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We describe an asynchronous algorithm to solve secure multiparty computation MPC over n players, when strictly less than a <InlineEquation ID=\"IEq1\" <EquationSource Format=\"TEX\"${1}\\over{8}$</EquationSource> </InlineEquation> fraction of the players are controlled by a static adversary. For any function f over a field that can be computed by a circuit with m gates, our algorithm requires each player to send a number of field elements and perform an amount of computation that is <InlineEquation ID=\"IEq2\" <EquationSource Format=\"TEX\"$\\tilde{O}\\frac{m}{n} + \\sqrt n$</EquationSource> </InlineEquation>. This significantly improves over traditional algorithms, which require each player to both send a number of messages and perform computation that is Ωnm. Additionaly, we define the threshold counting problem and present a distributed algorithm to solve it in the asynchronous communication model. Our algorithm is load balanced, with computation, communication and latency complexity of Ologn, and may be of independent interest to other applications with a load balancing goal in mind.

Quorums Quicken Queries: Efficient Asynchronous Secure Multiparty Computation