Geodesic
Probabilistic properties of statistical dependencies between input and output of Markovian iterative cipher with round transformations on Abelian groups
Matematičeskie voprosy kriptografii, Tome 12 (2021) no. 1, pp. 59-82 Cet article a éte moissonné depuis la source Math-Net.Ru

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We investigate the statistical dependencies between the input and output of an iterative cipher model, in which round keys are independent random variables, round transformations act on Abelian groups and depend on the round key and the round number. If the input and output of the cipher are uniformly distributed, then the statistical dependencies correspond the correlation coefficients between values of the characters. It is shown that for a cipher model with Markovian round mappings on Abelian groups the matrix of the second moments of the considered characteristics is equal to the product of the corresponding matrices constructed for round mappings. Upper and lower estimates for the expectations of absolute values of studied characteristics are obtained. 
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     author = {V. O. Drelikhov},
     title = {Probabilistic properties of statistical dependencies between input and output of {Markovian} iterative cipher with round transformations on {Abelian} groups},
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V. O. Drelikhov. Probabilistic properties of statistical dependencies between input and output of Markovian iterative cipher with round transformations on Abelian groups. Matematičeskie voprosy kriptografii, Tome 12 (2021) no. 1, pp. 59-82. http://geodesic.mathdoc.fr/item/MVK_2021_12_1_a2/

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

[2] Lai X., On the design and security of block ciphers, Diss. for the degree of Doctor of Techn. Sci., Swiss Federal Inst. Technology, Zürich, 1992, 118 pp. | MR

[3] Glukhov M. M., Elizarov V. P., Nechaev A. A., Algebra, Uchebnik, 2-e izd., ispr. i dop., Lan, SPb., 2015, 608 pp.

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

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

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