Abstract Security and efficiency have always been two critical factors in the development of post-quantum digital signatures. As the best-known scheme, (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 stage to reduce the rejections of the fourth condition, consequently resulting in some speedup in 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 , 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 $$47\%$$ 47 % ,
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