Privacy-Preserving Set Operations in the Presence of Rational Parties

Privacy-preserving set operations are useful for many data mining algorithms as building tools. Protocols for privacy-preserving set operations have considered semi-honest and malicious adversarial models in cryptographic settings, whereby an adversary is assumed to follow or arbitrarily deviate from the protocol. Semi-honest model provides weak security requiring small amount of computation, on the other hand, malicious model provides strong security requiring expensive computations like homomorphic encryption. However, efficient computation of such set operations are desirable for practical implementations. In this paper, we build efficient and private set operations avoiding the use of expensive tools like homomorphic encryption, zero knowledge proof, and oblivious transfer. Our protocol is constructed in game-theoretic model. In other words, instead of being semi-honest or malicious, the parties are viewed as rational and are assumed (only) to act in their self-interest. We show that our protocol satisfies computational Nash equilibrium.