Geodesic
On the way of constructing differentially $2\delta$-uniform permutations over $\mathbb{F}_{2^{2m}}$
Prikladnaya Diskretnaya Matematika. Supplement, no. 14 (2021), pp. 51-55

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The paper studies new ways of constructing differentially $2\delta$-uniform bijections over $\mathbb{F}_{2^{2m}}$, $m \ge 3$, that are based on $TU$-construction. Some well known results on the constructing differentially $4$-uniform permutations over $\mathbb{F}_{2^{2m}}$ are generalized in this work. The core idea is to use $TU$-construction and differentially $\delta$-uniform bijections to construct $2^t \cdot \delta$-uniform permutations. A generalized method for constructing $2m$-bit differentially $4$-uniform permutations is proposed, and new constructions of differentialy $6$ and $8$-uniform permutations are introduced.
Keywords: $S$-Box, differential uniformity
Mots-clés : permutation, $TU$-construction. 
@article{PDMA_2021_14_a9,
     author = {D. B. Fomin},
     title = {On the way of constructing differentially $2\delta$-uniform permutations over $\mathbb{F}_{2^{2m}}$},
     journal = {Prikladnaya Diskretnaya Matematika. Supplement},
     pages = {51--55},
     publisher = {mathdoc},
     number = {14},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PDMA_2021_14_a9/}
}
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D. B. Fomin. On the way of constructing differentially $2\delta$-uniform permutations over $\mathbb{F}_{2^{2m}}$. Prikladnaya Diskretnaya Matematika. Supplement, no. 14 (2021), pp. 51-55. http://geodesic.mathdoc.fr/item/PDMA_2021_14_a9/