Efficient structure-aware private set intersection with distributed interval function

Abstract

Structure-aware PSI protocol (Sa-PSI) allows both parties to identify pairs of points within a predefined distance threshold across their respective datasets. However, in previous work, the cost of computation scales linearly with the number of prefixes in the structure, which may become excessively large, and additionally, this protocol risks disclosing sensitive elements. In this work, we present a lightweight and efficient Sa-PSI protocol (LESa-PSI), which aims at achieving the computational cost independent of the number of prefixes in the structure while simultaneously minimizing information leakage. We formally define an FSS based on the two-sided intervals function — compact DIF. This compact DIF is instantiated for a single-dimensional two-sided interval function and then extended to $d$-dimensional, which may be of independent interest. By combining compact DIF with a novel variant of DPF, we achieve key size compression for the set. Meanwhile, a structural decomposition strategy is proposed to divide the structure set, thereby enabling efficient function evaluation and computing the intersection. We prove that the LESa-PSI is secure in the semi-honest model. Furthermore, a comprehensive analysis of compact DIF and LESa-PSI is conducted through theory and experiments, with a comparison against some state-of-the-art works. The experimental results show that our compact DIF has a smaller key size, while the LESa-PSI has better performance in the intersection search and Bob’s elements evaluation.