Geodesic
Periodical properties of multidimensional polynomial generator over Galois ring.~IV
Matematičeskie voprosy kriptografii, Tome 13 (2022), pp. 69-95

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$m$-dimensional polynomial substitutions of Galois rings consisting of $q^n$ elements and having the characteristic $p^n$ are investigated in this paper. The maximum cycle length in such substitutions is $L_m(R)=q^m(q^m-1)p^{n-2}$. Substitutions that contain an $L_m(R)$ length cycle are called full-length cycle substitutions (FLC-substitutions). A method permitting to construct FLC-substitutions is proposed. The number of substitutions that can be constructed by this method is estimated. The obtained results are applied to the synthesis of polynomial shift registers with a given cyclic structure. 
@article{MVK_2022_13_a3,
     author = {O. A. Kozlitin},
     title = {Periodical properties of multidimensional polynomial generator over {Galois} {ring.~IV}},
     journal = {Matemati\v{c}eskie voprosy kriptografii},
     pages = {69--95},
     publisher = {mathdoc},
     volume = {13},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MVK_2022_13_a3/}
}
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O. A. Kozlitin. Periodical properties of multidimensional polynomial generator over Galois ring.~IV. Matematičeskie voprosy kriptografii, Tome 13 (2022), pp. 69-95. http://geodesic.mathdoc.fr/item/MVK_2022_13_a3/