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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.

Keywords

Secret Sharing Multiplication Protocol Univariate Polynomial Full Proof Honest Party 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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