Abstract
Aim The additive differential cryptanalysis is a significant technique used in the analysis of ARX ciphers. In this paper, we will focus on accurately and efficiently calculating the additive differential probability of $$ x \lll d \oplus y \lll e $$ . Methods Inspired by the work of Niu et al . at Crypto 2022, we use a delicate partition of $$ \mathbf{F}_2^m \times \mathbf{F}_2^m $$ into subsets. Result We derive an algorithm that can calculate it with linear time complexity. Compared with our algorithm, the one proposed by Velichkov et al . is only suitable when $$ e=0 $$ . Conclusion For the ARX construction: $$ (x \boxplus y) \lll d \oplus y \lll e $$ , which appears in Alzette, Speck, etc. , our algorithm can find more accurate additive differential characteristics for such ARX constructions. It is essential to evaluate the resistance of such ARX primitives against Additive differential cryptanalysis.
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