Quantum private computation of cardinality of set intersection and union

Private Set Intersection Cardinality (PSI-CA) and Private Set Union Cardinality (PSU-CA) are cryptographic tasks whose goals are to compute the cardinalities of the intersection and the union of two private sets, respectively. There are lots of important and practical applications of PSI-CA and PSU-CA, such as privacy-preserving data mining and data analysis. The existing classical PSI-CA and PSU-CA protocols could not resist the attacks of quantum computers. In this article, we present a novel quantum approach to solve the PSI-CA and PSU-CA problems based on the principle of quantum mechanics, which can resist well-known quantum attacks. The proposed protocols take Bell states as quantum resources and only need to apply simple single-particle operators and Bell-based measurements. Therefore, it is feasible to implement these protocols with the present technology. Graphical abstract