Maximal differential uniformity polynomials

TL;DR

This paper identifies an infinite family of polynomial degrees over finite fields for which all polynomials exhibit maximal differential uniformity, confirming a conjecture in these cases.

Contribution

It provides an explicit infinite family of degrees with maximal differential uniformity and proves a related conjecture for these cases.

Findings

All polynomials of certain degrees have maximal differential uniformity for large n.

Confirmed a conjecture regarding differential uniformity for these polynomial degrees.

Abstract

We provide an explicit infinite family of integers $m$ such that all the polynomials of ${\mathbb F}_{2^n}[x]$ of degree $m$ have maximal differential uniformity for $n$ large enough. We also prove a conjecture of the third author in these cases.