Optimal Fair Computation

A computation scheme among n parties is fair if no party obtains the computation result unless all other \(n-1\) parties obtain the same result. A fair computation scheme is optimistic if n honest parties can obtain the computation result without resorting to a trusted third party. We prove, for the first time, a tight lower-bound on the message complexity of optimistic fair computation for n parties among which \(n-1\) can be malicious in an asynchronous network. We do so by relating the optimal message complexity of optimistic fair computation to the length of the shortest permutation sequence in combinatorics.

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