Journal of Cryptology

, Volume 6, Issue 2, pp 97–116

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

Authors

  • Oded Goldreich
    • Department of Computer ScienceTechnion
  • Eyal Kushilevitz
    • Department of Computer ScienceTechnion
Article

DOI: 10.1007/BF02620137

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

Abstract

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 proofs Perfect zero-knowledge Discrete logarithm

Copyright information

© International Association for Cryptologic Research 1993