|
This article is cited in 2 scientific papers (total in 2 papers)
Discrete Functions
$\mathrm{S}$-blocks with maximum component algebraic immunity on a small number of variables
D. A. Zyubinaab, N. N. Tokarevaacb a JetBrains Research
b Novosibirsk State University
c Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
Abstract:
Let $\pi$ be a permutation on $ n $ elements, $f$ be a Boolean function in $n$ variables. Define a vector Boolean function $F_\pi:\mathbb{F}_2^n\rightarrow\mathbb{F}_2^n$ as $F_\pi(x) = (f(x), f(\pi(x)), \cdots, f (\pi^{n-1}(x))))$. In this paper, we study the component algebraic immunity of the vector Boolean function $F_\pi$ as a function of the Boolean function $f$ and the permutation $\pi$ for $n = 3, 4, 5$. We obtain complete sets of Boolean and, partly, vector Boolean functions with maximum algebraic immunity in $3, 4$ and $5$ variables. If the function $F_\pi$ has maximum algebraic immunity, then the permutation $\pi$ is full cycle.
Keywords:
Boolean function, vector Boolean function, algebraic immunity, component algebraic immunity.
Citation:
D. A. Zyubina, N. N. Tokareva, “$\mathrm{S}$-blocks with maximum component algebraic immunity on a small number of variables”, Prikl. Diskr. Mat. Suppl., 2021, no. 14, 40–42
Linking options:
https://www.mathnet.ru/eng/pdma525 https://www.mathnet.ru/eng/pdma/y2021/i14/p40
|
Statistics & downloads: |
Abstract page: | 171 | Full-text PDF : | 66 | References: | 28 |
|