Attack Analysis on Two-party Signature and Threshold Signature Based on Dilithium
Xiang Wu, Bohao Li, Boyang Zhang, Xiaofan Liu, Wei Zhong Ren, Kim‐Kwang Raymond Choo · 2023
With the rapid development of post-quantum cryptography study, the Crystals-Dilithium digital signature algorithm based on the lattice has received much attention, and many extended studies have appeared on its basis. In this paper, we focus on the two-party signature protocol and$(t,\ n)$-threshold signature protocol based on Dilithium, and analyze their feasibility and security. After repeated experiments with the official rejection sampling code of the Aigis-sig scheme, it is shown that the two-party signature protocol basically cannot pass rejection sampling verification properly and is not feasible. At the same time, both protocols have a security risk that private key is divulged and internal members forge signatures. Through security analysis and experimental results, we found that there is close to 100% possibility that the internal members can crack the y value and private key information to complete the signature forgery. It will make the security of signatures unable to be guaranteed.