Bent functions from triples of permutation polynomials

TL;DR

This paper introduces new methods for constructing bent functions by utilizing triples of permutations, expanding beyond involutions to include various polynomial types.

Contribution

It presents novel constructions of bent functions using triples of permutations, including monomials, binomials, trinomials, and quadrinomials, broadening the existing framework.

Findings

New permutation-based bent function constructions

Inclusion of diverse polynomial types beyond involutions

Enhanced methods for bent function generation

Abstract

We provide constructions of bent functions using triples of permutations. This approach is due to Mesnager. In general, involutions have been mostly considered in such a machinery; we provide some other suitable triples of permutations, using monomials, binomials, trinomials, and quadrinomials.