Private Set Intersection with Linear Communication from General Assumptions
Brett Hemenway, Daniel E. Noble, Rafail Ostrovsky · 2019
This work presents a hashing-based algorithm for Private Set Intersection (PSI) in the honest-but-curious setting. The protocol is generic, modular and provides both asymptotic and concrete efficiency improvements over existing PSI protocols. If each player has m elements, our scheme requires only $O(m \secpar)$ communication between the parties, where $\secpar$ is a security parameter. Our protocol builds on the hashing-based PSI protocol of Pinkas et al. (USENIX 2014, USENIX 2015), but we replace one of the sub-protocols (handling the cuckoo "stash'') with a special-purpose PSI protocol that is optimized for comparing sets of unbalanced size. This brings the asymptotic communication complexity of the overall protocol down from $ømega(m \secpar)$ to $O(m\secpar)$, and provides concrete performance improvements (10-15% reduction in communication costs) over Kolesnikov et al. (CCS 2016) under real-world parameter choices. Our protocol is simple, generic and benefits from the permutation-hashing optimizations of Pinkas et al. (USENIX 2015) and the Batched, Relaxed Oblivious Pseudo Random Functions of Kolesnikov et al. (CCS 2016).