An Efficient Private Set Intersection Protocol for the Cloud Computing Environments

Private set intersection (PSI) is a hot topic in cryptography and has a wide range of applications such as privacy preserving personal properties matching and data mining. Many PSI protocols have been presented, which discussed the efficiency and formal security. However, there are few PSI protocols for the cloud computing environments, where the cloud server offers effective computations and storage capabilities to clients and performs the PSI computations for clients. In this paper, we propose an efficient PSI protocol for the cloud computing environments, which is based on homomorphic encryption, pseudorandom function, set polynomial representation, and point-value form of polynomials. Our PSI protocol enjoys the following advantages: (a) our protocol gives a natural secure data storage; (b) normal channels are suitable to our protocol; (c) the communication and computation complexity are linear to the dataset size; (d) our protocol provides a formal detailed simulated-based security proof; (e) our protocol is a scalable protocol that could be extended to multiple clients conveniently, and a formal simulated-based security proof is provided in details.