Cloud-Assisted Private Set Intersection via Multi-Key Fully Homomorphic Encryption

With the development of cloud computing and big data, secure multi-party computation, which can collaborate with multiple parties to deal with a large number of transactions, plays an important role in protecting privacy. Private set intersection (PSI), a form of multi-party secure computation, is a formidable cryptographic technique that allows the sender and the receiver to calculate their intersection and not reveal any more information. As the data volume increases and more application scenarios emerge, PSI with multiple participants is increasingly needed. Homomorphic encryption is an encryption algorithm designed to perform a mathematical-style operation on encrypted data, where the decryption result of the operation is the same as the result calculated using unencrypted data. In this paper, we present a cloud-assisted multi-key PSI (CMPSI) system that uses fully homomorphic encryption over the torus (TFHE) encryption scheme to encrypt the data of the participants and that uses a cloud server to assist the computation. Specifically, we design some TFHE-based secure computation protocols and build a single cloud server-based private set intersection system that can support multiple users. Moreover, security analysis and performance evaluation show that our system is feasible. The scheme has a smaller communication overhead compared to existing schemes.