Geodesic
Analysis of non-linear automata with delay 2 over a finite ring
Prikladnaâ diskretnaâ matematika, no. 1 (2010), pp. 68-85
Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

For invertible one-dimensional automata with delay 2 over the ring $\mathbf Z_{p^k}=(\mathbb Z_{p^k},\oplus,\circ)$, the structure of the transition graph is investigated, the sets of equivalent states are characterized, the problems of the parametric identification and of the initial state identification are solved, the sets of fixed points of mappings realized by initial automata are characterized.
Keywords: nonlinear automata, finite rings, simmetric stream ciphers, system of equations over finite rings. 
@article{PDM_2010_1_a5,
     author = {V. V. Skobelev and V. G. Skobelev},
     title = {Analysis of non-linear automata with delay~2 over a~finite ring},
     journal = {Prikladna\^a diskretna\^a matematika},
     pages = {68--85},
     year = {2010},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PDM_2010_1_a5/}
}
TY  - JOUR
AU  - V. V. Skobelev
AU  - V. G. Skobelev
TI  - Analysis of non-linear automata with delay 2 over a finite ring
JO  - Prikladnaâ diskretnaâ matematika
PY  - 2010
SP  - 68
EP  - 85
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/PDM_2010_1_a5/
LA  - ru
ID  - PDM_2010_1_a5
ER  - 
%0 Journal Article
%A V. V. Skobelev
%A V. G. Skobelev
%T Analysis of non-linear automata with delay 2 over a finite ring
%J Prikladnaâ diskretnaâ matematika
%D 2010
%P 68-85
%N 1
%U http://geodesic.mathdoc.fr/item/PDM_2010_1_a5/
%G ru
%F PDM_2010_1_a5
V. V. Skobelev; V. G. Skobelev. Analysis of non-linear automata with delay 2 over a finite ring. Prikladnaâ diskretnaâ matematika, no. 1 (2010), pp. 68-85. http://geodesic.mathdoc.fr/item/PDM_2010_1_a5/

[1] Skobelev V. V., Skobelev V. G., Analiz shifrsistem, IPMM NAN Ukrainy, Donetsk, 2009, 479 pp.

[2] Skobelev V. G., “Kombinatorno-algebraicheskie modeli v kriptografii”, Prikladnaya diskretnaya matematika, 2009, prilozhenie No 2, 74–114

[3] Glushkov V. M., Sintez tsifrovykh avtomatov, Fizmatlit, M., 1962, 476 pp. | MR

[4] Trakhtenbrot B. A., Barzdin Ya. M., Konechnye avtomaty (povedenie i sintez), Nauka, M., 1970, 400 pp. | MR | Zbl

[5] Kuznetsov S. P., Dinamicheskii khaos, Fizmatlit, M., 2001, 296 pp.

[6] Skobelev V. G., Tuboltseva O. V., “Shifr na osnove otobrazheniya Eno”, Vestnik Tomskogo gosuniversiteta. Prilozhenie, 2005, no. 14, 74–78

[7] Gill A., Vvedenie v teoriyu konechnykh avtomatov, Nauka, M., 1966, 272 pp. | MR | Zbl

[8] Bollobas B., Modern graph theory, Springer-Verlag, NY, 1998, 394 pp. | MR | Zbl

[9] Korshunov A. D., “O perechislenii konechnykh avtomatov”, Problemy kibernetiki, 34, Nauka, M., 1978, 5–82 | MR

[10] Kudryavtsev V. B., Aleshin S. V., Podkolzin A. S., Vvedenie v teoriyu konechnykh avtomatov, Nauka, M., 1985, 320 pp. | MR | Zbl