Paper 2021/915 Original: eprint.iacr.org/2021/915 ↗
A PCP Theorem for Interactive Proofs and Applications
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.
Metadata
- Available format(s)
PDF- Category
- Foundations
- Publication info
- Preprint.
- History
- 2023-01-17: last updated
- 2021-07-08: published
- Short URL
- https://ia.cr/2021/915
- License
- https://creativecommons.org/licenses/by/4.0/
BibTeX
@misc{cryptoeprint:2021/915,
author = {Gal Arnon and Alessandro Chiesa and Eylon Yogev},
title = {A PCP Theorem for Interactive Proofs and Applications},
howpublished = {Cryptology {ePrint} Archive, Paper 2021/915},
year = {2021},
url = {https://eprint.iacr.org/2021/915}
}