Secure Multiparty Computation With Partial Fairness
A protocol for computing a functionality is secure if an adversary in this protocol cannot cause more harm than in an ideal computation where parties give their inputs to a trusted party which returns the output of the functionality to all parties. This is formalized by requiring that for every adversary in the real world, there is an adversary in the ideal world, called simulator, such that the output of the real-world adversary and the simulator are indistinguishable in polynomial time. Such security can be achieved when there is a majority of honest parties. Secure computation is fair - all parties get the output. Cleve proved that, in general, fairness is not possible without an honest majority.