|
Эта публикация цитируется в 2 научных статьях (всего в 2 статьях)
Теоретические основы прикладной дискретной математики
A note on the properties of associated Boolean functions of quadratic APN functions
A. A. Gorodilovaab a Sobolev Institute of Mathematics, Novosibirsk, Russia
b Novosibirsk State University, Novosibirsk, Russia
Аннотация:
Let $F$ be a quadratic APN function in $n$ variables. The associated Boolean function $\gamma_F$ in $2n$ variables ($\gamma_F(a,b)=1$ if $a\neq\mathbf{0}$ and equation $F(x)+F(x+a)=b$ has solutions) has the form $\gamma_F(a,b) = \Phi_F(a) \cdot b + \varphi_F(a) + 1$ for appropriate functions $\Phi_F:\mathbb{F}_2^n\to \mathbb{F}_2^n$ and $\varphi_F:\mathbb{F}_2^n\to \mathbb{F}_2$. We summarize the known results and prove new ones regarding properties of $\Phi_F$ and $\varphi_F$. For instance, we prove that degree of $\Phi_F$ is either $n$ or less or equal to $n-2$. Based on computation experiments, we formulate a conjecture that degree of any component function of $\Phi_F$ is $n-2$. We show that this conjecture is based on two other conjectures of independent interest.
Ключевые слова:
a quadratic APN function, the associated Boolean function, degree of a function.
Образец цитирования:
A. A. Gorodilova, “A note on the properties of associated Boolean functions of quadratic APN functions”, ПДМ, 2020, no. 47, 16–21
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/pdm691 https://www.mathnet.ru/rus/pdm/y2020/i1/p16
|
Статистика просмотров: |
Страница аннотации: | 160 | PDF полного текста: | 83 | Список литературы: | 21 |
|