Journal of Cryptology

, Volume 11, Issue 1, pp 1–27 | Cite as

An Efficient Noninteractive Zero-Knowledge Proof System for NP with General Assumptions

  • Joe Kilian
  • Erez Petrank


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.

Key words. One-way permutations, Zero knowledge, Efficient proofs, Noninteractive zero knowledge, Circuit satisfiability. 


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Copyright information

© 1998 International Association for Criptologic Rese 1998

Authors and Affiliations

  • Joe Kilian
    • 1
  • Erez Petrank
    • 2
  1. 1.NEC Research InstituteUS
  2. 2.Department of Computer Science, University of Toronto, Toronto, Ontario, Canada M5B 1A4 CA

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