Aitps: A Two-Party Signature Scheme from Asymmetry Module Lattice Problems

Recent years, with the advancement of the IoT and blockchain, multi-party signature protocols have received renewed attention. Multi-party signature is a special digital signature that requires users to interact with each other to jointly generate a signature for a message and achieve the authentication. Compared with each user signing respectively, the advantage is that the key size can be greatly decreased, and every party cannot get a legal signature only by itself, which can be used to prevent the danger of being impersonated when user’s key is lost or hijacked. On the other hand, the progress of quantum computers poses a potential threat to the traditional public key cryptography scheme, the PQC(post-quantum cryptography) project was organized by the NIST(National Institute of Standards and Technology) in the US since 2016, and it determined the algorithm that was standardized in July 2022. At the same time, the multi-party signature based on its candidate digital signature schemes (such as CRYSTALS-Dilithium) also appeared. Chinese Association for Cryptologic Research(CACR) also held a national cryptographic algorithm design competition in 2019, Aigis-sig, which is the first prize signature algorithm, adopts the similar structure with Dilithium. In this paper, Aitps is proposed, which is a two-party signature based on Aigis-sig. Compared with the existing Dilithium-based two-party signatures, Aitps has better key sizes and signature sizes. For example, the signature sizes can be reduced by more than 20% at the same security level. Lastly, Aitps can also be extended to multi-party signature.