Geodesic
Properties of substitutions generated by a class of filtering generators
Matematičeskie voprosy kriptografii, Tome 14 (2023) no. 1, pp. 99-114 
A. V. Sarantsev. Properties of substitutions generated by a class of filtering generators. Matematičeskie voprosy kriptografii, Tome 14 (2023) no. 1, pp. 99-114. http://geodesic.mathdoc.fr/item/MVK_2023_14_1_a6/
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Voir la notice de l'article provenant de la source Math-Net.Ru

We consider a class of substitutions on a set of binary strings of length $n$ whose coordinate functions are equivalent with respect to the transformation implemented by the affine shift register. We describe nonlinear Boolean functions $f$ depending significantly only on the first three variables and affine feedback functions $l$ of the shift register such that this shift register along with the filter function $f$ generates a system of coordinate functions of substitution. The degree of nonlinearity and the difference characteristic for substitutions from this class are calculated. By means of these substitutions a class of nonlinear shift registers of period $2^n-1$ is constructed.

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