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 for NP 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 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.
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Received 20 November 1995 and revised 7 October 1996
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Kilian, J., Petrank, E. An Efficient Noninteractive Zero-Knowledge Proof System for NP with General Assumptions . J. Cryptology 11, 1–27 (1998). https://doi.org/10.1007/s001459900032
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DOI: https://doi.org/10.1007/s001459900032