Geodesic
An upper bound for the number of functions satisfying the strict avalanche criterion
Diskretnaya Matematika, Tome 17 (2005) no. 2, pp. 95-101
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The strict avalanche criterion was introduced by Webster and Tavares while studying some cryptographic functions. We say that a binary function $f(x)$, $x \in V_n$, satisfies this criterion if replacing any coordinate of the vector $x$ by its complement changes the values of $f(x)$ exactly in a half of cases. In this paper we establish an upper bound for the number of such functions for $n$ large enough. 
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K. N. Pankov. An upper bound for the number of functions satisfying the strict avalanche criterion. Diskretnaya Matematika, Tome 17 (2005) no. 2, pp. 95-101. http://geodesic.mathdoc.fr/item/DM_2005_17_2_a6/

[1] Webster A. F., Tavares S. E., “On the design of $S$-boxes”, Lecture Notes Comput. Sci., 218, 1986, 523–534

[2] Cusick T. W., “Bounds on the number of functions satisfying the strict avalanche criterion”, Inform. Processing Lett., 57 (1996), 261–263 | DOI | MR | Zbl

[3] Cusick T. W., Stanica P., “Bounds on the number of functions satisfying the strict avalanche criterion”, Inform. Processing Lett., 60 (1996), 215–219 | DOI | MR

[4] Youssef A. M., Tavares S. E., “Comment on bounds on the number of functions satisfying the strict avalanche criterion”, Inform. Processing Lett., 60 (1996), 271–275 | DOI | MR

[5] Bliss D. K., “A lower bound on the number of functions satisfying the strict avalanche criterion”, Discrete Math., 185 (1998), 29–39 | DOI | MR

[6] O'Connor L., “An upper bound on the number of functions satisfying the strict avalanche criterion”, Inform. Processing Lett., 52 (1994), 325–327 | DOI | MR

[7] Bkhattachariya R. N., Ranga Rao R., Approksimatsiya normalnym raspredeleniem i asimptoticheskie razlozheniya, Nauka, Moskva, 1982 | MR