Geodesic
Description of the feedback function of a nonlinear shift register
Matematičeskie voprosy kriptografii, Tome 15 (2024), pp. 101-112

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We consider a nonlinear shift register with a feedback function $F$ such that its period coincides with the period of some linear shift register. For this nonlinear shift register we study the methods of construction of a balanced mapping such that its coordinate functions are equivalent to the superposition of the binary function $f$ of $n$ variables and the transformation $\rho_l$ implemented by the shift register with the feedback function $l$. For a concrete function $f$ of the nonlinearity degree $3$ a polynomial of the function $F$ is obtained and its degree is calculated. 
@article{MVK_2024_15_a5,
     author = {A. V. Sarantsev},
     title = {Description of the feedback function of a nonlinear shift register},
     journal = {Matemati\v{c}eskie voprosy kriptografii},
     pages = {101--112},
     publisher = {mathdoc},
     volume = {15},
     year = {2024},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MVK_2024_15_a5/}
}
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A. V. Sarantsev. Description of the feedback function of a nonlinear shift register. Matematičeskie voprosy kriptografii, Tome 15 (2024), pp. 101-112. http://geodesic.mathdoc.fr/item/MVK_2024_15_a5/