A Zero-Knowledge PCP Theorem

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 con- struction of perfect zero-knowledge PCPs for #P (STOC 2024) and the seminal work of Kilian, Petrank and Tardos (STOC 1997).