Two-Round Threshold Lattice-Based Signatures from Threshold Homomorphic Encryption

Much recent work has developed efficient protocols for threshold signatures, where n parties share a signing key and some threshold t of those parties must interact to produce a signature. Yet efficient threshold signatures with post-quantum security have been elusive, with the state-of-the-art being a two-round scheme by Damgård et al. (PKC’21) based on lattices that supports only the full threshold case (i.e., \(t=n\) ). We show here a two-round threshold signature scheme based on standard lattice assumptions that supports arbitrary thresholds \(t\le n\) . Estimates of our scheme’s performance at the 128-bit security level show that in the 3-out-of-5 case, we obtain signatures of size 46.6 KB and public keys of size 13.6 KB. We achieve \(\approx 5\times \) improved parameters if only a small number of signatures are ever issued with the same key. As an essential building block and independent contribution, we construct an actively secure threshold (linearly) homomorphic encryption scheme that supports arbitrary thresholds \(t \le n\) .