Distributed-Prover Interactive Proofs

Sourav Das*, Rex Fernando, Ilan Komargodski, Elaine Shi, Pratik Soni

*Corresponding author for this work

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

Abstract

Interactive proof systems enable a verifier with limited resources to decide an intractable language (or compute a hard function) by communicating with a powerful but untrusted prover. Such systems guarantee soundness: the prover can only convince the verifier of true statements. This is a central notion in computer science with far-reaching implications. One key drawback of the classical model is that the data on which the prover operates must be held by a single machine. In this work, we initiate the study of distributed-prover interactive proofs (dpIPs): an untrusted cluster of machines, acting as a distributed prover, interacts with a single verifier. The machines in the cluster jointly store and operate on a massive data-set that no single machine can store. The goal is for the machines in the cluster to convince the verifier of the validity of some statement about its data-set. We formalize the communication and space constraints via the massively parallel computation (MPC) model, a widely accepted analytical framework capturing the computational power of massive data-centers. Our main result is a compiler that generically augments any verification algorithm in the MPC model with a (computational) soundness guarantee. Concretely, for any language L for which there is an MPC algorithm verifying whether x∈ L, we design a new MPC protocol capable of convincing a verifier of the validity of x∈ L and where if x∉ L, the verifier rejects with overwhelming probability. The new protocol requires only slightly more rounds, i.e., a poly(log N) blowup, and a slightly bigger memory per machine, i.e., poly(λ) blowup, where N is the total size of the dataset and λ is a security parameter independent of N. En route, we introduce distributed-prover interactive oracle proofs (dpIOPs), a natural adaptation of the (by now classical) IOP model to the distributed prover setting. We design a dpIOP for verification algorithms in the MPC model and then translate them to “plain model” dpIPs via an adaptation of existing polynomial commitment schemes into the distributed prover setting.

Original languageAmerican English
Title of host publicationTheory of Cryptography - 21st International Conference, TCC 2023, Proceedings
EditorsGuy Rothblum, Hoeteck Wee
PublisherSpringer Science and Business Media Deutschland GmbH
Pages91-120
Number of pages30
ISBN (Print)9783031486142
DOIs
StatePublished - 2023
Event21st International conference on Theory of Cryptography Conference, TCC 2023 - Taipei, Taiwan, Province of China
Duration: 29 Nov 20232 Dec 2023

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume14369 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference21st International conference on Theory of Cryptography Conference, TCC 2023
Country/TerritoryTaiwan, Province of China
CityTaipei
Period29/11/232/12/23

Bibliographical note

Publisher Copyright:
© 2023, International Association for Cryptologic Research.

Fingerprint

Dive into the research topics of 'Distributed-Prover Interactive Proofs'. Together they form a unique fingerprint.

Cite this