Paper 2024/566

A $3$-Round Near-Linear Third-Party Private Set Intersection Protocol

Abstract

Third-party private set intersection (PSI) enables two parties, each holding a private set to compute their intersection and reveal the result only to an inputless third party. In this paper, we present an efficient third-party PSI protocol requiring only 3 communication rounds, while significantly lowering the computational workload compared to prior work. Our work is motivated by real-world applications such as contact tracing whereby expedition is essential while concurrently preserving privacy. Our construction attains a near-linear computational complexity of $O(n^{1+\varepsilon})$ for large dataset size $n$, where $\varepsilon>0$ is any fixed constant, and achieves post-quantum security. Our improvements stem from algorithmic changes and the incorporation of new techniques along with precise parameter selections to achieve a tight asymptotic bound. Furthermore, we also present a third-party PSI cardinality protocol which has not been explored in prior third-party PSI work. In a third-party PSI cardinality setting, only the third-party obtains the size of the intersection and nothing else. Our construction to achieve the cardinality functionality attains a quasilinear computational complexity for the third-party.