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.