Secure Set Intersection in the Presence of a Rational Adversary

Abstract

Secure set intersection protocols confronting with covert adversary are efficient and guarantee correctness with a non-negligible probability, which is smaller than 1. However, they are not desirable when correctness is required to be achieved with probability 1, since correctness may be broken when the covert adversary successfully cheats. In order to get desirable result about correctness, we introduce a rational adversary instead of a covert adversary into the secure set-intersection protocol using smartcard tokens. The rational adversary has the same “deterrence factor” as a covert adversary but additionally has utilities defined as in the game theory. The main target of the rational adversary is to maximize his utilities by cheating in the protocol. Note that cheating does not bring him optimal utility, thus he has no incentives to cheat. We prove that given proper utilities, the strategy not to cheat induces Nash equilibrium for the rational adversary. Therefore, correctness can be guaranteed with probability 1. Furthermore, our protocol has the same round complexity as the secure setintersection protocol using smartcard tokens since the introduction of a rational adversary does not increase the round complexity.