Probabilistically checkable proofs of proximity with zero-knowledge

Yuval Ishai, Mor Weiss

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

15 Scopus citations

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 â̂̂ 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′ â̂̂ 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. 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). 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.

Original languageEnglish
Title of host publicationTheory of Cryptography - 11th Theory of Cryptography Conference, TCC 2014, Proceedings
PublisherSpringer Verlag
Pages121-145
Number of pages25
ISBN (Print)9783642542411
DOIs
StatePublished - 2014
Externally publishedYes
Event11th Theory of Cryptography Conference on Theory of Cryptography, TCC 2014 - San Diego, CA, United States
Duration: 24 Feb 201426 Feb 2014

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume8349 LNAI
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference11th Theory of Cryptography Conference on Theory of Cryptography, TCC 2014
Country/TerritoryUnited States
CitySan Diego, CA
Period24/02/1426/02/14

Bibliographical note

Funding Information:
Research supported by the European Union’s Tenth Framework Programme (FP10/ 2010-2016) under grant agreement no. 259426 ERC-CaC. The first author was additionally supported by ISF grant 1361/10 and BSF grants 2008411 and 2012366.

Funding

Research supported by the European Union’s Tenth Framework Programme (FP10/ 2010-2016) under grant agreement no. 259426 ERC-CaC. The first author was additionally supported by ISF grant 1361/10 and BSF grants 2008411 and 2012366.

FundersFunder number
United States-Israel Binational Science Foundation2008411, 2012366
Israel Science Foundation1361/10
Seventh Framework Programme259426 ERC-CaC, FP10/ 2010-2016

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