# Darmstadt-Warsaw Research Seminar on Cryptography and Blockchains: ZK-PCPs from Leakage-Resilient Secret Sharing

09.06.2021 13:00-14:00

Speaker: Prof. Carmit Hazay (Bar-Ilan University) | Location: Online (Networking afterwards)

Organizer:
Prof. Stefan Dziembowski (University of Warsaw)

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.

Based on joint work with Muthuramakrishnan Venkitasubramaniam and Mor Weiss.

Biography