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85 lines
2.6 KiB
85 lines
2.6 KiB
# Sage impl of the powers of tau,
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# a Go implementation can be found at: https://github.com/arnaucube/eth-kzg-ceremony-alt
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load("bls12-381.sage") # file from https://github.com/arnaucube/math/blob/master/bls12-381.sage
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e = Pairing()
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def new_empty_SRS(nG1, nG2):
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g1s = [None] * nG1
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g2s = [None] * nG2
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for i in range(0, nG1):
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g1s[i] = e.G1
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for i in range(0, nG2):
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g2s[i] = e.G2
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return [g1s, g2s]
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def new_tau(random):
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return e.F1(random)
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def compute_contribution(new_tau, prev_srs):
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g1s = [None] * len(prev_srs[0])
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g2s = [None] * len(prev_srs[1])
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srs = [g1s, g2s]
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Q = e.r
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# compute [τ'⁰]₁, [τ'¹]₁, [τ'²]₁, ..., [τ'ⁿ⁻¹]₁, where n = len(prev_srs.G1s)
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for i in range(0, len(prev_srs[0])):
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srs[0][i] = (new_tau^i) * prev_srs[0][i]
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# compute [τ'⁰]₂, [τ'¹]₂, [τ'²]₂, ..., [τ'ⁿ⁻¹]₂, where n = len(prev_srs.G2s)
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for i in range(0, len(prev_srs[1])):
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srs[1][i] = (new_tau^i) * prev_srs[1][i]
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return srs
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def generate_proof(tau, prev_srs, new_srs):
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# g_1^{tau'} = g_1^{p * tau} = SRS_G1s[1] * p
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g1_ptau = prev_srs[0][1] * tau
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# g_2^{p}
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g2_p = tau * e.G2
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return [g1_ptau, g2_p]
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def verify(prev_srs, new_srs, proof):
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# 1. check that elements of the newSRS are valid points
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for i in range(0, len(new_srs[0])-1):
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assert new_srs[0][i] != None
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assert new_srs[0][i] != e.E1(0)
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assert new_srs[0][i] in e.E1
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for i in range(0, len(new_srs[1])-1):
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assert new_srs[1][i] != None
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assert new_srs[1][i] != e.E2(0)
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assert new_srs[1][i] in e.E2
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# 2. check proof.G1PTau == newSRS.G1Powers[1]
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assert proof[0] == new_srs[0][1]
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# 3. check newSRS.G1s[1] (g₁^τ'), is correctly related to prev_srs.G1s[1] (g₁^τ)
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# e([τ]₁, [p]₂) == e([τ']₁, [1]₂)
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assert e.pair(prev_srs[0][1], proof[1]) == e.pair(new_srs[0][1], e.G2)
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# 4. check newSRS following the powers of tau structure
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# i) e([τ'ⁱ]₁, [τ']₂) == e([τ'ⁱ⁺¹]₁, [1]₂), for i ∈ [1, n−1]
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for i in range(0, len(new_srs[0])-1):
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assert e.pair(new_srs[0][i], new_srs[1][1]) == e.pair(new_srs[0][i+1], e.G2)
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# ii) e([τ']₁, [τ'ʲ]₂) == e([1]₁, [τ'ʲ⁺¹]₂), for j ∈ [1, m−1]
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for i in range(0, len(new_srs[1])-1):
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assert e.pair(new_srs[0][1], new_srs[1][i]) == e.pair(e.G1, new_srs[1][i+1])
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(prev_srs) = new_empty_SRS(5, 3)
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random = 12345
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tau = new_tau(random)
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new_srs = compute_contribution(tau, prev_srs)
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proof = generate_proof(tau, prev_srs, new_srs)
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verify(prev_srs, new_srs, proof)
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