On the conjecture about the nonexistence of rotation symmetric bent functions

TL;DR

This paper presents a new proof approach for the nonexistence of homogeneous rotation symmetric bent functions of degree greater than 2, supporting the conjecture and characterizing degree 2 cases using polynomial GCDs.

Contribution

It introduces a novel proof method for the conjecture and characterizes degree 2 functions via polynomial GCDs, advancing understanding of rotation symmetric bent functions.

Findings

Homogeneous rotation symmetric bent functions of degree >2 do not exist.

New proof approach supports the conjecture.

Degree 2 functions characterized by polynomial GCDs.

Abstract

In this paper, we describe a different approach to the proof of the nonexistence of homogeneous rotation symmetric bent functions. As a result, we obtain some new results which support the conjecture made in this journal, i.e., there are no homogeneous rotation symmetric bent functions of degree >2. Also we characterize homogeneous degree 2 rotation symmetric bent functions by using GCD of polynomials.