp256k1
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+p = 2^256-2^32-977
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+q = 0xfffffffffffffffffffffffffffffffebaaedce6af48a03bbfd25e8cd0364141
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+Fp = GF(p)
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+Fq = GF(q)
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+Ep = EllipticCurve(Fp, [0, 7])
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+Ep.set_order(q)
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+
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+# Base point
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+g = Ep([
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+ 0x79be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798,
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+ 0x483ada7726a3c4655da4fbfc0e1108a8fd17b448a68554199c47d08ffb10d4b8,
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+])
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+
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+# Key Generation
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+# ==============
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+xi = []
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+Xi = []
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+Xi_proofs = []
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+for i in range(n):
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+ x_i = Fq.random_element()
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+ X_i = g * x_i
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+ xi.append(x_i)
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+ Xi.append(X_i)
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+
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+ # Schnorr proof of knowledge
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+ k = Fq.random_element()
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+ R = k * g
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+ hasher = sha256()
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+ hasher.update(str(X_i.xy()))
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+ hasher.update(str(R.xy()))
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+ e = Fq(int(hasher.hexdigest(), 16))
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+ s = k + e * x_i
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+ Xi_proofs.append((R, s))
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+ # Verifier computes: e = hash(X || r), s*g == R+e*X
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parazyd