Compact and Malicious Private Set Intersection for Small Sets

Abstract

We describe a protocol for two-party private set intersection (PSI) based on Diffie-Hellman key agreement. The protocol is proven secure against malicious parties, in the ideal permutation + random oracle model. For small sets (500 items or fewer), our protocol requires the least time and communication of any known PSI protocol, even ones that are only semi-honest secure and ones that are not based on Diffie-Hellman. It is one of the few significant improvements to the 20-year old classical Diffie-Hellman PSI protocol of Huberman, Franklin, and Hogg (ACM Elec. Commerce 1999). Our protocol is actually a generic transformation that constructs PSI from a class of key agreement protocols. This transformation is inspired by a technique of Cho, Dachman-Soled, and Jarecki (CT-RSA 2016), which we streamline and optimize in several important ways to achieve our superior efficiency.