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- q = 0x40000000000000000000000000000000224698fc0994a8dd8c46eb2100000001
- K = GF(q)
- a = K(0x00)
- b = K(0x05)
- E = EllipticCurve(K, (a, b))
- G = E(0x40000000000000000000000000000000224698fc0994a8dd8c46eb2100000000, 0x02)
- p = 0x40000000000000000000000000000000224698fc094cf91b992d30ed00000001
- assert E.order() == p
- Scalar = GF(p)
- k = 3
- n = 2^k
- a = [Scalar(110), Scalar(56), Scalar(89), Scalar(6543),
- Scalar(2), Scalar(110), Scalar(44), Scalar(78)]
- x = Scalar.random_element()
- b = [x^i for i in range(n)]
- G = [E.random_element(), E.random_element(), E.random_element(),
- E.random_element(), E.random_element(), E.random_element(),
- E.random_element(), E.random_element()]
- assert len(a) == len(b) == len(G) == n
- # Dot product
- def dot(x, y):
- result = None
- for x_i, y_i in zip(x, y):
- if result is None:
- result = int(x_i) * y_i
- else:
- result += int(x_i) * y_i
- return result
- challenges = []
- commits = []
- # Iterate k times where n = 2^k
- for k in range(k, 0, -1):
- half = 2^(k - 1)
- assert half * 2 == len(a)
- L = dot(a[half:], G[:half])
- R = dot(a[:half], G[half:])
- #z_L = dot(a[half:], b[:half])
- #z_R = dot(a[:half], b[half:])
- commits.append((L, R))
- challenge = Scalar.random_element()
- challenges.append(challenge)
- a = [a[i] + challenge^-1 * a[half + i] for i in range(half)]
- G = [G[i] + int(challenge) * G[half + i] for i in range(half)]
- assert len(a) == len(G) == half
- if k == 0:
- print("Last round")
- assert len(a[-1]) == 1
- assert len(G[-1]) == 1
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