Prikladnaya Diskretnaya Matematika. Supplement
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Prikladnaya Diskretnaya Matematika. Supplement, 2020, Issue 13, Pages 41–43
DOI: https://doi.org/10.17223/2226308X/13/13
(Mi pdma493)
 

Discrete Functions

Cryptographic properties of a simple S-box construction based on a Boolean function and a permutation

D. A. Zyubinaabc, N. N. Tokarevaab

a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
b Novosibirsk State University
c JetBrains Research
References:
Abstract: We propose a simple method of constructing S-boxes using Boolean functions and permutations. Let $\pi$ be an arbitrary permutation on $n$ elements, $f$ be a Boolean function in $n$ variables. Define a vectorial Boolean function $F_{\pi}: \mathbb{F}_2^n \to \mathbb{F}_2^n$ as $F_{\pi}(x) = (f(x), f(\pi(x)), f(\pi^2(x)), \ldots, f(\pi^{n-1}(x)))$. We study cryptographic properties of $F_{\pi}$ such as high nonlinearity, balancedness, low differential $\delta$-uniformity in dependence on properties of $f$ and $\pi$ for small $n$.
Keywords: Boolean function, vectorial Boolean function, S-box, high nonlinearity, balancedness, low differential $\delta$-uniformity, high algebraic degree.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation 075-15-2019-1613
The work is supported by Mathematical Center in Akademgorodok under agreement No. 075-15-2019-1613 with the Ministry of Science and Higher Education of the Russian Federation and Laboratory of Cryptography JetBrains Research.
Document Type: Article
UDC: 519.7
Language: English
Citation: D. A. Zyubina, N. N. Tokareva, “Cryptographic properties of a simple S-box construction based on a Boolean function and a permutation”, Prikl. Diskr. Mat. Suppl., 2020, no. 13, 41–43
Citation in format AMSBIB
\Bibitem{ZyuTok20}
\by D.~A.~Zyubina, N.~N.~Tokareva
\paper Cryptographic properties of a simple S-box construction based on a Boolean function and a permutation
\jour Prikl. Diskr. Mat. Suppl.
\yr 2020
\issue 13
\pages 41--43
\mathnet{http://mi.mathnet.ru/pdma493}
\crossref{https://doi.org/10.17223/2226308X/13/13}
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