Two infinite classes of rotation symmetric bent functions with simple representation

Abstract

In the literature, few n-variable rotation symmetric bent functions have been constructed. In this paper, we present two infinite classes of rotation symmetric bent functions on $${\mathbb {F}}_2^{n}$$ of the two forms: where $$n=2m$$ , $${\upgamma }(X_0,X_1,\ldots , X_{m-1})$$ is any rotation symmetric polynomial, and $$m/\textit{gcd}(m,t)$$ is odd. The class (i) of rotation symmetric bent functions has algebraic degree ranging from 2 to m and the other class (ii) has algebraic degree ranging from 3 to m. Moreover, the two classes of rotation symmetric bent functions are disjoint.