PROPERTIES OF COMPONENTS FOR SOME CLASSES OF VECTORIAL BOOLEAN FUNCTIONS

In the class of invertible vectorial Boolean functions in n variables with coordinate functions depending on all variables, we consider the subclasses K-n and K-n', where the functions are obtained using n independent transpositions, respectively, from the identity permutation and from the permutation with coordinate functions essentially dependent on exactly one variable. We show that, for any F = (f(1)...f(n)) is an element of K-n boolean OR K-n' and i is an element of {1,..., n}, the coordinate function f(i) has a single linear variable, each component function vF with vector v is an element of F-2(n) of a weight greater than 1 has no fictitious and linear variables, the nonlinearity N-F, the degree deg F, and the component algebraic immunity AI(comp)(F) are 2, n - 1, and 2 respectively.