Paper 2026/2409 Original: eprint.iacr.org/2026/2409 ↗

Mercury: Fuzzy Private Set Intersection with Communication and Computation Logarithmic in the Threshold

Abstract

Private Set Intersection (PSI) allows two mutually distrusting parties to compute the intersection of their sets without revealing any additional information and has found numerous applications. The approximate matching required by various applications has led to the development of Fuzzy PSI (FPSI), a variant of PSI that identifies approximate intersection elements under a public distance threshold \(\delta\). Reducing computation and communication costs remains an important challenge for FPSI. In this paper, we present a new FPSI protocol, called Mercury, which achieves logarithmic computation and communication complexity with respect to threshold \(\delta\). Our protocol exploits the correlation of the intersection and the point pairs held by the parties, and efficiently identifies the neighboring point pairs by a mixed protocol from homomorphic encryption and secure two-party computation using a "mask-then-compare" technique. We implemented Mercury and evaluated both its sender-private and standard FPSI variants. For balanced two-dimensional inputs, Mercury-SP achieves \(9.0\sim63.9\times\) runtime speedups and reduces communication by a factor of \(8.7\sim26.1\) across the evaluated thresholds and set sizes in the LAN setting, compared to the FPSI protocol by Dang et al. (CCS'25). In the completed unbalanced experiments, Mercury-SP achieves \(55.7\sim132.4\times\) WAN runtime speedups compared to the FPSI protocol by Piske et al. (CCS'25).