How to Achieve Perfect Simulation and a Complete Problem for Non-interactive Perfect Zero-Knowledge

Abstract

This paper studies perfect zero-knowledge proofs. Such proofs do not allow any simulation errors, and therefore techniques from the study of statistical zero-knowledge (where a small error is allowed) do not apply to them. We introduce a new error shifting technique for building perfect simulators. Using this technique we give the first complete problem for the class of problems admitting non-interactive perfect zero-knowledge (NIPZK) proofs, a hard problem for the class of problems admitting public-coin PZK proofs, and other applications.