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

Some properties of modular addition

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
Received 06.II.2018
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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}


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