Journal of Cryptology

, Volume 6, Issue 2, pp 97–116

A perfect zero-knowledge proof system for a problem equivalent to the discrete logarithm

  • Oded Goldreich
  • Eyal Kushilevitz

DOI: 10.1007/BF02620137

Cite this article as:
Goldreich, O. & Kushilevitz, E. J. Cryptology (1993) 6: 97. doi:10.1007/BF02620137


An interactive proof system is calledperfect zero-knowledge if the probability distribution generated by any probabilistic polynomial-time verifier interacting with the prover on input theoremϕ, can be generated by another probabilistic polynomial-time machine which only getsϕ as input (and interacts with nobody!).

In this paper we present aperfect zero-knowledge proof system for a decision problem which is computationally equivalent to the Discrete Logarithm Problem. Doing so we provide additional evidence to the belief thatperfect zero-knowledge proof systems exist in a nontrivial manner (i.e., for languages not inBPP). Our results extend to the logarithm problem in any finite Abelian group.

Key words

Interactive proofsPerfect zero-knowledgeDiscrete logarithm

Copyright information

© International Association for Cryptologic Research 1993

Authors and Affiliations

  • Oded Goldreich
    • 1
  • Eyal Kushilevitz
    • 1
  1. 1.Department of Computer ScienceTechnionHaifaIsrael