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 Prikl. Diskr. Mat. Suppl., 2017, Issue 10, Pages 96–99 (Mi pdma327)

Mathematical Methods of Cryptography

On characteristics of local primitive matrices and digraphs

V. M. Fomichevabcd

a Financial University under the Government of the Russian Federation, Moscow
b National Engineering Physics Institute "MEPhI", Moscow
c Federal Research Center "Computer Science and Control" of Russian Academy of Sciences, Moscow
d "Security Code", Moscow

Abstract: For local primitive $n$-vertex digraphs and matrices of order $n$, the following new characteristics are introduced: a matex is defined as a matrix $(\gamma_{i,j})$ of order $n$, where $\gamma_{i,j}=(i,j)-\exp\Gamma$, $1\leq i,j\leq n$; $k,r$-exporadius $\operatorname{exrd}_{k,r}\Gamma$ is defined as $\min_{I\times J\colon|I|=k, |J|=r}\gamma_{I,J}$, where $\gamma_{I,J}=\max_{(i,j)\in I\times J}\gamma_{i,j}$; $k,r$-expocenter is defined as a set $I\times J$, where $|I|=k$, $|J|=r$, $\gamma_{I,J}=\operatorname{exrd}_{k,r}\Gamma$. An approach to build the perfect $s$-boxes of order $k\times r$ using introduced characteristics is proposed. This approach is based on iterations of $n$-dimensional Boolean vectors set transformations with $n>\max(k,r)$. An exemplification of the function construction for perfect $s$-boxes of order $k\times r$ is presented.

Keywords: local primitive matrix (digraph), local exponent.

 Funding Agency Grant Number Russian Foundation for Basic Research 16-01-00226

DOI: https://doi.org/10.17223/2226308X/10/39

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UDC: 519.1

Citation: V. M. Fomichev, “On characteristics of local primitive matrices and digraphs”, Prikl. Diskr. Mat. Suppl., 2017, no. 10, 96–99

Citation in format AMSBIB
\Bibitem{Fom17} \by V.~M.~Fomichev \paper On characteristics of local primitive matrices and digraphs \jour Prikl. Diskr. Mat. Suppl. \yr 2017 \issue 10 \pages 96--99 \mathnet{http://mi.mathnet.ru/pdma327} \crossref{https://doi.org/10.17223/2226308X/10/39} 

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Citing articles on Google Scholar: Russian citations, English citations
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This publication is cited in the following articles:
1. V. M. Fomichev, “Semigroup and metric characteristics of locally primitive matrices and graphs”, J. Appl. Industr. Math., 12:2 (2018), 243–254
2. L. A. Karpova, I. A. Pankratova, “Peremeshivayuschie svoistva nekotorykh klassov podstanovok na $\mathbb{F}_2^n$”, PDM. Prilozhenie, 2019, no. 12, 47–50
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