Geodesic
Combinatorial properties of differentially $2$-uniform substitutions
Matematičeskie voprosy kriptografii, Tome 6 (2015) no. 1, pp. 159-179 
V. N. Sachkov. Combinatorial properties of differentially $2$-uniform substitutions. Matematičeskie voprosy kriptografii, Tome 6 (2015) no. 1, pp. 159-179. http://geodesic.mathdoc.fr/item/MVK_2015_6_1_a7/
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Voir la notice de l'article provenant de la source Math-Net.Ru

A combinatorial approach to the investigation and methods of construction of differentially $2$-uniform substitutions of the vector space over the finite field $F_2$ is proposed. Necessary and sufficient conditions for the family of sets associated with a differentially $2$-uniform substitution to be a symmetric block design are given. It is shown that a substitution is differentially $2$-uniform if and only if it is a solution of a similarity equations system connecting a family of translations with a family of unequal weights involutions. We suggest methods of construction of differentially $2$-uniform substitutions by means of the Cayley table of an additive group of finite field $F_{2^m}$.

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