A PCP Theorem for Interactive Proofs and Applications

Gal Arnon; Alessandro Chiesa; Eylon Yogev

doi:10.1007/978-3-031-07085-3_3

A PCP Theorem for Interactive Proofs and Applications

Gal Arnon, Alessandro Chiesa, Eylon Yogev

Department of Computer Science

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

3 Scopus citations

Abstract

The celebrated PCP Theorem states that any language in NP can be decided via a verifier that reads O(1) bits from a polynomially long proof. Interactive oracle proofs (IOP), a generalization of PCPs, allow the verifier to interact with the prover for multiple rounds while reading a small number of bits from each prover message. While PCPs are relatively well understood, the power captured by IOPs (beyond NP ) has yet to be fully explored. We present a generalization of the PCP theorem for interactive languages. We show that any language decidable by a k(n)-round IP has a k(n)-round public-coin IOP, where the verifier makes its decision by reading only O(1) bits from each (polynomially long) prover message and O(1) bits from each of its own (random) messages to the prover. Our result and the underlying techniques have several applications. We get a new hardness of approximation result for a stochastic satisfiability problem, we show IOP-to-IOP transformations that previously were known to hold only for IPs, and we formulate a new notion of PCPs (index-decodable PCPs) that enables us to obtain a commit-and-prove SNARK in the random oracle model for nondeterministic computations.

Original language	English
Title of host publication	Advances in Cryptology – EUROCRYPT 2022 - 41st Annual International Conference on the Theory and Applications of Cryptographic Techniques, 2022, Proceedings
Editors	Orr Dunkelman, Stefan Dziembowski
Publisher	Springer Science and Business Media Deutschland GmbH
Pages	64-94
Number of pages	31
ISBN (Print)	9783031070846
DOIs	https://doi.org/10.1007/978-3-031-07085-3_3
State	Published - 2022
Event	41st Annual International Conference on the Theory and Applications of Cryptographic Techniques, EUROCRYPT 2022 - Trondheim, Norway Duration: 30 May 2022 → 3 Jun 2022

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	13276 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	41st Annual International Conference on the Theory and Applications of Cryptographic Techniques, EUROCRYPT 2022
Country/Territory	Norway
City	Trondheim
Period	30/05/22 → 3/06/22

Bibliographical note

Publisher Copyright:
© 2022, International Association for Cryptologic Research.

Keywords

Interactive oracle proofs
Interactive proofs
Probabilistically checkable proofs

Access to Document

10.1007/978-3-031-07085-3_3

Cite this

Arnon, G., Chiesa, A., & Yogev, E. (2022). A PCP Theorem for Interactive Proofs and Applications. In O. Dunkelman, & S. Dziembowski (Eds.), Advances in Cryptology – EUROCRYPT 2022 - 41st Annual International Conference on the Theory and Applications of Cryptographic Techniques, 2022, Proceedings (pp. 64-94). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 13276 LNCS). Springer Science and Business Media Deutschland GmbH. https://doi.org/10.1007/978-3-031-07085-3_3

Arnon, Gal ; Chiesa, Alessandro ; Yogev, Eylon. / A PCP Theorem for Interactive Proofs and Applications. Advances in Cryptology – EUROCRYPT 2022 - 41st Annual International Conference on the Theory and Applications of Cryptographic Techniques, 2022, Proceedings. editor / Orr Dunkelman ; Stefan Dziembowski. Springer Science and Business Media Deutschland GmbH, 2022. pp. 64-94 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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Arnon, G, Chiesa, A & Yogev, E 2022, A PCP Theorem for Interactive Proofs and Applications. in O Dunkelman & S Dziembowski (eds), Advances in Cryptology – EUROCRYPT 2022 - 41st Annual International Conference on the Theory and Applications of Cryptographic Techniques, 2022, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 13276 LNCS, Springer Science and Business Media Deutschland GmbH, pp. 64-94, 41st Annual International Conference on the Theory and Applications of Cryptographic Techniques, EUROCRYPT 2022, Trondheim, Norway, 30/05/22. https://doi.org/10.1007/978-3-031-07085-3_3

A PCP Theorem for Interactive Proofs and Applications. / Arnon, Gal; Chiesa, Alessandro; Yogev, Eylon.
Advances in Cryptology – EUROCRYPT 2022 - 41st Annual International Conference on the Theory and Applications of Cryptographic Techniques, 2022, Proceedings. ed. / Orr Dunkelman; Stefan Dziembowski. Springer Science and Business Media Deutschland GmbH, 2022. p. 64-94 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 13276 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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Arnon G, Chiesa A, Yogev E. A PCP Theorem for Interactive Proofs and Applications. In Dunkelman O, Dziembowski S, editors, Advances in Cryptology – EUROCRYPT 2022 - 41st Annual International Conference on the Theory and Applications of Cryptographic Techniques, 2022, Proceedings. Springer Science and Business Media Deutschland GmbH. 2022. p. 64-94. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-031-07085-3_3