Zero-Knowledge Proofs on Secret-Shared Data via Fully Linear PCPs

Dan Boneh, Elette Boyle, Henry Corrigan-Gibbs, Niv Gilboa, Yuval Ishai

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

13 Scopus citations

Abstract

We introduce and study the notion of fully linear probabilistically checkable proof systems. In such a proof system, the verifier can make a small number of linear queries that apply jointly to the input and a proof vector. Our new type of proof system is motivated by applications in which the input statement is not fully available to any single verifier, but can still be efficiently accessed via linear queries. This situation arises in scenarios where the input is partitioned or secret-shared between two or more parties, or alternatively is encoded using an additively homomorphic encryption or commitment scheme. This setting appears in the context of secure messaging platforms, verifiable outsourced computation, PIR writing, private computation of aggregate statistics, and secure multiparty computation (MPC). In all these applications, there is a need for fully linear proof systems with short proofs. While several efficient constructions of fully linear proof systems are implicit in the interactive proofs literature, many questions about their complexity are open. We present several new constructions of fully linear zero-knowledge proof systems with sublinear proof size for “simple” or “structured” languages. For example, in the non-interactive setting of fully linear PCPs, we show how to prove that an input vector (Formula Presented), for a finite field (Formula Presented), satisfies a single degree-2 equation with a proof of size(Formula Presented) and (Formula Presented) linear queries, which we show to be optimal. More generally, for languages that can be recognized by systems of constant-degree equations, we can reduce the proof size to (Formula Presented) at the cost of (Formula Presented) rounds of interaction. We use our new proof systems to construct new short zero-knowledge proofs on distributed and secret-shared data. These proofs can be used to improve the performance of the example systems mentioned above. Finally, we observe that zero-knowledge proofs on distributed data provide a general-purpose tool for protecting MPC protocols against malicious parties. Applying our short fully linear PCPs to “natural” MPC protocols in the honest-majority setting, we can achieve unconditional protection against malicious parties with sublinear additive communication cost. We use this to improve the communication complexity of recent honest-majority MPC protocols. For instance, using any pseudorandom generator, we obtain a 3-party protocol for Boolean circuits in which the amortized communication cost is only one bit per AND gate per party (compared to 10 bits in the best previous protocol), matching the best known protocols for semi-honest parties.

Original languageEnglish
Title of host publicationAdvances in Cryptology – CRYPTO 2019 - 39th Annual International Cryptology Conference, Proceedings
EditorsDaniele Micciancio, Alexandra Boldyreva
PublisherSpringer Verlag
Pages67-97
Number of pages31
ISBN (Print)9783030269531
DOIs
StatePublished - 1 Jan 2019
Event39th Annual International Cryptology Conference, CRYPTO 2019 - Santa Barbara, United States
Duration: 18 Aug 201922 Aug 2019

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume11694 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference39th Annual International Cryptology Conference, CRYPTO 2019
Country/TerritoryUnited States
CitySanta Barbara
Period18/08/1922/08/19

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