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DiLizium 2.0: Revisiting Two-Party Crystals-Dilithium

In previous years there has been an increased interest in designing threshold signature schemes. Most of the recent works focus on constructing threshold versions of ECDSA or Schnorr signature schemes due to their appealing usage in blockchain technologies. Additionally, a lot of research is being done on cryptographic schemes that are resistant against quantum computer attacks. Presently, the most popular family of post-quantum algorithms is lattice-based cryptography, because its structure allows creation of cryptographic protocols that go beyond encryption and digital signature schemes. In this work, we propose a new version of the two-party Crystals-Dilithium signature scheme. The security of our scheme is based on the hardness of Module-LWE and Module-SIS problems. In our construction, we follow a similar logic as Damg̊ard et al. (PKC 2021) and use an additively homomorphic commitment scheme. However, compared to them, our protocol uses signature compression techniques from the original Crystals-Dilithium signature scheme which makes it closer to the version submitted to the NIST PQC competition.