An Efficient Noninteractive Zero-Knowledge Proof System for NP with General Assumptions
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- Kilian, J. & Petrank, E. J. Cryptology (1998) 11: 1. doi:10.1007/s001459900032
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We consider noninteractive zero-knowledge proofs in the shared random string model proposed by Blum et al. . Until recently there was a sizable polynomial gap between the most efficient noninteractive proofs for NP based on general complexity assumptions  versus those based on specific algebraic assumptions . Recently, this gap was reduced to a polylogarithmic factor ; 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. . We show how to prove that an n -gate circuit is satisfiable, with error probability 1/nO(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.