Private Set Intersection via Public Key Encryption with Multiple Keywords Search

We introduce the technique of searchable encryption into the problem of secure two-party computation, and obtain a novel approach to accomplish Private Set Intersection (PSI), which uses the Public Key Encryption with Multiple Keywords Search (MPEKS) as the basic tool. We aim to achieve PSI in computationally asymmetric settings which can be instantiated by Cloud Computing. Our protocol satisfies the privacy with respect to semi-honest behaviors and the client only needs to compute m multiplications, m MapToPoint operations and one modular exponentiation to obtain the intersection, where m denotes the cardinality of the client´s set.