Abstract
An interactive proof is called perfect zero-knowledge if the probability distribution generated by any probabilistic polynomial-time verifier interacting with the prover on input a theorem φ, can be generated by another probabilistic polynomial time machine which only gets φ as input (and interacts with nobody!).
In this paper we present a perfect 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 that perfect zero-knowledge proofs exist in a non-trivial manner (i.e. for languages not in BPP). Our results extend to the logarithm problem in any finite Abelian group.
Research was partially supported by the Fund for Basic Research Administered by the Israeli Academy of Sciences and Humanities.
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Goldreich, O., Kushilevitz, E. (1990). A Perfect Zero-Knowledge Proof for a Problem Equivalent to Discrete Logarithm. In: Goldwasser, S. (eds) Advances in Cryptology — CRYPTO’ 88. CRYPTO 1988. Lecture Notes in Computer Science, vol 403. Springer, New York, NY. https://doi.org/10.1007/0-387-34799-2_5
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