Collusion-Free Rational Secure Sum Protocol

The secure sum protocol is a useful basic protocol of Secure multiparty computation (SMC). And it has numerous applications. However traditional secure sum protocol can not guarantee the fairness. In addition, most previous protocols can not resist the collusion-attack. This paper proposes a collusion-free rational secure sum protocol in which we combine game theory with the multiparty secure sum protocol. In the setting of rational secure sum protocol, the gain of following the protocol is more than the gain of deviating, and no player of the coalition parties can do better, even if the whole coalition parties cheat. Analysis shows that the protocol can resist the collusion attack with at most $n-2$ players, and rational players have to abide by the protocols. Unlike previous secure sum algorithms, this paper aims at obtaining complete fairness even though without a majority of honest parties.