Geodesic
On mixing linear transforms for block ciphers
Matematičeskie voprosy kriptografii, Tome 2 (2011) no. 2, pp. 5-39 Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider AES-type block ciphers over the finite field with linear mixing transforms of three classes: maximally mixing, block-uniform and composite. Transition probability matrices of pairs of input blocks for these schemes with random indepРμndent equiprobable round keys are investigated. A minimum number of rounds sufficient for the generation of doubly transitive set of permutations are found for schemes without mixing transforms in odd rounds. 
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M. M. Gluhov. On mixing linear transforms for block ciphers. Matematičeskie voprosy kriptografii, Tome 2 (2011) no. 2, pp. 5-39. http://geodesic.mathdoc.fr/item/MVK_2011_2_2_a0/

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