Geodesic
Cryptographic properties of orthomorphic permutations
Prikladnaya Diskretnaya Matematika. Supplement, no. 13 (2020), pp. 29-31 Cet article a éte moissonné depuis la source Math-Net.Ru

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In this paper, we consider bijective mappings $F:\mathbb{Z}_2^n \rightarrow \mathbb{Z}_2^n$ called orthomorphisms such that the mappings $G(x) = F(x) \oplus x$ are also bijective. It is used in the Lai — Massey scheme as a mixing element between rounds and it also can be used to construct cryptographically strong $\mathrm{S}$-boxes. The main cryptographic properties are studied, namely nonlinearity and differential uniformity. It was revealed that, for $n=2,3,4$, the linear approximation tables of orthomorphisms consist of the values $0$ and $\pm 2^{n-1}$, and the difference distribution tables consist of the values $0$ and $2^n$. It turned out that orthomorphisms of a small number of variables are not resistant to linear and differential cryptanalysis.
Keywords: orthomorphic permutation, linear approximation table, difference distribution table. 
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     author = {J. P. Maksimluk},
     title = {Cryptographic properties of orthomorphic permutations},
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J. P. Maksimluk. Cryptographic properties of orthomorphic permutations. Prikladnaya Diskretnaya Matematika. Supplement, no. 13 (2020), pp. 29-31. http://geodesic.mathdoc.fr/item/PDMA_2020_13_a6/

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