An Improvement of Multi-Party Private Set Intersection Based on Oblivious Programmable PRFs

Multi-party Private Set Intersection (PSI) allows parties to compute the set intersection of their private data sets without revealing outside the intersection. Kolesnikov et al. (ACM CCS 2017) introduced the Oblivious Programmable Pseudorandom Function (OPPRF) and showed a practical multi-party PSI protocol secure for arbitrary collusion of parties in the semi-honest model. We point out that some OPPRFs in their protocol are overkill to construct it. Based on this observation, we improve their PSI protocol by replacing these OPPRFs with more lightweight procedures. More precisely, we introduce a new functionality called Extended Programmable Pseudorandom Function (EPPRF). It provides functionality that excludes an expensive public-key operation from the OPPRF. We show that a multi-party PSI protocol can be realized even if the OPPRFs are replaced with EPPRFs. As a result of the replacement, we reduce n − 1 public-key operations from Kolesnikov et al.’s protocol, where n is the number of parties.