Efficient Differentially Private Set Intersection

Xinyu Peng, Yufei Wang, Weiran Liu, Liqiang Peng, Feng Han, Zhen Gu, Jianling Sun, Yuan Hong

Abstract: Private Set Intersection (PSI) enables a sender and a receiver to jointly compute the intersection of their sets without disclosing other information about items not in the intersection. However, in many cases of joint data analysis, it is not just the items outside the intersection that are sensitive but the items within it. To protect such sensitive information, prior work presents a Differentially Private version of PSI (DPSI) based on a circuit-PSI using Fully Homomorphic Encryption. However, their concrete protocol is somewhat inefficient compared with the state-of-the-art (SOTA) circuit-PSI. In this paper, we revisit the DPSI definition and formalize its ideal functionality. We identify the key desiderata required by PSI-related tools to construct DPSI and propose two frameworks to construct efficient DPSI protocols. The first one generalizes the idea of existing DPSI, showing that any circuit-PSI can be used to construct DPSI. We obtain a more efficient DPSI protocol by plugging the SOTA circuit-PSI protocol in the framework. The second one helps to obtain a more efficient DPSI protocol based on the multi-query Reverse Private Membership Test (mqRPMT) that was previously used to construct Private Set Operation (PSO). However, mqRPMT additionally leaks the intersection size to the sender. We bound such leakage using differential privacy by padding random dummy items in input sets. We implement numerous constructions based on our frameworks. Experiments show that our protocols significantly outperform the existing DPSI construction, 2.5-22.6$\times$ more communication efficient and up to 110.5-151.8$\times$ faster. Our work also shows a new use case for mqRPMT besides obtaining PSO.