Geodesic
Nonlinear permutations recursively generated over the Galois ring of characteristic 4
Matematičeskie voprosy kriptografii, Tome 5 (2014) no. 4, pp. 5-15 
A. V. Abornev. Nonlinear permutations recursively generated over the Galois ring of characteristic 4. Matematičeskie voprosy kriptografii, Tome 5 (2014) no. 4, pp. 5-15. http://geodesic.mathdoc.fr/item/MVK_2014_5_4_a0/
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Voir la notice de l'article provenant de la source Math-Net.Ru

The class of nonlinear permutations $\pi_F$ of a space $\mathrm{GF}(2^r)^m$ of any dimension $m\ge3$ is constructed. Each permutation $\pi_F$ is recursively generated by the characteristic polynomial $F(x)$ over the Galois ring $\mathrm{GR}(2^{2r},4)$. Results of the paper by A. A. Nechaev and the author are generalized to an arbitrary Galois ring of characteristic 4.

[1] Abornev A. V., “Postroenie podstanovok s ispolzovaniem razryadno-podstanovochnykh preobrazovanii modulya nad koltsom Galua kharakteristiki 4”, Prikl. diskr. matem., 2014, no. 1, 9–19

[2] Kuzmin A. S., Nechaev A. A., “Lineinye rekurrentnye posledovatelnosti nad koltsami Galua”, Algebra i logika, 34:2 (1995), 169–189 | MR | Zbl

[3] Nechaev A. A., Abornev A. V., “Nonlinear permutations on a space over a finite field induced by linear transformations of a module over a Galois ring”, Matematicheskie voprosy kriptografii, 4:2 (2013), 81–100

[4] Nikonov V. G., Sarantsev A. V., “Metody kompaktnoi realizatsii biektivnykh otobrazhenii, zadannykh regulyarnymi sistemami odnotipnykh bulevykh funktsii”, Vestnik RUDN, Ser. Prikl. i kompyut. matem., 2:1 (2003), 84–95