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

TL;DR

This paper introduces a systematic method to construct rotation symmetric bent functions for any even number of variables, achieving any algebraic degree from 2 up to half the number of variables, overcoming previous limitations.

Contribution

It provides the first comprehensive construction for rotation symmetric bent functions with arbitrary algebraic degrees for any even number of variables.

Findings

Constructed functions with algebraic degrees from 2 to m

Applicable to any even number of variables n=2m

Overcomes previous restrictions on algebraic degree and variable count

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.