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- # Notes from paper:
- # "Efficient Zero-Knowledge Arguments for Arithmetic Circuits in the
- # Discrete Log Setting" by Bootle and others (EUROCRYPT 2016)
- from finite_fields import finitefield
- import numpy as np
- q = 0x40000000000000000000000000000000224698fc094cf91b992d30ed00000001
- fq = finitefield.IntegersModP(q)
- # Number of variables
- m = 16
- # Number of rows for multiplication statements
- n = 2
- N = n * m
- # Initialize zeroed table
- aux = np.full(m, fq(0))
- # From the zk-explainer document, we will represent the function:
- #
- # def foo(w, a, b):
- # if w:
- # return a * b
- # else:
- # return a + b
- #
- # Which can be translated mathematically to the statements:
- #
- # ab = m
- # w(m - a - b) = v - a - b
- # w^2 = w
- #
- # Where m is an intermediate value.
- one = 0
- aux[one] = fq(1)
- a = 1
- b = 2
- w = 3
- aux[a] = fq(110)
- aux[b] = fq(4)
- aux[w] = fq(1)
- # Calculate intermediate advice values
- m = 4
- aux[m] = aux[a] * aux[b]
- # Calculate public input values
- v = 5
- aux[v] = aux[w] * (aux[a] * aux[b]) + \
- (aux[one] - aux[w]) * (aux[a] + aux[b])
- # Just a quick enforcement check:
- assert aux[a] * aux[b] == aux[m]
- assert aux[w] * (aux[m] - aux[a] - aux[b]) == aux[v] - aux[a] - aux[b]
- assert aux[w] * aux[w] == aux[w]
- # Setup the gates. For each row of a, b and c, the statement a b = c holds
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