Geodesic
On sufficient conditions to generate the alternating group by $SA$-permutations
Trudy Instituta matematiki, Tome 15 (2007) no. 2, pp. 58-68

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$SA$-permutations, the common building components of block ciphers, are constructed as a composition of confusion ($S$-boxes) and diffusion (linear or affine $A$-boxes) transformations. We obtain conditions on $S$- and $A$-boxes, which guarantee that these permutations generate the alternating group. 
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     author = {A. S. Maslov},
     title = {On sufficient conditions to generate the alternating group by $SA$-permutations},
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A. S. Maslov. On sufficient conditions to generate the alternating group by $SA$-permutations. Trudy Instituta matematiki, Tome 15 (2007) no. 2, pp. 58-68. http://geodesic.mathdoc.fr/item/TIMB_2007_15_2_a6/