Perfectly-Secure Multiplication for Any t < n/3

  • Gilad Asharov
  • Yehuda Lindell
  • Tal Rabin
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6841)

Abstract

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.

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Copyright information

© International Association for Cryptologic Research 2011

Authors and Affiliations

  • Gilad Asharov
    • 1
  • Yehuda Lindell
    • 1
  • Tal Rabin
    • 2
  1. 1.Bar-Ilan UniversityIsrael
  2. 2.IBM T.J. Watson ResearchUSA

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