Reliable Homomorphic Matching for Fuzzy Labeled PSI at Scale

Computer Science > Cryptography and Security [Submitted on 26 Jun 2026] Reliable Homomorphic Matching for Fuzzy Labeled PSI at Scale Erkam Uzun Fuzzy Labeled Private Set Intersection (FLPSI) lets a receiver learn the labels of enrolled records similar to its query, and nothing else. Constructions based on a set-threshold reduction reach practical performance: a query matches a record when the two agree on a threshold number of components, and the private matching is delegated to an inner set-threshold kernel. We study its homomorphic form, which combines leveled-BFV homomorphic encryption (HE), a garbled circuit, and secret sharing to decide the match under encryption and release the record's label. We identify a composition gap in this kernel: efficiency is bought with a per-trial false-accept probability, but one query runs a trial for every record, so the error compounds with the database size into the kernel's realization soundness error (RSE), the rate at which it accepts a query the plaintext matcher would reject. The RSE is a reliability property of the cryptographic matching layer, not the matcher's accuracy, and a sound kernel must contribute zero or negligible RSE of its own. We formalize this as a composable security property, give a closed-form bound on the receiver's advantage, and close the gap with CSTPSI, a kernel that runs independent token rounds and raises the per-trial bound to a matching power. We prove CSTPSI secure in the semi-honest model. The bound sets the round count: two token rounds suffice for million-scale databases and three for billion-scale at the 10^{-6} engineering threshold. Our evaluation confirms this: at a million records the baseline kernel's RSE reaches 100% while CSTPSI holds it at 0 in every measured configuration. For large labels at small to moderate scale CSTPSI is more than 20x faster than the baseline, with up to 93% less communication, converging to the baseline only at million-scale. Our implementation, with a one-command reproducibility harness, is publicly available. Subjects: Cryptography and Security (cs.CR) Cite as: arXiv:2606.27803 [cs.CR]   (or arXiv:2606.27803v1 [cs.CR] for this version)   https://doi.org/10.48550/arXiv.2606.27803 Focus to learn more Submission history From: Erkam Uzun [view email] [v1] Fri, 26 Jun 2026 07:40:03 UTC (276 KB) Access Paper: HTML (experimental) view license Current browse context: cs.CR < prev   |   next > new | recent | 2026-06 Change to browse by: cs References & Citations NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)