Thresholdizing Standardized FALCON Signatures

Threshold signatures allow a quorum of parties to jointly produce a signature while preventing any smaller subset from doing so. Following NIST's post-quantum standardization, designing threshold schemes compatible with the newly selected primitives is a pressing task. In particular, no prior threshold signature scheme produces signatures verifiable under the unmodified FALCON verification algorithm -the NIST-selected post-quantum scheme with the smallest signatures and keys. In this work, we present the first such threshold FALCON signing protocol, establishing its feasibility. Our technical contributions are threefold. First, we adapt the MPC-based discrete Gaussian sampling protocol of Wei et al. [WYF + 23] to support private centers and standard deviations, as required by FALCON's signing process. Second, we carry out a Rényi divergence analysis of the Klein sampler under fixed-point arithmetic, showing that 73 bits of precision suffice to achieve the same security as the FALCON specification. Third, we design an efficient MPC protocol for the Klein sampler that exploits the fixed trapdoor basis to construct a pseudorandom correlation generator for authenticated VOLE using only two-party DPFs, reducing per-signature communication significantly over standard authenticated triple generation. We implement and benchmark our protocol in two settings: N -party signing with all-but-one corruption, and 3-party signing with honest majority, demonstrating that threshold FALCON signing is feasible for applications where compatibility with the FALCON standard is required.