A PCP Theorem for Interactive Proofs and Applications

Gal Arnon, Alessandro Chiesa, Eylon Yogev

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

1 Scopus citations


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 languageEnglish
Title of host publicationAdvances in Cryptology – EUROCRYPT 2022 - 41st Annual International Conference on the Theory and Applications of Cryptographic Techniques, 2022, Proceedings
EditorsOrr Dunkelman, Stefan Dziembowski
PublisherSpringer Science and Business Media Deutschland GmbH
Number of pages31
ISBN (Print)9783031070846
StatePublished - 2022
Event41st Annual International Conference on the Theory and Applications of Cryptographic Techniques, EUROCRYPT 2022 - Trondheim, Norway
Duration: 30 May 20223 Jun 2022

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume13276 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference41st Annual International Conference on the Theory and Applications of Cryptographic Techniques, EUROCRYPT 2022

Bibliographical note

Funding Information:
Keywords: Interactive proofs · Probabilistically checkable proofs · Interactive oracle proofs G. Arnon—Supported in part by a grant from the Israel Science Foundation (no. 2686/20) and by the Simons Foundation Collaboration on the Theory of Algorithmic Fairness. A. Chiesa—Funded by the Ethereum Foundation. E. Yogev—Part of this project was performed when Eylon Yogev was in Tel Aviv University where he was funded by the ISF grants 484/18, 1789/19, Len Blavatnik and the Blavatnik Foundation, and The Blavatnik Interdisciplinary Cyber Research Center at Tel Aviv University.

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


  • Interactive oracle proofs
  • Interactive proofs
  • Probabilistically checkable proofs


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