On constructing bent functions from cyclotomic mappings

TL;DR

This paper introduces new methods for constructing Boolean bent functions using cyclotomic mappings, resulting in explicit infinite families and revealing connections to previous constructions.

Contribution

It presents three generic constructions of bent functions from cyclotomic mappings, expanding the known classes and showing their equivalence to existing methods.

Findings

Derived several new explicit infinite families of bent functions and their duals.

Identified that some previous constructions are special cases of the new methods.

Found examples EA-inequivalent to known classes of monomials, Dillon, and Niho polynomials.

Abstract

We study a new method of constructing Boolean bent functions from cyclotomic mappings. Three generic constructions are obtained by considering different branch functions such as Dillon functions, Niho functions and Kasami functions over multiplicative cosets and additive cosets respectively. As a result, several new explicit infinite families of bent functions and their duals are derived. We demonstrate that some previous constructions are special cases of our simple constructions. In addition, by studying their polynomial forms, we observe that the last construction provides some examples which are EA-inequivalent to five classes of monomials, Dillon type and Niho type polynomials.