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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     author = {K. N. Pankov},
     title = {An upper bound for the number of functions satisfying the strict avalanche criterion},
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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/