Geodesic
$\otimes_{\mathbf{W}}$-markovianity of XSL-block ciphers connected with properties of their round functions
Matematičeskie voprosy kriptografii, Tome 10 (2019) no. 1, pp. 115-142 Cet article a éte moissonné depuis la source Math-Net.Ru

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Earlier we have described conditions for the existence of permutation homomorphisms for some class of a $\otimes_{\mathbf{W}}$-markovian block ciphers. In this paper we give conditions on $S$-boxes and on linear transformations which guaranteing the $\otimes_{\mathbf{W}}$-markovian property. In particular, we provide sufficient conditions on these transformations under which the corresponding XSL-block cipher is $\otimes_{\mathbf{W}}$-markovian. 
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B. A. Pogorelov; M. A. Pudovkina. $\otimes_{\mathbf{W}}$-markovianity of XSL-block ciphers connected with properties of their round functions. Matematičeskie voprosy kriptografii, Tome 10 (2019) no. 1, pp. 115-142. http://geodesic.mathdoc.fr/item/MVK_2019_10_1_a6/

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