Post-quantum secure multi-party private set-intersection in star network topology

In many realistic scenarios, participants wish to perform some secret set operations such as intersection, union, cardinality of intersection, etc. on their private data sets. Private Set Intersection (PSI) plays a major role in addressing such problems. PSI is one of the widely used secure multi-party computation technique that allows the participants to securely compute the intersection of their private input sets and nothing beyond that. It is generally executed between two parties. When the number of entities is more than two, it is known as multi-party PSI (MPSI). Today, the security of all the existing MPSI protocols are based on number theoretic assumptions. However, these will become insecure once large enough quantum computers are built. As a consequence, designing of quantum computer resistant MPSI becomes an interesting direction of research work. This paper addresses the issue by presenting the first post-quantum MPSI protocol in the so-called star network topology, using lattice-based public key encryption scheme. We utilize space-efficient probabilistic data structure (Bloom filter) as building blocks of our design. It attains security in standard model (without random oracles) under the decisional learning with errors (DLWE) assumption.