In this paper we systematically study the differential properties of addition modulo 2n. We derive Θ(log n)-time algorithms for most of the properties, including differential probability of addition.We also present log-time algorithms for finding good differentials. Despite the apparent simplicity of modular addition, the best known algorithms require naive exhaustive computation. Our results represent a significant improvement over them. In the most extreme case, we present a complexity reduction from Ω(24n) to Θ(log n).
CITATION STYLE
Lipmaa, H., & Moriai, S. (2002). Efficient algorithms for computing differential properties of addition. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 2355, pp. 336–350). Springer Verlag. https://doi.org/10.1007/3-540-45473-X_28
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