Properties of components for some classes of vectorial Boolean functions | Prikladnaya Diskretnaya Matematika - Applied Discrete Mathematics. 2019. № 44. DOI: 10.17223/20710410/44/1

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 = (f₁... f_n) G K_n ^K_n and i G {1,... ,n}, the coordinate function f_i has a single linear variable, each component function vF with vector v G F₂ⁿ of a weight greater than 1 has no fictitious and linear variables , the nonlinearity NF , the degree deg F, and the component algebraic immunity AIcomp ( F ) are 2, n - 1, and 2 respectively.