Privacy-preserving techniques for processing sets of information have attracted the research community’s attention in recent years due to society’s increasing dependency on the availability of data at any time. One of the fundamental problems in set operations is known asPrivate Set Intersection(PSI). The problem requires two parties to compute the intersection between their sets while preserving correctness and privacy. Although several efficient two-party PSI protocols already exist, protocols for PSI in the multi-party setting (MPSI) currently scale poorly with a growing number of parties, even though this applies to many real-life scenarios. This paper fills this gap by proposing two multi-party protocols based on Bloom filters and threshold homomorphic PKEs, which are secure in the semi-honest model. The first protocol is a multi-party PSI, whereas the second provides a more subtle functionality -thresholdmulti-party PSI (T-MPSI) - which outputs items of the server that appear in at least some number of other private sets. The protocols are inspired by the Davidson-Cid protocol based on Bloom filters. We compare our MPSI protocol against Kolesnikovet al., which is among the fastest known MPSI protocols. Our MPSI protocol performs better than Kolesnikovet al.in terms of run time, given that the sets are small and there is a large number of parties. Our T-MPSI protocol performs better than other existing works: the computational and communication complexities are linear in the number of elements in the largest set given a fixed number of colluding parties. We conclude that our MPSI and T-MPSI protocols are practical solutions suitable for emerging use-case scenarios with many parties, where previous solutions did not scale well.

Multi-Party Private Set Intersection (MPSI) is an attractive topic in research since a practical MPSI protocol can be deployed in several real-world scenarios, including but not limited to finding the common list of customers among several companies or privacy-preserving analyses of data from different stakeholders. Several solutions have been proposed in the literature however, the existing solutions still suffer from performance related challenges such as long run-time and high bandwidth demand, particularly when the number of involved parties grows. In this paper, we propose a new approach based on threshold additively homomorphic encryption scheme, e.g., Paillier, which enables us to process the bit-set representation of sets under encryption. By doing so, it is feasible to securely compute the intersection of several data sets in an efficient manner. To prove our claims on performance, we compare the communication complexity of our approach with the existing solutions and show performance test results. We also show how the proposed protocol can be extended to securely compute other set operations on multi-party data sets.

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