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ZK-PCPs from Leakage-Resilient Secret Sharing

Authors:
Carmit Hazay
Muthuramakrishnan Venkitasubramaniam
Mor Weiss
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DOI: 10.1007/s00145-022-09433-3
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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∗ q ∗ on the queries of a malicious verifier (i.e., q=polylog⁡(q∗) 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 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) 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.
BibTeX
@article{jofc-2022-32786,
  title={ZK-PCPs from Leakage-Resilient Secret Sharing},
  journal={Journal of Cryptology},
  publisher={Springer},
  volume={35},
  doi={10.1007/s00145-022-09433-3},
  author={Carmit Hazay and Muthuramakrishnan Venkitasubramaniam and Mor Weiss},
  year=2022
}