Unbalanced private set intersection cardinality protocol with low communication cost

Abstract Private set intersection cardinality (PSI-CA) allows two parties, the sender and receiver, to compute the cardinality of the intersection, without revealing anything more to the other party. This paper focuses on the unbalanced private data sets case, where two parties hold sets of private data items, such as the users’ identifiers; and where the size of the receiver’s private data set is significantly smaller than the size of the sender’s private data set. Two parties want to learn the cardinality of the intersection, but nothing else. The commutative encryption inspires authors to develop a novel protocol to solve the problem. Furthermore, by the application of the Bloom filter, the receiver can compute the output more easily than by the method that the encryption is carried out on the sender’s private data set when low-power mobile IoT devices are used. In the semi-honest model, we can prove the security of our protocol when the sender’s data set is big enough. The experiment shows the deviation of our protocol is negligible and the computation costs of our protocol.