Cryptology ePrint Archive: Report 2017/176

Probabilistically Checkable Proofs of Proximity with Zero-Knowledge

Yuval Ishai and Mor Weiss

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 "$x\in L$" by querying only few bits of the proof. A PCP of proximity (PCPP) has the additional feature of allowing the verifier to query only few bits of the input $x$, where if the input is accepted then the verifier is guaranteed that (with high probability) the input is close to some $x'\in L$.

Motivated by their usefulness for sublinear-communication cryptography, we initiate the study of a natural zero-knowledge variant of PCPP (ZKPCPP), where the view of any verifier making a bounded number of queries can be efficiently simulated by making the same number of queries to the input oracle alone. This new notion provides a useful extension of the standard notion of zero-knowledge PCPs. We obtain two types of results.

1. Constructions. We obtain the first constructions of query-efficient ZKPCPPs via a general transformation which combines standard query-efficient PCPPs with protocols for secure multiparty computation. As a byproduct, our construction provides a conceptually simpler alternative to a previous construction of honest-verifier zero-knowledge PCPs due to Dwork et al. (Crypto '92).

2. Applications. We motivate the notion of ZKPCPPs by applying it towards sublinear-communication implementations of commit-and-prove functionalities. Concretely, we present the first sublinear-communication commit-and-prove protocols which make a black-box use of a collision-resistant hash function, and the first such multiparty protocols which offer information-theoretic security in the presence of an honest majority.

Category / Keywords: Probabilistically Checkable Proofs, Zero-Knowledge, Verifiable Secret Sharing

Original Publication (in the same form): IACR-TCC-2014

Date: received 21 Feb 2017, last revised 21 Feb 2017

Contact author: mormorweiss at gmail com

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Version: 20170227:145135 (All versions of this report)

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