Private Set Operations from Oblivious Switching

Private set intersection reveals the intersection of two private sets, but many real-world applications require the parties to learn only partial information about the intersection. In this paper we introduce a new approach for computing arbitrary functions of the intersection, provided that it is safe to also reveal the cardinality of the intersection. In the most general case, our new protocol provides the participants with secret shares of the intersection, which can be fed into any generic 2PC protocol. Certain computations on the intersection can also be done even more directly and efficiently, avoiding this secret-sharing step. These cases include computing only the cardinality of intersection, or the “cardinality-sum” application proposed in Ion et al. (ePrint 2017). Compared to the state-of-the-art protocol for computing on intersection (Pinkas et al., Eurocrypt 2019), our protocol has about \(2.5-3\times \) less communication, and has faster running time on slower (50 Mbps) networks.