, Volume 6, Issue 2, pp 97-116

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

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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.

Communicated by Ernest F. Brickell
This research was partially supported by the Fund for Basic Research Administered by the Israeli Academy of Sciences and Humanities. An early version of this paper appeared inAdvances in Cryptology —Crypto 88 (Proceedings), S. Goldwasser (ed.), pp. 57–70, Lecture Notes in Computer Science, vol. 403, Springer-Verlag, Berlin, 1990.