Discrete Functions
About the components of some classes of invertible vectorial Boolean functions
I. A. Pankratova Tomsk State University
Abstract:
In the class of invertible vectorial Boolean functions in
$n$ variables with coordinate functions depending on all variables, we consider the subclasses
$\mathcal{K}_{n}$ and
$\mathcal{K}'_{n}$, the functions in which are obtained using
$n$ independent transpositions, respectively, from the identity permutation and from the permutation, each coordinate function of which essentially depends on some one variable. It is shown that, for any $F=(f_1\ldots f_n)\in\mathcal{K}_{n}\cup\mathcal{K}'_{n}$ and
$i=1,\ldots,n$, the coordinate function
$f_i$ has a single linear variable, the component function
$vF$ has no nonessential and linear variables for each vector
$v\in{\mathbb F}_2^n$ weight of which is greater than
$1$, the nonlinearity, the degree, and the component algebraic immunity are
$2$,
$n-1$, and
$2$ respectively.
Keywords:
vectorial Boolean functions, invertible functions, nonlinearity, component algebraic immunity.
UDC:
519.7
DOI:
10.17223/2226308X/12/20
Fulltext:
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