Special Bent and Near-bent Functions

TL;DR

This paper introduces a method to construct new classes of bent functions in higher dimensions using special near-bent functions, expanding the known families of these cryptographically significant functions.

Contribution

It presents a novel construction technique for bent functions based on special near-bent functions, leading to new families of bent functions with specific derivatives.

Findings

Constructed new families of bent functions in dimension 2t

Demonstrated the existence of bent functions with specific derivatives

Extended the understanding of near-bent to bent function transformations

Abstract

Starting from special near-bent functions in dimension 2t-1 we construct bent functions in dimension 2t having a specific derivative. We deduce new famillies of bent functions