1/p-secure multiparty computation without honest majority and the best of both worlds

Amos Beimel, Yehuda Lindell, Eran Omri, Ilan Orlov

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

33 Scopus citations

Abstract

A protocol for computing a functionality is secure if an adversary in this protocol cannot cause more harm than in an ideal computation, where parties give their inputs to a trusted party which returns the output of the functionality to all parties. In particular, in the ideal model such computation is fair - all parties get the output. Cleve (STOC 1986) proved that, in general, fairness is not possible without an honest majority. To overcome this impossibility, Gordon and Katz (Eurocrypt 2010) suggested a relaxed definition - 1/p-secure computation - which guarantees partial fairness. For two parties, they construct 1/p-secure protocols for functionalities for which the size of either their domain or their range is polynomial (in the security parameter). Gordon and Katz ask whether their results can be extended to multiparty protocols. We study 1/p-secure protocols in the multiparty setting for general functionalities. Our main result is constructions of 1/p-secure protocols that are resilient against any number of corrupt parties provided that the number of parties is constant and the size of the range of the functionality is at most polynomial (in the security parameter n). If less than 2/3 of the parties are corrupt, the size of the domain is constant, and the functionality is deterministic, then our protocols are efficient even when the number of parties is log log n. On the negative side, we show that when the number of parties is super-constant, 1/p-secure protocols are not possible when the size of the domain is polynomial. Thus, our feasibility results for 1/p-secure computation are essentially tight. We further motivate our results by constructing protocols with stronger guarantees: If in the execution of the protocol there is a majority of honest parties, then our protocols provide full security. However, if only a minority of the parties are honest, then our protocols are 1/p-secure. Thus, our protocols provide the best of both worlds, where the 1/p-security is only a fall-back option if there is no honest majority.

Original languageEnglish
Title of host publicationAdvances in Cryptology - CRYPTO 2011 - 31st Annual Cryptology Conference, Proceedings
PublisherSpringer Verlag
Pages277-296
Number of pages20
ISBN (Print)9783642227912
DOIs
StatePublished - 1 Jan 2011
Event31st Annual International Cryptology Conference, CRYPTO 2011 - Santa Barbara, CA, United States
Duration: 14 Aug 201118 Aug 2011

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume6841 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference31st Annual International Cryptology Conference, CRYPTO 2011
Country/TerritoryUnited States
CitySanta Barbara, CA
Period14/08/1118/08/11

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