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 has been 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. Our approach allows to produce \(\approx 10\) KB signatures within 3 rounds of communication. 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 (Future Generation Computer Systems 2023) which aimed to construct distributed lattice-based signature protocol.