Fast and Private Computation of Cardinality of Set Intersection and Union

With massive amounts of electronic information stored, transferred, and shared every day, legitimate needs for sensitive information must be reconciled with natural privacy concerns. This motivates various cryptographic techniques for privacy-preserving information sharing, such as Private Set Intersection (PSI) and Private Set Union (PSU). Such techniques involve two parties – client and server – each with a private input set. At the end, client learns the intersection (or union) of the two respective sets, while server learns nothing. However, if desired functionality is private computation of cardinality rather than contents, of set intersection, PSI and PSU protocols are not appropriate, as they yield too much information. In this paper, we design an efficient cryptographic protocol for Private Set Intersection Cardinality (PSI-CA) that yields only the size of set intersection, with security in the presence of both semi-honest and malicious adversaries. To the best of our knowledge, it is the first protocol that achieves complexities linear in the size of input sets. We then show how the same protocol can be used to privately compute set union cardinality. We also design an extension that supports authorization of client input.