Zero-Knowledge Proofs via Polynomial Representations

Under the existence of commitment schemes with homomorphic properties, we construct a constant-round zero-knowledge proof system for an NP-complete language that requires a number of commitments that is sublinear in the size of the (best known) witness verification predicate. The overall communication complexity improves upon best known results for the specific NP-complete language [1,2] and results that could be obtained using zero-knowledge proof systems for the entire NP class (most notably, [3,2,4]). Perhaps of independent interest, our techniques build a proof system after reducing the theorem to be proved to statements among low-degree polynomials over large fields and using Schwartz-Zippel lemma to prove polynomial identities among committed values.