Differential uniformity of polynomials of degree 10

TL;DR

This paper proves that certain degree-10 polynomials over large finite fields of even characteristic have high differential uniformity, specifically at least 6, under specific coefficient conditions.

Contribution

It establishes a lower bound of 6 on the differential uniformity for a class of degree-10 polynomials over finite fields of even characteristic, expanding understanding of their cryptographic properties.

Findings

Polynomials of degree 10 with specific coefficients have differential uniformity ≥ 6.

The result holds for all sufficiently large extensions of the base field.

Provides conditions under which high differential uniformity is guaranteed.

Abstract

We prove that polynomials of degree 10 over finite fields of even characteristic with some conditions on theirs coefficients have a differential uniformity greater than or equal to 6 over $\mathbb{F}_{2^n}$ for all $n$ sufficiently large.