**ZK-PCPs from Leakage-Resilient Secret Sharing**

*Carmit Hazay and Muthuramakrishnan Venkitasubramaniam and Mor Weiss*

**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., $q=polylog(q^*)$), 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 $q^*/q=O(sqrt(n))$ 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.

**Category / Keywords: **foundations / Zero Knowledge, Probabilistically Checkable Proofs, PCPs of Proximity, Leakage Resilience, Secret Sharing

**Original Publication**** (with major differences): **ITC 2021

**Date: **received 10 May 2021, last revised 10 May 2021

**Contact author: **mor weiss at biu ac il

**Available format(s): **PDF | BibTeX Citation

**Version: **20210517:061129 (All versions of this report)

**Short URL: **ia.cr/2021/606

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