Geodesic
The differential uniformity of piecewise-linear substitutions over the field $\mathbb{F}_{2^{n}}$
Diskretnaya Matematika, Tome 35 (2023) no. 4, pp. 58-68

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In this paper, we give lower and upper bounds on the differential uniformity of substitutions over the field $\mathbb{F}_{2^{n}}$ with restrictions to cosets of $H$ in $\mathbb{F}^{\times}_{2^{n}}$, $H\mathbb{F}^{\times}_{2^{n}}$, $|H|=l$, $l\cdot r=2^{n}-1$, being the maps $x\mapsto c_{i}x$, $c_{i}\in\mathbb{F}^{\times}_{2^{n}}$, $i=0,\dots,r-1$.
Keywords: block cipher nonlinear confusion components, permutation of a finite field, $s$-box, piecewise-linear function, adapted spectral-differential method. 
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     author = {A. V. Menyachikhin},
     title = {The differential uniformity of piecewise-linear substitutions over the field $\mathbb{F}_{2^{n}}$},
     journal = {Diskretnaya Matematika},
     pages = {58--68},
     publisher = {mathdoc},
     volume = {35},
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     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2023_35_4_a3/}
}
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A. V. Menyachikhin. The differential uniformity of piecewise-linear substitutions over the field $\mathbb{F}_{2^{n}}$. Diskretnaya Matematika, Tome 35 (2023) no. 4, pp. 58-68. http://geodesic.mathdoc.fr/item/DM_2023_35_4_a3/