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Fast Multi-party Private Set Operations in the Star Topology from Secure ANDs and ORs

Today, our society produces massive amounts of data, part of which are strictly private. So, a long line of research has worked to design protocols that perform functions on such private data without revealing them. One function that has attracted significant interest is a multi-party private set operation, where each party’s input is a set. The parties commonly intend to compute these sets’ collective intersection (MPSI) or union (MPSU), which finds uses in various applications, including private scheduling and threat intelligence. Most current protocols use integer-based homomorphic encryption, with large elements and expensive operations, or oblivious transfers, which require communicationally-expensive pairwise interactions between all parties. Thus, existing solutions introduce significant overhead that hinders practical use. This paper considers a certain class of previously-proposed MPSI and MPSU protocols. We propose to express them in terms of new private AND or OR operations among all parties and use elliptic curves to realize these operations efficiently. We achieve a significant performance gain: Firstly, our protocols take only three rounds of communication. Secondly, our constant-time open-source implementation is two orders of magnitude faster than the state-of-the-art MPSI for small universes and outperforms the state-of-the-art MPSI for large universes for three parties or more.