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 Mat. Vopr. Kriptogr.: Year: Volume: Issue: Page: Find

 Mat. Vopr. Kriptogr., 2019, Volume 10, Issue 2, Pages 75–88 (Mi mvk285)

V. V. Vysotskaya

JSC “InfoTeCS”, Moscow, Russia

Abstract: 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).

Key words: modular addition, partitions, differential cryptanalysis.

DOI: https://doi.org/10.4213/mvk285

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UDC: 519.719.2
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Citation: V. V. Vysotskaya, “Some properties of modular addition”, Mat. Vopr. Kriptogr., 10:2 (2019), 75–88

Citation in format AMSBIB
\Bibitem{Vys19} \by V.~V.~Vysotskaya \paper Some properties of modular addition \jour Mat. Vopr. Kriptogr. \yr 2019 \vol 10 \issue 2 \pages 75--88 \mathnet{http://mi.mathnet.ru/mvk285} \crossref{https://doi.org/10.4213/mvk285}