2026-07-21T19:24:39Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:14325 2024-03-06T10:53:47Z ddc:004 open_access

ZK-PCPs from Leakage-Resilient Secret Sharing Hazay, Carmit Venkitasubramaniam, Muthuramakrishnan Weiss, Mor Zero Knowledge Probabilisitically Checkable Proofs PCPs of Proximity Leakage Resilience Secret Sharing Zero-Knowledge PCPs (ZK-PCPs; Kilian, Petrank, and Tardos, STOC `97) are PCPs with the additional zero-knowledge guarantee that the view of any (possibly malicious) verifier making a bounded number of queries to the proof can be efficiently simulated up to a small statistical distance. Similarly, ZK-PCPs of Proximity (ZK-PCPPs; Ishai and Weiss, TCC `14) are PCPPs in which the view of an adversarial verifier can be efficiently simulated with few queries to the input. Previous ZK-PCP constructions obtained an exponential gap between the query complexity q of the honest verifier, and the bound q^* on the queries of a malicious verifier (i.e., q = poly log (q^*)), but required either exponential-time simulation, or adaptive honest verification. This should be contrasted with standard PCPs, that can be verified non-adaptively (i.e., with a single round of queries to the proof). The problem of constructing such ZK-PCPs, even when q^* = q, has remained open since they were first introduced more than 2 decades ago. This question is also open for ZK-PCPPs, for which no construction with non-adaptive honest verification is known (not even with exponential-time simulation). We resolve this question by constructing the first ZK-PCPs and ZK-PCPPs which simultaneously achieve efficient zero-knowledge simulation and non-adaptive honest verification. Our schemes have a square-root query gap, namely q^*/q = O(√n) where n is the input length. Our constructions combine the "MPC-in-the-head" technique (Ishai et al., STOC `07) with leakage-resilient secret sharing. Specifically, we use the MPC-in-the-head technique to construct a ZK-PCP variant over a large alphabet, then employ leakage-resilient secret sharing to design a new alphabet reduction for ZK-PCPs which preserves zero-knowledge. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Carmit Hazay and Muthuramakrishnan Venkitasubramaniam and Mor Weiss 2021 Is Part Of LIPIcs, Volume 199, 2nd Conference on Information-Theoretic Cryptography (ITC 2021) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.ITC.2021.6 urn:nbn:de:0030-drops-143250 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITC.2021.6 eng https://creativecommons.org/licenses/by/4.0/legalcode