Two classes of power mappings with boomerang uniformity 2

作者：Haode Yan, Zhen Li, Zhitian Song, Rongquan Feng · 发表于：Advances in Mathematics of Communications · 年份：2022 · DOI：10.3934/amc.2022046 · 被引用次数：9 · 研究领域：Coding theory and cryptography、graph theory and CDMA systems、Cancer Mechanisms and Therapy

Let \begin{document}$ q $\end{document} be an odd prime power. Let \begin{document}$ F_1(x) = x^{d_1} $\end{document} and \begin{document}$ F_2(x) = x^{d_2} $\end{document} be power mappings over \begin{document}$ \mathrm{GF}(q^2) $\end{document} , where \begin{document}$ d_1 = q-1 $\end{document} and \begin{document}$ d_2 = d_1+\frac{q^2-1}{2} = \frac{(q-1)(q+3)}{2} $\end{document} . In this paper, we study the boomerang uniformity of \begin{document}$ F_1 $\end{document} and \begin{document}$ F_2 $\end{document} via their differential properties. It is shown that the boomerang uniformity of \begin{document}$ F_i $\end{document} ( \begin{document}$ i = 1,2 $\end{document} ) is 2 with some conditions on \begin{document}$ q $\end{document} .