Geodesic
Some properties of modular addition
Matematičeskie voprosy kriptografii, Tome 10 (2019) no. 2, pp. 75-88 Cet article a éte moissonné depuis la source Math-Net.Ru

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We study a problem which emerged during an attempt to apply a differential cryptanalysis method to the “Magma” algorithm. We obtain a general formula of distribution in the difference distribution table of addition modulo $2^n$ and provide an efficient method for computing the distribution in a row with given index. By means of this formula an asymptotic estimate of the number of different distributions is established. Finally, we design an algorithm generating all distributions in $2^{O(\sqrt{n})}$ operations (whereas the corresponding brute-force method takes $2^{\Omega(n)}$ operations). 
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V. V. Vysotskaya. Some properties of modular addition. Matematičeskie voprosy kriptografii, Tome 10 (2019) no. 2, pp. 75-88. http://geodesic.mathdoc.fr/item/MVK_2019_10_2_a5/

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