Your Reputation’s Safe with Me: Framing-Free Distributed Zero-Knowledge Proofs

Carmit Hazay, Muthuramakrishnan Venkitasubramaniam, Mor Weiss

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

Abstract

Distributed Zero-Knowledge (dZK) proofs, recently introduced by Boneh et al. (CRYPTO‘19), allow a prover P to prove NP statements on an input x which is distributed between k verifiers V1, …, Vk, where each Vi holds only a piece of x. As in standard ZK proofs, dZK proofs guarantee Completeness when all parties are honest; Soundness against a malicious prover colluding with t verifiers; and Zero Knowledge against a subset of t malicious verifiers, in the sense that they learn nothing about the NP witness and the input pieces of the honest verifiers. Unfortunately, dZK proofs provide no correctness guarantee for an honest prover against a subset of maliciously corrupted verifiers. In particular, such verifiers might be able to “frame” the prover, causing honest verifiers to reject a true claim. This is a significant limitation, since such scenarios arise naturally in dZK applications, e.g., for proving honest behavior, and such attacks are indeed possible in existing dZKs (Boneh et al., CRYPTO‘19). We put forth and study the notion of strong completeness for dZKs, guaranteeing that true claims are accepted even when t verifiers are maliciously corrupted. We then design strongly-complete dZK proofs using the “MPC-in-the-head” paradigm of Ishai et al. (STOC‘07), providing a novel analysis that exploits the unique properties of the distributed setting. To demonstrate the usefulness of strong completeness, we present several applications in which it is instrumental in obtaining security. First, we construct a certifiable version of Verifiable Secret Sharing (VSS), which is a VSS in which the dealer additionally proves that the shared secret satisfies a given NP relation. Our construction withstands a constant fraction of corruptions, whereas a previous construction of Ishai et al. (TCC‘14) required k= poly(t). We also design a reusable version of certifiable VSS that we introduce, in which the dealer can prove an unlimited number of predicates on the same shared secret. Finally, we extend a compiler of Boneh et al. (CRYPTO‘19), who used dZKs to transform a class of “natural” semi-honest protocols in the honest-majority setting into maliciously secure ones with abort. Our compiler uses strongly-complete dZKs to obtain identifiable abort.

Original languageEnglish
Title of host publicationTheory of Cryptography - 21st International Conference, TCC 2023, Proceedings
EditorsGuy Rothblum, Hoeteck Wee
PublisherSpringer Science and Business Media Deutschland GmbH
Pages34-64
Number of pages31
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.

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