Privacy-preserving distributed set intersection and union have been widely applied in many scenarios and lots of work has paid attention to the problem. Existing solutions to privacy-preserving set intersection and union are built on secure multiparty computation protocols, which can theoretically solve it, but result in heavy computation and communication overhead. Worse still, most of the existing schemes cannot work once some participant fails. In this paper, we propose two differentially private approaches for distributed set intersection and union, respectively. In our schemes, each data contributor possesses a secret data set and perturbs it by randomized response technique to satisfy local differential privacy. Then the collector gathers all contributors' perturbed data sets and utilizes maximum likelihood estimation to gain an accurate estimation of intersection and union. Compared to existing schemes, the proposed schemes can dramatically reduce computation and communication overhead, and tolerate participant's failure. We formally prove that the proposed schemes satisfy local differential privacy, and leverage extensive experiments to evaluate the proposed approaches. The results indicate that our schemes have low computation and communication complexity, strong robustness and good utility.
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