(2026-06) Reliable Homomorphic Matching for Fuzzy Labeled PSI at Scale
2026-06-26
Fuzzy Labeled Private Set Intersection (FLPSI) lets a receiver learn the labels of enrolled records that are similar to its query, and nothing else. FLPSI can be built in several ways. 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. These constructions delegate the private matching 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, an instance of a protocol-level problem: 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. On a spurious accept the kernel also returns a value the plaintext matcher would never produce. A sound kernel must contribute zero or negligible RSE of its own. We formalize this requirement 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 closed-form bound sets the round count: two token rounds suffice for million-scale databases and three for billion-scale at the engineering threshold. Our evaluation confirms the prediction. At a million records the baseline kernel's RSE reaches while CSTPSI holds it at in every measured configuration. CSTPSI decouples threshold-checking and upload costs from label size. For large labels at small to moderate scale it is more than faster than the baseline kernel, with up to less communication. It converges to the baseline only at the million-scale database size. Our implementation, with a one-command reproducibility harness, is publicly available.