Speedup signing: pre-rejection sampling towards dilithium

Security and efficiency have always been two critical factors in the development of post-quantum digital signatures. As the best-known scheme, Dilithium (Ducas et al., TCHES 2018) is SUF-CMA in QROM and has a relatively fast efficiency with many untrivial optimizations. The goal of this paper is to propose some techniques that can promote signing speed without sacrificing security. We first propose the pre-rejection sampling technique in KeyGen stage to reduce the rejections of the fourth condition, consequently resulting in some speedup in Sign stage. To prove security, we propose the c -selected MLWE problem, a variant of MLWE that can offer the equivalent security as original MLWE. Applying these two techniques to Dilithium , we obtain an advanced signature scheme with better efficiency, and without any other losses except some pre-computations. Security reduction demonstrates that our scheme is also SUF-CMA in QROM. The experimental results show that pre-rejection sampling achieves a 47 % , 22 % , and 17 % reduction in the rejection probability of the fourth condition over Dilithium scheme when the parameter set corresponds to NIST’s security levels 2, 3 and 5, respectively. This type of reduction increases signing speed by approximately 1 % under the parameter set 2 of Dilithium .