Post‐quantum protocol for computing set intersection cardinality with linear complexity

Abstract

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.