In an example embodiment, a protocol for private set intersection is introduced that provides for two-party computation. Each party has a private data set and both parties want to securely compute the intersection of their sets, such that only the result is revealed and nothing else. Construction rules are provided that rely on the evaluation of a branching program (BP) using a fully homomorphic encryption (FHE) scheme. Using the properties of an FHE scheme, a non-interactive protocol is built with extendable functionalities. Thus, not only can the intersection be securely computed but the result can be used for further secure computations. Furthermore, the communication overhead for practical applications is independent of the server's set size, allowing for easy scalability.