A Zero-Knowledge PCP Theorem

TL;DR

This paper introduces zero-knowledge PCPs for NP and NEXP, achieving perfect zero knowledge against adaptive and polynomial-time adversaries, respectively, with polynomial or exponential proof sizes and constant query complexity.

Contribution

It presents the first polynomial-size, constant-query, perfect zero-knowledge PCPs for NP and NEXP, improving previous constructions and extending zero-knowledge properties.

Findings

Zero-knowledge PCPs for NP with perfect zero knowledge against adaptive adversaries.

Exponential-size zero-knowledge PCPs for NEXP with perfect zero knowledge.

Improved upon previous zero-knowledge PCP constructions for #P and related work.

Abstract

We show that for every polynomial q* there exist polynomial-size, constant-query, non-adaptive PCPs for NP which are perfect zero knowledge against (adaptive) adversaries making at most q* queries to the proof. In addition, we construct exponential-size constant-query PCPs for NEXP with perfect zero knowledge against any polynomial-time adversary. This improves upon both a recent construction of perfect zero-knowledge PCPs for #P (STOC 2024) and the seminal work of Kilian, Petrank and Tardos (STOC 1997).