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Mat. Vopr. Kriptogr., 2015, Volume 6, Issue 1, Pages 159–179 (Mi mvk156)  

This article is cited in 9 scientific papers (total in 9 papers)

Combinatorial properties of differentially $2$-uniform substitutions

V. N. Sachkov

Academy of Cryptography of the Russian Federation, Moscow

Abstract: A combinatorial approach to the investigation and methods of construction of differentially $2$-uniform substitutions of the vector space over the finite field $F_2$ is proposed. Necessary and sufficient conditions for the family of sets associated with a differentially $2$-uniform substitution to be a symmetric block design are given. It is shown that a substitution is differentially $2$-uniform if and only if it is a solution of a similarity equations system connecting a family of translations with a family of unequal weights involutions. We suggest methods of construction of differentially $2$-uniform substitutions by means of the Cayley table of an additive group of finite field $F_{2^m}$.

Key words: differentially $2$-uniform substitutions, family of sets associated with a substitution, $(\alpha,\beta)$-configurations, unequal weights involutions.

DOI: https://doi.org/10.4213/mvk156

Full text: PDF file (555 kB)
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Bibliographic databases:

UDC: 519.719.2+519.12
Received 23.IX.2014

Citation: V. N. Sachkov, “Combinatorial properties of differentially $2$-uniform substitutions”, Mat. Vopr. Kriptogr., 6:1 (2015), 159–179

Citation in format AMSBIB
\Bibitem{Sac15}
\by V.~N.~Sachkov
\paper Combinatorial properties of differentially $2$-uniform substitutions
\jour Mat. Vopr. Kriptogr.
\yr 2015
\vol 6
\issue 1
\pages 159--179
\mathnet{http://mi.mathnet.ru/mvk156}
\crossref{https://doi.org/10.4213/mvk156}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3528064}
\elib{http://elibrary.ru/item.asp?id=23211529}


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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. A. A. Gorodilova, “O differentsialnoi ekvivalentnosti kvadratichnykh APN-funktsii”, PDM. Prilozhenie, 2016, no. 9, 21–24  mathnet  crossref
    2. A. A. Gorodilova, “Ot kriptoanaliza shifra k kriptograficheskomu svoistvu bulevoi funktsii”, PDM, 2016, no. 3(33), 16–44  mathnet  crossref
    3. A. A. Gorodilova, “Lineinyi spektr kvadratichnykh APN-funktsii”, PDM, 2016, no. 4(34), 5–16  mathnet  crossref
    4. M. M. Glukhov, “O priblizhenii diskretnykh funktsii lineinymi funktsiyami”, Matem. vopr. kriptogr., 7:4 (2016), 29–50  mathnet  crossref  mathscinet  elib
    5. V. N. Sachkov, I. A. Kruglov, “Vesovye defitsity involyutsii i podstanovok”, Matem. vopr. kriptogr., 7:4 (2016), 95–116  mathnet  crossref  mathscinet  elib
    6. A. V. Menyachikhin, “Spectral-linear and spectral-differential methods for generating S-boxes having almost optimal cryptographic parameters”, Matem. vopr. kriptogr., 8:2 (2017), 97–116  mathnet  crossref  mathscinet  elib
    7. 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
    8. A. V. Miloserdov, “Permutation binomial functions over finite fields”, J. Appl. Industr. Math., 12:4 (2018), 694–705  mathnet  crossref  crossref  elib
    9. 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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