## Cryptology ePrint Archive: Report 2015/451

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

Sihong Su and Xiaohu Tang

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 $n=2m\ge2$, a first systemic construction of $n$-variable rotation symmetric bent functions, with any possible algebraic degrees ranging from $2$ to $m$, is proposed.

Category / Keywords: Orbit, rotation symmetric function, Walsh transform, bent function, algebraic degree.