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Mat. Vopr. Kriptogr., 2016, Volume 7, Issue 4, Pages 95–116 (Mi mvk206)  

This article is cited in 2 scientific papers (total in 2 papers)

Weight deficits of involutions and substitutions

V. N. Sachkov, I. A. Kruglov

Academy of Cryptography of the Russian Federation, Moscow

Abstract: Let $E_{2^m}$ be an ordered additive group of the finite field with $2^m$ elements. For the substitution $S: E_{2^m}\to E_{2^m}$ we introduce and investigate the index of the weight deficit of involution corresponding to the substitution $S$. By means of this index the security of $S$-boxes against the differential method of cryptoanalysis may be estimated. Some enumeration algorithms for involutions with given values of weight deficits are described.

Key words: subctitutions, involutions, weight deficit, enumeration problems.

DOI: https://doi.org/10.4213/mvk206

Full text: PDF file (194 kB)
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Bibliographic databases:

Document Type: Article
UDC: 519.719.2+519.712
Received 30.V.2016

Citation: V. N. Sachkov, I. A. Kruglov, “Weight deficits of involutions and substitutions”, Mat. Vopr. Kriptogr., 7:4 (2016), 95–116

Citation in format AMSBIB
\Bibitem{SacKru16}
\by V.~N.~Sachkov, I.~A.~Kruglov
\paper Weight deficits of involutions and substitutions
\jour Mat. Vopr. Kriptogr.
\yr 2016
\vol 7
\issue 4
\pages 95--116
\mathnet{http://mi.mathnet.ru/mvk206}
\crossref{https://doi.org/10.4213/mvk206}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3621525}
\elib{http://elibrary.ru/item.asp?id=28931408}


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  • https://doi.org/10.4213/mvk206
  • http://mi.mathnet.ru/eng/mvk/v7/i4/p95

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. V. N. Sachkov, “Involyutsii s dannym vesovym defitsitom, sootvetstvuyuschie tablitse Keli konechnoi abelevoi gruppy”, Matem. vopr. kriptogr., 8:4 (2017), 117–134  mathnet  crossref  mathscinet  elib
    2. V. N. Sachkov, I. A. Kruglov, “Momenty vesovogo defitsita sluchainoi ravnoveroyatnoi involyutsii, deistvuyuschei na vektornom prostranstve nad polem iz dvukh elementov”, Matem. vopr. kriptogr., 9:4 (2018), 101–124  mathnet  crossref
  • Математические вопросы криптографии
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