Abstract

We consider noninteractive zero-knowledge proofs in the shared random string model proposed by Blum, Feldman and Micali [BFM88]. Until recently there was a sizable polynomial gap between the most efficient noninteractive proofs for NP based on general complexity assumptions [FLS90] versus those based on specific algebraic assumptions [Dam92]. Recently, this gap was reduced to a polylogarithmic factor [Kil94]; 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 based on the random committed bit model introduced by Feige, Lapidot and Shamir. We show how to prove that an n-gate circuit is satisfiable, with error probability 1=n O(1) , 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. 1 Introduction A ba...

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