Geodesic
Cryptographic properties of a simple S-box construction based on a Boolean function and a permutation
Prikladnaya Diskretnaya Matematika. Supplement, no. 13 (2020), pp. 41-43.

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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. 
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     author = {D. A. Zyubina and N. N. Tokareva},
     title = {Cryptographic properties of a simple {S-box} construction based on a {Boolean} function and a permutation},
     journal = {Prikladnaya Diskretnaya Matematika. Supplement},
     pages = {41--43},
     publisher = {mathdoc},
     number = {13},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PDMA_2020_13_a12/}
}
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D. A. Zyubina; N. N. Tokareva. Cryptographic properties of a simple S-box construction based on a Boolean function and a permutation. Prikladnaya Diskretnaya Matematika. Supplement, no. 13 (2020), pp. 41-43. http://geodesic.mathdoc.fr/item/PDMA_2020_13_a12/

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