ZK-PCPs from Leakage-Resilient Secret Sharing

Authors Carmit Hazay, Muthuramakrishnan Venkitasubramaniam, Mor Weiss

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Author Details

Carmit Hazay
  • Bar-Ilan University, Ramat Gan, Israel
Muthuramakrishnan Venkitasubramaniam
  • University of Rochester, NY, USA
Mor Weiss
  • Bar-Ilan University, Ramat Gan, Israel


We thank the anonymous ITC`21 reviewers for their helpful comments, in particular for pointing out the connection to RPEs and noting that the ZK code of [Scott E. Decatur et al., 1999] is equivocal.

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Carmit Hazay, Muthuramakrishnan Venkitasubramaniam, and Mor Weiss. ZK-PCPs from Leakage-Resilient Secret Sharing. In 2nd Conference on Information-Theoretic Cryptography (ITC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 199, pp. 6:1-6:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


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.

Subject Classification

ACM Subject Classification
  • Security and privacy → Information-theoretic techniques
  • Theory of computation → Cryptographic protocols
  • Security and privacy → Cryptography
  • Theory of computation → Proof complexity
  • Zero Knowledge
  • Probabilisitically Checkable Proofs
  • PCPs of Proximity
  • Leakage Resilience
  • Secret Sharing


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