Differential uniformity properties of some classes of permutation polynomials
Abstract
The notion of -differential uniformity has recently received a lot of attention since its proposal~\cite{Ellingsen}, and recently a characterization of perfect -nonlinear functions in terms of difference sets in some quasigroups was obtained in~\cite{AMS22}. Independent of their applications as a measure for certain statistical biases, the construction of functions, especially permutations, with low -differential uniformity is an interesting mathematical problem in this area, and recent work has focused heavily in this direction. We provide a few classes of permutation polynomials with low -differential uniformity. The used technique involves handling various Weil sums, as well as analyzing some equations in finite fields, and we believe these can be of independent interest.
Keywords
Cite
@article{arxiv.2212.01931,
title = {Differential uniformity properties of some classes of permutation polynomials},
author = {Kirpa Garg and Sartaj Ul Hasan and Pantelimon Stanica},
journal= {arXiv preprint arXiv:2212.01931},
year = {2023}
}