Perfectly-secure multiplication for any t < n/3

Gilad Asharov, Yehuda Lindell, Tal Rabin

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

9 Scopus citations


In the setting of secure multiparty computation, a set of n parties with private inputs wish to jointly compute some functionality of their inputs. One of the most fundamental results of information-theoretically secure computation was presented by Ben-Or, Goldwasser and Wigderson (BGW) in 1988. They demonstrated that any n-party functionality can be computed with perfect security, in the private channels model. The most technically challenging part of this result is a protocol for multiplying two shared values, with perfect security in the presence of up to t < n/3 malicious adversaries. In this paper we provide a full specification of the BGW perfect multiplication protocol and prove its security. This includes one new step for the perfect multiplication protocol in the case of n/4 ≤ t < n/3. As in the original BGW protocol, this protocol works whenever the parties hold univariate (Shamir) shares of the input values. In addition, we present a new multiplication protocol that utilizes bivariate secret sharing in order to achieve higher efficiency while maintaining a round complexity that is constant per multiplication. Both of our protocols are presented with full proofs of security.

Original languageEnglish
Title of host publicationAdvances in Cryptology - CRYPTO 2011 - 31st Annual Cryptology Conference, Proceedings
PublisherSpringer Verlag
Number of pages19
ISBN (Print)9783642227912
StatePublished - 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


Conference31st Annual International Cryptology Conference, CRYPTO 2011
Country/TerritoryUnited States
CitySanta Barbara, CA

Bibliographical note

Place of conference:Santa Barbara, California


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