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Random mappings of sets with restrictions on parameters. I
Matematičeskie voprosy kriptografii, Tome 3 (2012) no. 1, pp. 125-144 Cet article a éte moissonné depuis la source Math-Net.Ru

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Random mappings $\sigma\colon X\to X$ of $n$-set $X$ with constraints on degrees of vertices in a directed graph $\Gamma(\sigma)$ are considered. Mappings corresponding to the binary shift register of length $l$ with a random feedback function are particular cases of this model. 
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V. N. Sachkov. Random mappings of sets with restrictions on parameters. I. Matematičeskie voprosy kriptografii, Tome 3 (2012) no. 1, pp. 125-144. http://geodesic.mathdoc.fr/item/MVK_2012_3_1_a4/

[1] Arney Y., Bender E., “Random mappings with constraints on coalescence and number of origins”, Pacific J. Math., 103:2 (1982), 269–294 | MR | Zbl

[2] Sachkov V. N., Vvedenie v kombinatornye metody diskretnoi matematiki, 2-e izd., MTsNMO, M., 2004