Rationality and Adversarial Behavior in Multy-Party Computation

In this paper, we study multi-party computation in the model where none of the participating parties are honest: they are either rational, acting in their selfish interest to maximize their utility, or adversarial, acting arbitrarily. In this new model, which we call the mixed-behavior model, we define a class of functions that can be correctly computed in the presence of an adversary using a trusted mediator. We then give a protocol that allows the rational parties to to emulate the mediator and jointly compute a function such that (1) assuming that each rational party prefers that it learns the output while others do not, no rational party will have an incentive to deviate from the protocol; and (2) the rational parties are protected from the malicious adversary controlling a minority of the participants in the following sense: if the adversary controls up to dn 2 e − 2 of n participants, then the adversary can only either cause all rational participants to abort (so no one learns the function they are trying to compute), or can only learn whatever information about their inputs is implied by the output of the function. We also present a slightly modified protocol that achieves a different trade-off between the above properties; where namely, adversarial abort can be tolerated if rational parties’ desired behavior is appropriately relaxed.