A new construction of rotation symmetric bent functions with maximal algebraic degree
Sihong Su · Advances in Mathematics of Communications · 2019
In this paper, for any even integer $ n = 2m\ge4 $, a new construction of $ n $-variable rotation symmetric bent function with maximal algebraic degree $ m $ is given as \begin{document}$ f(x_0,x_1\cdots,x_{n-1}) = \bigoplus\limits_{i = 0}^{m-1}(x_ix_{m+i})\oplus \bigoplus\limits_{i = 0}^{n-1}(x_ix_{i+1}\cdots x_{i+m-2} \overline{x_{i+m}} ), $\end{document} whose dual function is \begin{document}$ \widetilde{f}(x_0,x_1\cdots,x_{n-1}) = \bigoplus\limits_{i = 0}^{m-1}(x_ix_{m+i})\oplus \bigoplus\limits_{i = 0}^{n-1}(x_ix_{i+1}\cdots x_{i+m-2} \overline{x_{i+n-2}} ), $\end{document} where $ \overline{x_{i}} = x_{i}\oplus 1 $ and the subscript of $ x $ is modulo $ n $.