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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
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.
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
Linking options:
https://www.mathnet.ru/eng/pdma493 https://www.mathnet.ru/eng/pdma/y2020/i13/p41
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Abstract page: | 157 | Full-text PDF : | 71 | References: | 14 |
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