Geodesic
Finite-state generators with maximal period
Prikladnaya Diskretnaya Matematika. Supplement, no. 17 (2024), pp. 152-154.

Voir la notice de l'article provenant de la source Math-Net.Ru

The periodic properties of a two-stage finite-state generator $G=A_1\cdot A_2$ are studied, where $A_1=(\mathbb{F}_2^n,\mathbb{F}_2, g_1, f_1)$ (it is autonomous), $A_2 = (\mathbb{F}_2,\mathbb{F}_2^m,\mathbb{F}_2,g_2,f_2)$, $n,m\geq 1$. Some necessary conditions for such a generator with the maximum period are formulated, namely: 1) the output sequence of $A_1$ is purely periodic and the period length is $2^n$; 2) the function $f_1$ has an odd weigth; 3) substitutions $g(0,\cdot)$ and $g(1,\cdot)$ have different parities. Some sufficient conditions have been also formulated, for example, the function $g_2(u,y)$ must be injective in $u$ and the weigth of the function $f_2$ must be odd. A method for constructing a generator having maximum period has been proposed.
Keywords: finite-state generator, maximum period
Mots-clés : substitutions. 
@article{PDMA_2024_17_a38,
     author = {E. S. Prudnikov},
     title = {Finite-state generators with maximal period},
     journal = {Prikladnaya Diskretnaya Matematika. Supplement},
     pages = {152--154},
     publisher = {mathdoc},
     number = {17},
     year = {2024},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PDMA_2024_17_a38/}
}
TY  - JOUR
AU  - E. S. Prudnikov
TI  - Finite-state generators with maximal period
JO  - Prikladnaya Diskretnaya Matematika. Supplement
PY  - 2024
SP  - 152
EP  - 154
IS  - 17
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/PDMA_2024_17_a38/
LA  - ru
ID  - PDMA_2024_17_a38
ER  - 
%0 Journal Article
%A E. S. Prudnikov
%T Finite-state generators with maximal period
%J Prikladnaya Diskretnaya Matematika. Supplement
%D 2024
%P 152-154
%N 17
%I mathdoc
%U http://geodesic.mathdoc.fr/item/PDMA_2024_17_a38/
%G ru
%F PDMA_2024_17_a38
E. S. Prudnikov. Finite-state generators with maximal period. Prikladnaya Diskretnaya Matematika. Supplement, no. 17 (2024), pp. 152-154. http://geodesic.mathdoc.fr/item/PDMA_2024_17_a38/

[1] Agibalov G. P., Pankratova I. A., “O dvukhkaskadnykh konechno-avtomatnykh kriptograficheskikh generatorakh i metodakh ikh kriptoanaliza”, Prikladnaya diskretnaya matematika, 2017, no. 35, 38–47 | MR

[2] Agibalov G. P., “Kriptoavtomaty s funktsionalnymi klyuchami”, Prikladnaya diskretnaya matematika, 2017, no. 36, 59–72 | Zbl

[3] Borovkova I. V., Pankratova I. A., Semenova E. V., “Kriptoanaliz dvukhkaskadnogo konechno-avtomatnogo generatora s funktsionalnym klyuchom”, Prikladnaya diskretnaya matematika, 2018, no. 42, 48–56 | MR | Zbl

[4] Obukhov P. K., Pankratova I. A., “Periodicheskie svoistva konechno-avtomatnogo generatora”, Prikladnaya diskretnaya matematika. Prilozhenie, 2023, no. 16, 141–143