Geodesic
Nonlinear permutations of a space over a finite field induced by linear transformations of a module over a Galois ring
Matematičeskie voprosy kriptografii, Tome 4 (2013) no. 2, pp. 81-100 
A. A. Nechaev; A. V. Abornev. Nonlinear permutations of a space over a finite field induced by linear transformations of a module over a Galois ring. Matematičeskie voprosy kriptografii, Tome 4 (2013) no. 2, pp. 81-100. http://geodesic.mathdoc.fr/item/MVK_2013_4_2_a7/
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Voir la notice de l'article provenant de la source Math-Net.Ru

Nonlinear permutations of $m$-dimensional vector space $P^{(m)}$ over a finite field $P=\mathrm{GF}(q)$ induced by linear transforms of a module $R^{(m)}$ over a Galois ring $R=\mathrm{GR}(q^2,p^2)$, $q=p^r$, are constructed. The transforms constructed by iteration of linear recurrent transforms are studied separately. Some applications in cryptography are discussed.

[1] Lidl R., Niederreiter H., Finite Fields, second edition, Cambridge University Press, 1997 | MR

[2] Kuzmin A. S., Nechaev A. A., “Linear recurring sequences over Galois rings”, Algebra and Logic, 34:2 (1995), 87–100 | DOI | MR

[3] Gluhov M. M., “On numerical parameters associated with the definition of finite groups by systems of generating elements”, Trudy po diskretnoi matematike, 1, TVP, M., 1997, 43–66 (in Russian) | MR

[4] Diedonné J.-A., La Géometrie des Groupes Classiques, Ergebnisse der Mathematik und ihrer Grenzgebiete, 5, Springer-Verlag, 1971 | MR

[5] Kuzmin A. S., Nechaev A. A., Trace-function on a Galois ring in coding theory, Lect. Notes Comput. Sci., 1255, Springer-Verlag, 1997 | MR | Zbl

[6] Cameron P. J., “Finite permutation groups and finite simple groups”, Bull. London Math. Soc., 13:1 (1981), 1–22 | DOI | MR | Zbl

[7] Pogorelov B. A., “Permutation groups. I. (A survey for 1981–1995)”, Trudy po diskretnoi matematike, 2, TVP, M., 1998, 237–281 (in Russian) | MR | Zbl

[8] Pogorelov Ayu V., Bases of permutation groups theory, v. I, General questions, Moscow, 1986, 316 pp. (in Russian) | Zbl

[9] Nikonov V. G., Sarantsev A. V., “On the complexity of joint realization of Boolean functions regular systems in DNF basis”, Mathematical Aspects of Cryptography, 1:3 (2010), 45–65 (in Russian)

[10] Nechaev A. A., “Criterion for the completeness of systems of functions of $p^n$-valued logic containing operations of addition and multiplication modulo $p^n$”, Metody Diskretnogo Analiza, 34 (1980), 74–87 (in Russian) | MR | Zbl

[11] Gluhov M. M., “On 2-transitive products of regular permutation groups”, Trudy po diskretnoi matematike, 3, Fizmatlit, M., 2000, 37–52 (in Russian)

[12] Pogorelov B. A., “Primitive permutation group that contain a $2^m$-cycle”, Algebra i Logika, 19:2 (1980), 147–155 (in Russian) | DOI | MR | Zbl

[13] Knapp W., “On Burnside's method”, J. Algebra, 175 (1995), 644–660 | DOI | MR | Zbl