The knowledge complexity of interactive proof systems
SIAM Journal on Computing
Journal of the ACM (JACM)
A note on efficient zero-knowledge proofs and arguments (extended abstract)
STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
Algebraic methods for interactive proof systems
Journal of the ACM (JACM)
Journal of the ACM (JACM)
On the existence of pseudorandom generators
SIAM Journal on Computing
Journal of the ACM (JACM)
Linear zero-knowledge—a note on efficient zero-knowledge proofs and arguments
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Fast Probabilistic Algorithms for Verification of Polynomial Identities
Journal of the ACM (JACM)
Efficient Identification and Signatures for Smart Cards
CRYPTO '89 Proceedings of the 9th Annual International Cryptology Conference on Advances in Cryptology
Non-Interactive and Information-Theoretic Secure Verifiable Secret Sharing
CRYPTO '91 Proceedings of the 11th Annual International Cryptology Conference on Advances in Cryptology
Zero-Knowledge Proofs for Finite Field Arithmetic; or: Can Zero-Knowledge be for Free?
CRYPTO '98 Proceedings of the 18th Annual International Cryptology Conference on Advances in Cryptology
Zero-Knowledge Proofs from Secure Multiparty Computation
SIAM Journal on Computing
An improved protocol for demonstrating possession of discrete logarithms and some generalizations
EUROCRYPT'87 Proceedings of the 6th annual international conference on Theory and application of cryptographic techniques
Simulatable commitments and efficient concurrent zero-knowledge
EUROCRYPT'03 Proceedings of the 22nd international conference on Theory and applications of cryptographic techniques
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Under the existence of commitment schemes with homomorphic properties, we construct a constant-round zero-knowledge proof system for an $\mathcal NP$-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 $\mathcal NP$-complete language [1,2] and results that could be obtained using zero-knowledge proof systems for the entire $\mathcal NP$ 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.