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127 lines
2.9 KiB
127 lines
2.9 KiB
# Plonk-CCS (https://eprint.iacr.org/2023/552) Sage prototype
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# utils
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def matrix_vector_product(M, v):
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n = M.nrows()
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r = [F(0)] * n
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for i in range(0, n):
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for j in range(0, M.ncols()):
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r[i] += M[i][j] * v[j]
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return r
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def hadamard_product(a, b):
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n = len(a)
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r = [None] * n
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for i in range(0, n):
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r[i] = a[i] * b[i]
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return r
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def vec_add(a, b):
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n = len(a)
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r = [None] * n
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for i in range(0, n):
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r[i] = a[i] + b[i]
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return r
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def vec_elem_mul(a, s):
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r = [None] * len(a)
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for i in range(0, len(a)):
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r[i] = a[i] * s
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return r
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# end of utils
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# can use any finite field, using a small one for the example
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F = GF(101)
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# F = GF(21888242871839275222246405745257275088696311157297823662689037894645226208583)
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# The following CCS instance values have been provided by Carlos
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# (https://github.com/CPerezz) and Edu (https://github.com/ed255),
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# and this sage script was made to check the CCS relation.
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## Checks performed by this Plonk/CCS instance:
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# - binary check for x0, x1
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# - 2*x2 + 2*x3 == x4
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M0 = matrix([
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[F(0), 1, 0, 0, 0, 0, 0],
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[0, 0, 1, 0, 0, 0, 0],
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[0, 0, 0, 1, 0, 0, 0],
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[0, 0, 0, 0, 0, 0, 1],
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])
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M1 = matrix([
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[F(0), 1, 0, 0, 0, 0, 0],
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[0, 0, 1, 0, 0, 0, 0],
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[0, 0, 0, 0, 1, 0, 0],
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[0, 0, 0, 0, 0, 0, 1],
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])
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M2 = matrix([
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[F(0), 1, 0, 0, 0, 0, 0],
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[0, 0, 1, 0, 0, 0, 0],
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[0, 0, 0, 0, 0, 1, 0],
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[0, 0, 0, 0, 0, 0, 1],
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])
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M3 = matrix([
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[F(1), 0, 0, 0, 0, 0, 0],
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[1, 0, 0, 0, 0, 0, 0],
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[0, 0, 0, 0, 0, 0, 0],
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[0, 0, 0, 0, 0, 0, 0],
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])
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M4 = matrix([
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[F(0), 0, 0, 0, 0, 0, 0],
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[0, 0, 0, 0, 0, 0, 0],
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[2, 0, 0, 0, 0, 0, 0],
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[0, 0, 0, 0, 0, 0, 0],
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])
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M5 = matrix([
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[F(0), 0, 0, 0, 0, 0, 0],
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[0, 0, 0, 0, 0, 0, 0],
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[2, 0, 0, 0, 0, 0, 0],
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[0, 0, 0, 0, 0, 0, 0],
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])
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M6 = matrix([
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[F(-1), 0, 0, 0, 0, 0, 0],
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[-1, 0, 0, 0, 0, 0, 0],
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[-1, 0, 0, 0, 0, 0, 0],
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[0, 0, 0, 0, 0, 0, 0],
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])
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M7 = matrix([
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[F(0), 0, 0, 0, 0, 0, 0],
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[0, 0, 0, 0, 0, 0, 0],
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[0, 0, 0, 0, 0, 0, 0],
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[0, 0, 0, 0, 0, 0, 0],
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])
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z = [F(1), 0, 1, 2, 3, 10, 42]
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print("z:", z)
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assert len(z) == M0.ncols()
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# CCS parameters
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n = M0.ncols() # == len(z)
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m = M0.nrows()
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t=8
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q=5
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d=3
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S = [[3,0,1], [4,0], [5,1], [6,2], [7]]
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c = [1, 1, 1, 1, 1]
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M = [M0,M1,M2,M3,M4,M5,M6,M7]
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print("CCS values:")
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print("n: %s, m: %s, t: %s, q: %s, d: %s" % (n, m, t, q, d))
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print("M:", M)
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print("z:", z)
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print("S:", S)
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print("c:", c)
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# check CCS relation (this is agnostic to Plonk, for any CCS instance)
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r = [F(0)] * m
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for i in range(0, q):
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hadamard_output = [F(1)]*m
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for j in S[i]:
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hadamard_output = hadamard_product(hadamard_output,
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matrix_vector_product(M[j], z))
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r = vec_add(r, vec_elem_mul(hadamard_output, c[i]))
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print("\nCCS relation check (∑ cᵢ ⋅ ◯ Mⱼ z == 0):", r == [0]*m)
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assert r == [0]*m
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