Geodesic
Multipermutations and perfect diffusion of partitions
Prikladnaya Diskretnaya Matematika. Supplement, no. 16 (2023), pp. 8-11.

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Multipermutations are introduced by C.-P. Schnorr and S. Vaudenay as formalization of perfect diffusion in block ciphers. In this paper, we consider an abelian group $X$ and a set $H$ of transformations on $X^2$ introduced by S. Vaudenay. Any bijective transformation from $H$ is a multipermutation. Multipermutations from $H$ are defined by orthomorphisms on $X$. The set $H$ is nonempty iff there exists an orthomorphism on $X$. We consider a set $W$ of distinct cosets of $W_{0}$ in $X$. We describe multipermutations from $H$ such that they perfectly diffuse one of partitions $W^2$ or $X \times W$. As an example, we prove that $8$-bit and $16$-bit transformations of CS-cipher perfectly diffuse such partitions.
Mots-clés : multipermutation, Quasi-Hadamard transformation, perfect diffusion of partitions
Keywords: orthomorphism, CS-cipher. 
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B. A. Pogorelov; M. A. Pudovkina. Multipermutations and perfect diffusion of partitions. Prikladnaya Diskretnaya Matematika. Supplement, no. 16 (2023), pp. 8-11. http://geodesic.mathdoc.fr/item/PDMA_2023_16_a1/

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