Paper 2026/2604

Balsamic: One-round Threshold UOV from GPU-Accelerated FHE

Abstract

Universal thresholdizers offer one-round threshold signatures, but require evaluating an entire signer under fully homomorphic encryption (FHE). We present Balsamic, a complete homomorphic Unbalanced Oil and Vinegar (UOV) signer and its application to one-round threshold UOV signature. UOV's short salted target hash shifts the encrypted workload to finite-field linear solving, which we integrate with coin derivation and hashing in a packed discrete-CKKS circuit. Our paired-pivot solver selects both pivots before first-pivot normalization, then applies their coupled update with one inversion stage per pair and cubic field work. Pivot-success certificates enable encrypted retry selection without residual evaluation. In 2-out-of-3 semihonest threshold UOV signing, each partial signing (online) takes $10.7$ seconds on NVIDIA RTX 6000 Ada and $7.77$ seconds on NVIDIA GB300, with $5.25$ MB per response. These measurements demonstrate that complete homomorphic signing can provide the computational core of one-round threshold signatures without intermediate openings or per-signature interactive preprocessing.