A Full Proof of the BGW Protocol for Perfectly-Secure Multiparty

Gilad Asharov, Yehuda Lindell

Research output: Contribution to journalArticlepeer-review

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. When the adversary is semi-honest this holds as long as t < n/2 parties are corrupted, and when the adversary is malicious this holds as long as t < n/3 parties are corrupted. Unfortunately, a full detailed proof of these results was never given. In this paper, we remedy this situation and provide a full proof of security of the BGW protocol. We also derive corollaries for security in the presence of adaptive adversaries and under concurrent general composition (equivalently, universal composability). In addition, we give a full specification of the protocol for the malicious setting. This includes one new step for the perfect multiplication protocol in the case of n/4 ≤ t < n/3.
Original languageAmerican English
Article number36
Number of pages76
JournalElectronic Colloquium on Computational Complexity
Volume18
StatePublished - 8 Jul 2011

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