Private set intersection (PSI) is a cryptographic protocol that enables two parties to securely determine the intersection of their private datasets without revealing anything except the intersection. Most of the existing PSI protocols are based on traditional number theoretic problems, such as discrete logarithm problem and factorisation problem. Unfortunately, these protocols would be broken if efficient quantum computer emerges. The post-quantum PSI is an important alternative to traditional PSI protocols for its potential to resist future attacks of quantum computers. In this work, we present first post-quantum PSI protocol that achieves size-hiding property. Space-efficient probabilistic data structure Bloom filter along with lattice-based public key encryption are used as building blocks of our construction. It attains linear complexity and security in standard model under the decisional learning with errors (DLWE) assumption. Moreover, we extend our post-quantum PSI to its authorised variant APSI retaining all the properties.

Nowadays, the necessity of electronic information increases rapidly. As a consequence, often, that information needs to be shared among mutually distrustful parties. In this area, private set intersection (PSI) and its variants play an important role when the participants wish to do secret operations on their input sets. Unlike the most modern public key cryptosystems relying on number theoretic problems, lattice‐based cryptographic constructions provide security in the presence of a quantum computer. Consequently, developing PSI and its variants using lattice based cryptosystem becomes an interesting direction for research. This study presents the first size‐hiding post quantum PSI cardinality (PSI‐CA) protocol whose complexity is linear in the size of the sets of the participants. The authors use space‐efficient probabilistic data structure (Bloom filter) as its building block. Further, they extend the authors’ PSI‐CA to its authorised version, i.e. authorised PSI‐CA. Security for both of them is achieved in the standard model based on the hardness of the decisional learning with errors problem.