feat: Gray code indexing #17
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AaronFeickert
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During verification, the verifier must compute a product of
fterms that depends on index decomposition. This ends up being quite inefficient.As noted in #16, it's possible to replace standard index decomposition with a Gray code design. This is beneficial since successive indexes will differ only in a single digit. This means that successive products of
fterms can be computed with only two multiplications, one of which is the inverse of a scalar element off. We can further take advantage of the curve library's scalar batch inversion functionality to efficiently compute all such inverses at once.This PR adds this functionality. It introduces a new
GrayIteratorthat iteratively identifies digit changes between successive index decompositions, and modifies the prover and verifier to account for the change.Closes #16.