Efficient Unbalanced Private Set Intersection Cardinality and User-friendly Privacy-preserving Contact Tracing

An unbalanced private set intersection cardinality (PSI-CA) protocol is a protocol to securely get the intersection cardinality of two sets X and Y without disclosing anything else, in which |Y| < |X|. In this paper, we propose efficient unbalanced PSI-CA protocols based on fully homomorphic encryption (FHE). To handle the long item issue in PSI-CA protocols, we invent two techniques: virtual Bloom filter and polynomial links. The former can encode a long item into several independent shorter ones. The latter fragments each long item into shorter slices and builds links between them. Our FHE-based unbalanced PSI-CA protocols have the lowest communication complexity O(|Y|log(|X|), which is much cheaper than the existing balanced PSI-CA protocols with O(|Y|+|X|). When |X|=228 and |Y|=2048, our protocols are 172× ∼ 412× cheaper than the best balanced PSI-CA protocol. Our protocols can be easily modified into unbalanced PSI protocols. Compared with Cong et al. (CCS'21), one of our unbalanced PSI protocols can save 42.04% ∼ 58.85% communication costs and accelerate the receiver querying time. We apply our lightweight unbalanced PSI-CA protocols to design a privacy-preserving contact tracing system. We demonstrate that our system outperforms existing schemes in terms of security and performance.