On the constructions of Markov maps
Matematičeskie voprosy kriptografii, Tome 15 (2024) no. 1, pp. 21-34 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Markov cipher models are used in linear analysis and differential analysis of block ciphers. We consider mappings defined on algebraic objects of various types (Abelian groups, vector spaces, etc.) and having Markovian properties. A lower estimate for the cardinality of a set $K$ of values of a random variable $k$ defining the Markov map of Abelian groups ${f_{k}}(x)$ is established.
@article{MVK_2024_15_1_a1,
     author = {V. O. Drelikhov},
     title = {On the constructions of {Markov} maps},
     journal = {Matemati\v{c}eskie voprosy kriptografii},
     pages = {21--34},
     year = {2024},
     volume = {15},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MVK_2024_15_1_a1/}
}
TY  - JOUR
AU  - V. O. Drelikhov
TI  - On the constructions of Markov maps
JO  - Matematičeskie voprosy kriptografii
PY  - 2024
SP  - 21
EP  - 34
VL  - 15
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/MVK_2024_15_1_a1/
LA  - ru
ID  - MVK_2024_15_1_a1
ER  - 
%0 Journal Article
%A V. O. Drelikhov
%T On the constructions of Markov maps
%J Matematičeskie voprosy kriptografii
%D 2024
%P 21-34
%V 15
%N 1
%U http://geodesic.mathdoc.fr/item/MVK_2024_15_1_a1/
%G ru
%F MVK_2024_15_1_a1
V. O. Drelikhov. On the constructions of Markov maps. Matematičeskie voprosy kriptografii, Tome 15 (2024) no. 1, pp. 21-34. http://geodesic.mathdoc.fr/item/MVK_2024_15_1_a1/

[1] Lai X., Massey J. L., Murphy S., “Markov ciphers and differential cryptanalysis”, EuroCrypt 1991, Lect. Notes Comput. Sci., 547, 1991, 17–38 | DOI | MR | Zbl

[2] Pogorelov B. A., Pudovkina M. A., “Razbieniya na bigrammakh i markovost algoritmov blochnogo shifrovaniya”, Matematicheskie voprosy kriptografii, 8:1 (2017), 107–142 | DOI | MR | Zbl

[3] Kemeni D., Snell D., Konechnye tsepi Markova, Nauka, M., 1970, 272 pp. | MR

[4] Denisov O. V., “Kriterii markovosti algoritmov blochnogo shifrovaniya”, Prikladnaya diskretnaya matematika, 2018, no. 41, 28–37 | Zbl

[5] Drelikhov V. O., “Veroyatnostnye svoistva statisticheskikh svyazei mezhdu vkhodom i vykhodom markovskogo iterativnogo shifra s raundovymi otobrazheniyami na abelevykh gruppakh”, Matematicheskie voprosy kriptografii, 12:1 (2021), 59–82 | DOI | MR | Zbl

[6] Glukhov M. M., Elizarov V. P., Nechaev A. A., Algebra, Uchebnik dlya vuzov, 5-e izd., ster., Lan, SPb., 2024, 608 pp.