Fast and private computation of cardinality of set intersection and union

In many everyday scenarios, sensitive information must be shared between parties without complete mutual trust. Private set operations are particularly useful to enable sharing information with privacy, as they allow two or more parties to jointly compute operations on their sets (e.g., intersection, union, etc.), such that only the minimum required amount of information is disclosed. In the last few years, the research community has proposed a number of secure and efficient techniques for Private Set Intersection (PSI), however, somewhat less explored is the problem of computing the magnitude, rather than the contents, of the intersection we denote this problem as Private Set Intersection Cardinality (PSI-CA). This paper explores a few PSI-CA variations and constructs several protocols that are more efficient than the state-of-the-art.