Hybrid commitments and their applications to zero-knowledge proof systems
Theoretical Computer Science
Weak Verifiable Random Functions
TCC '09 Proceedings of the 6th Theory of Cryptography Conference on Theory of Cryptography
New Techniques for Noninteractive Zero-Knowledge
Journal of the ACM (JACM)
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We give two applications of Nisan-Wigderson-type (NW-type) (“noncryptographic”) pseudorandom generators in cryptography. Specifically, assuming the existence of an appropriate NW-type generator, we construct the following two protocols: (1) a one-message witness-indistinguishable proof system for every language in NP, based on any trapdoor permutation. This proof system does not assume a shared random string or any setup assumption, so it is actually an “NP proof system.” (2) a noninteractive bit-commitment scheme based on any one-way function. The specific NW-type generator we need is a hitting set generator fooling nondeterministic circuits. It is known how to construct such a generator if $E = DTIME(2^{O(n)})$ has a function of nondeterministic circuit complexity $2^{\Omega(n)}$. Our witness-indistinguishable proofs are obtained by using the NW-type generator to derandomize the ZAPs of Dwork and Naor [Proceedings of the 41st Annual ACM Symposium on Foundations of Computer Science, 2000, pp. 283-293]. To our knowledge, this is the first construction of an NP proof system achieving a secrecy property. Our commitment scheme is obtained by derandomizing the interactive commitment scheme of Naor [J. Cryptology, 4 (1991), pp. 151-158]. Previous constructions of noninteractive commitment schemes were known only under incomparable assumptions.