Rotation Symmetric Bent Boolean Functions for n = 2p

TL;DR

This paper investigates the existence of rotation symmetric bent Boolean functions, proving that certain sums must include specific degree-two functions and confirming the conjecture for n=2p variables.

Contribution

It proves that sums of short-cycle rotation symmetric bent functions contain specific degree-two monomials and confirms the conjecture for n=2p variables, extending to nonhomogeneous cases.

Findings

Sums of short-cycle rotation symmetric bent functions contain specific degree-two monomials.

Most cases of the conjecture are proven for n=2p, p>2 prime.

Extended results to nonhomogeneous functions.

Abstract

It has been conjectured that there are no homogeneous rotation symmetric bent Boolean functions of degree greater than two. In this paper we begin by proving that sums of short-cycle rotation symmetric bent Boolean functions must contain a specific degree two monomial rotation symmetric Boolean function. We then prove most cases of the conjecture in n=2p, p>2 prime, variables and extend this work to the nonhomogeneous case.