Subcontracted Rational SFE

In their paper, “Rational Secure Computation and Ideal Mechanism Design,” Izmalkov, Lepinski and Micali show that any one-shot mediated game can be simulated by the players themselves, without the help of a trusted mediator, using physical envelopes and a ballot-box. We show that communication between the players is not essential to the ILM protocol. That is, we provide a protocol for rational secure function evaluation (Rational SFE) where the players just send a set of envelopes to a referee who simply performs a sequence of publicly verifiable actions. That is, the players can “subcontract” all of the computation to an untrusted referee. In addition to providing a communication structure that more closely matches the ideal game, our protocol also enables us to better simulate mediated games in which abort is not a dominated action.