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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

Funding

The first and third authors are supported by the BIU Center for Research in Applied Cryptography and Cyber Security in conjunction with the Israel National Cyber Bureau in the Prime Minister’s Office. The first author is supported by ISF grant No. 1316/18. The first and second authors are supported by DARPA under Contract No. HR001120C0087. Any opinions, findings and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of DARPA.

Acknowledgements

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.

Cite As Get BibTex

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) https://doi.org/10.4230/LIPIcs.ITC.2021.6

Abstract

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
Keywords
  • Zero Knowledge
  • Probabilisitically Checkable Proofs
  • PCPs of Proximity
  • Leakage Resilience
  • Secret Sharing

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