Geodesic
Probabilistic properties of modular addition
Matematičeskie voprosy kriptografii, Tome 12 (2021) no. 1, pp. 109-130 Cet article a éte moissonné depuis la source Math-Net.Ru

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We study the applicability of differential cryptanalysis to the operation of addition modulo $2^n$ used in different cryptosystems. We obtain an analytical formula for expected value of entropy $H_n$ of rows of the difference distribution table of the corresponding mapping. Moreover, the moments of $2^{H_n}$ are studied. In particular, asymptotic inequalities describing the behavior of values $\mathbb{E}2^{qH_n}$ (for $q \in \mathbb{N}$) and $\mathbb{D}2^{H_n}$ as $n \to \infty$ are obtained. We also find a simple analytical formula for the number of table rows with the same distribution. It permits to compute efficiently the statistical characteristics of the entropy. 
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V. V. Vysotskaya. Probabilistic properties of modular addition. Matematičeskie voprosy kriptografii, Tome 12 (2021) no. 1, pp. 109-130. http://geodesic.mathdoc.fr/item/MVK_2021_12_1_a5/

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