On the Systematic Constructions of Rotation Symmetric Bent Functions with Any Possible Algebraic Degrees

Abstract

In the literature, few constructions of $n$-variable rotation symmetric bent functions have been presented, which either have restriction on $n$ or have algebraic degree no more than $4$. In this paper, for any even integer $n=2m\ge 2$, a first systemic construction of $n$-variable rotation symmetric bent functions, with any possible algebraic degrees ranging from $2$ to $m$, is proposed.