Journal of Cryptology

, Volume 6, Issue 2, pp 97-116

First online:

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

  • Oded GoldreichAffiliated withDepartment of Computer Science, Technion
  • , Eyal KushilevitzAffiliated withDepartment of Computer Science, Technion

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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