## Cryptology ePrint Archive: Report 2002/085

Efficient and Player-Optimal Strong Consensus

Matthias Fitzi and Juan A. Garay

Abstract: In the {\em strong consensus} problem, $n$ players attempt to reach agreement on a value initially held by {\em one of the good players}, despite the (malicious) behavior of up to $t$ of them. Although the problem is closely related to the standard consensus problem (aka Byzantine agreement), the only known solution with the optimal number of players requires exponential computation and communication in the unconditional setting.

In this paper we study this problem, and present {\em efficient} protocols and tight lower bounds for several standard distributed computation models --- unconditional, computational, synchronous, and asynchronous.

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