Geodesic
Partitions on bigrams and Markov property of block ciphers
Matematičeskie voprosy kriptografii, Tome 8 (2017) no. 1, pp. 107-142 Cet article a éte moissonné depuis la source Math-Net.Ru

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A model of iterated block ciphers with alphabet $X$, independent uniform round keys and a key addition group $(X,\otimes)$ is considered. We find conditions ensuring the preservation of Markov property under lumping of Markov chain with state space $X^2$ corresponding to bigrams of intermediate ciphertexts. We describe properties of Markov ciphers considered and lumping transforms. 
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B. A. Pogorelov; M. A. Pudovkina. Partitions on bigrams and Markov property of block ciphers. Matematičeskie voprosy kriptografii, Tome 8 (2017) no. 1, pp. 107-142. http://geodesic.mathdoc.fr/item/MVK_2017_8_1_a8/

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