An upper bound for the number of functions satisfying the strict avalanche criterion

The strict avalanche criterion was introduced by Webster and Tavares while studying some cryptographic functions. We say that a binary function ƒ(x), x ∈ V_n, satisfies this criterion if replacing any coordinate of the vector x by its complement changes the values of ƒ(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.