PSI from Ring-OLE

Private set intersection (PSI) is one of the most extensively studied instances of secure computation. PSI allows two parties to compute the intersection of their input sets without revealing anything else. Other useful variants include PSI-Payload, where the output includes payloads associated with members of the intersection, and PSI-Sum, where the output includes the sum of the payloads instead of individual ones. In this work, we make two related contributions. First, we construct simple and efficient protocols for PSI and PSI-Payload from a ring version of oblivious linear function evaluation (ring-OLE) that can be efficiently realized using recent ring-LPN based protocols. A standard OLE over a field F allows a sender with a,b F to deliver ax + b to a receiver who holds x F. Ring-OLE generalizes this to a ring F, in particular, a polynomial ring over F. Our second contribution is an efficient general reduction of a variant of PSI-Sum to PSI-Payload and secure inner product. Our protocols have better communication cost than state-of-the-art PSI protocols, especially when requiring security against malicious parties and when allowing input-independent preprocessing. Compared to previous maliciously secure PSI protocols that have a similar computational cost, our online communication is 2x better for small sets (28-212 elements) and 20% better for large sets (220-224). Our protocol is also simpler to describe and implement. We obtain even bigger improvements over the state of the art (4-5x better running time) for our variant of PSI-Sum.