## 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 language | English |
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Title of host publication | Theory of Cryptography - 11th Theory of Cryptography Conference, TCC 2014, Proceedings |

Publisher | Springer Verlag |

Pages | 121-145 |

Number of pages | 25 |

ISBN (Print) | 9783642542411 |

DOIs | |

State | Published - 2014 |

Externally published | Yes |

Event | 11th Theory of Cryptography Conference on Theory of Cryptography, TCC 2014 - San Diego, CA, United States Duration: 24 Feb 2014 → 26 Feb 2014 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 8349 LNAI |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 11th Theory of Cryptography Conference on Theory of Cryptography, TCC 2014 |
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Country/Territory | United States |

City | San Diego, CA |

Period | 24/02/14 → 26/02/14 |

### 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.

Funders | Funder number |
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United States-Israel Binational Science Foundation | 2008411, 2012366 |

Israel Science Foundation | 1361/10 |

Seventh Framework Programme | 259426 ERC-CaC, FP10/ 2010-2016 |