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- # Reed Solomon check in an elliptic curve context, used in scrape.sage
- t = 3 # Threshold
- n = 10 # Participants
- # Pallas
- p = 0x40000000000000000000000000000000224698fc094cf91b992d30ed00000001
- q = 0x40000000000000000000000000000000224698fc0994a8dd8c46eb2100000001
- Fp = GF(p)
- Fq = GF(q)
- Ep = EllipticCurve(Fp, (0, 5))
- Ep.set_order(q)
- g = Ep.random_point()
- h = Ep.random_point()
- # Secret
- s = Fq.random_element()
- alpha = [s]
- for i in range(t-1):
- alpha.append(Fq.random_element())
- R.<ω> = PolynomialRing(Fq)
- poly = R(alpha)
- # Secret shares
- shares = [poly(i) for i in range(1, n+1)]
- # Share commitments
- commits = [g * share for share in shares]
- # Reed Solomon check
- RS.<σ> = PolynomialRing(Fq)
- σ_coeff = [Fq.random_element() for _ in range(n-t)]
- v_poly = RS(σ_coeff)
- assert v_poly.degree() == n-t-1
- v_p = Ep(0)
- for i in range(n):
- c_perp = v_poly(Fq(i))
- for j in range(n):
- if i != j:
- c_perp *= (Fq(i)-Fq(j)).inverse()
- v_p += commits[i] * c_perp
- assert v_p == Ep(0)
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