TOPCOAT: Towards Practical Two-Party Crystals-Dilithium

Abstract

The development of threshold protocols based on lattice-signature schemes has been of increasing interest in the past several years. The main research focus was towards protocols constructed for various variants of Crystals-Dilithium, future NIST digital signature standard known as ML-DSA. In this work, we propose TOPCOAT, a two-party lattice-based signature algorithm that embodies Dilithium's compression techniques. The aforesaid result is achieved by introducing a new hinting mechanism that allows parties to collaboratively calculate $\textsf{HighBits}$. Our hinting mechanism allows public key compression similar to Dilithium. Additionally, we suggest an optimization technique to minimize number of restarts both parties need to produce a valid signature. We prove security of our scheme under MLWE and MSIS assumptions in ROM, and provide implementation of our proposed scheme. As additional contribution, we present vulnerabilities and inconsistencies found in Liu et al. work which aimed to construct distributed lattice-based signature protocol.