Making the Best of a Leaky Situation: Zero-Knowledge PCPs from Leakage-Resilient Circuits

Abstract

A Probabilistically Checkable Proof (PCP) allows a randomized verifier, with oracle access to a purported proof, to probabilistically verify an input statement of the form “x ∈ L ” by querying only few bits of the proof. A zero-knowledge PCP (ZKPCP) is a PCP with the additional guarantee that the view of any verifier querying a bounded number of proof bits can be efficiently simulated given the input x alone, where the simulated and actual views are statistically close. Originating from the first ZKPCP construction of Kilian et al. (STOC ’97), all previous constructions relied on locking schemes, an unconditionally secure oracle-based commitment primitive. The use of locking schemes makes the verifier inherently adaptive, namely, it needs to make at least two rounds of queries to the proof. Motivated by the goal of constructing non-adaptively verifiable ZKPCPs, we suggest a new technique for compiling standard PCPs into ZKPCPs. Our approach is based on leakage-resilient circuits, which are circuits that withstand certain “side-channel ” attacks, in the sense that these attacks reveal nothing about the (properly encoded) input, other than the output. We observe that the verifier’s oracle queries constitute a side-channel attack on the wire-values of the circuit