Bounds on the differential uniformity of the Wan-Lidl polynomials

TL;DR

This paper investigates the differential uniformity of Wan-Lidl polynomials over finite fields, providing new bounds and identifying permutation polynomials with low differential uniformity, supported by computational evidence.

Contribution

It introduces a general upper bound on differential uniformity for Wan-Lidl polynomials and identifies permutation polynomials with uniformity at most 5 over certain fields.

Findings

Established a field-size independent upper bound.

Identified permutation polynomials with differential uniformity ≤ 5.

Provided computational validation of theoretical bounds.

Abstract

We study the differential uniformity of the Wan-Lidl polynomials over finite fields. A general upper bound, independent of the order of the field, is established. Additional bounds are established in settings where one of the parameters is restricted. In particular, we establish a class of permutation polynomials which have differential uniformity at most 5 over fields of order $3\bmod 4$, irrespective of the field size. Computational results are also given.