An efficient noninteractive zero-knowledge proof system for NP with general assumptions

Abstract

We consider noninteractive zero-knowledge proofs in the shared random string model proposed by Blum et al. [5]. Until recently there was a sizable polynomial gap between the most efficient noninteractive proofs forNP based on general complexity assumptions [11] versus those based on specific algebraic assumptions [7]. Recently, this gap was reduced to a polylogarithmic factor [17]; we further reduce the gap to a constant factor. Our proof system relies on the existence of one-way permutations (or trapdoor permutations for bounded provers). Our protocol is stated in the hidden bit model introduced by Feige et al. [11 ]. We show how to prove that an n-gate circuit is satisfiable, with error probability l/n°"', using only O(n lg n) random committed bits. For this error probability, this result matches to within a constant factor the number of committed bits required by the most efficient known interactive proof systems. © 1998 International Association for Cryptologic Research.