Multiparty Cardinality Testing for Threshold Private Intersection

Threshold Private Set Intersection (PSI) allows multiple parties to compute the intersection of their input sets if and only if the intersection is larger than ????−????, where n is the size of each set and t is some threshold. The main appeal of this primitive is that, in contrast to standard PSI, known upper-bounds on the communication complexity only depend on the threshold t and not on the sizes of the input sets. Current threshold PSI protocols split themselves into two components: A Cardinality Testing phase, where parties decide if the intersection is larger than some threshold; and a PSI phase, where the intersection is computed. The main source of inefficiency of threshold PSI is the former part. In this work, we present a new Cardinality Testing protocol that allows N parties to check if the intersection of their input sets is larger than ????−????. The protocol incurs in ????̃(????????2) communication complexity. We thus obtain a Threshold PSI scheme for N parties with communication complexity ????̃(????????2).