Solving Set Relations with Secure Bloom Filters Keeping Cardinality Private

We propose in this work to solve privacy preserving set relations performed by a third party in an outsourced configuration. We argue that solving the disjointness relation based on Bloom filters is a new contribution in particular by having another layer of privacy on the sets cardinality. We propose to compose the set relations in a slightly different way by applying a keyed hash function. Besides discussing the correctness of the set relations, we analyze how this impacts the privacy of the sets content as well as providing privacy on the sets cardinality. We are in particular interested in how having bits overlapping in the Bloom filters impacts the privacy level of our approach. Finally, we present our results with real-world parameters in two concrete scenarios