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In multi-party threshold private set intersection (PSI), n parties each with a private set wish to compute the intersection of their sets if the intersection is sufficiently large. Previously, Ghosh and Simkin (CRYPTO 2019) studied this problem for the two-party case and demonstrated interesting lower and upper bounds on the communication complexity. In this work, we investigate the communication complexity of the multi-party setting . We consider two functionalities for multi-party threshold PSI. In the first, parties learn the intersection if each of their sets and the intersection differ by at most T. In the second functionality, parties learn the intersection if the union of all their sets and the intersection differ by at most T.

For both functionalities, we show that any protocol must have communication complexity . We build protocols with a matching upper bound of O(nT) communication complexity for both functionalities assuming …