Power Functions over Finite Fields with Low $c$-Differential Uniformity
Abstract
Very recently, a new concept called multiplicative differential (and the corresponding -differential uniformity) was introduced by Ellingsen \textit{et al} in [C-differentials, multiplicative uniformity and (almost) perfect c-nonlinearity, IEEE Trans. Inform. Theory, 2020] which is motivated from practical differential cryptanalysis. Unlike classical perfect nonlinear functions, there are perfect -nonlinear functions even for characteristic two. The objective of this paper is to study power function over finite fields with low -differential uniformity. Some power functions are shown to be perfect -nonlinear or almost perfect -nonlinear. Notably, we completely determine the -differential uniformity of almost perfect nonlinear functions with the well-known Gold exponent. We also give an affirmative solution to a recent conjecture proposed by Bartoli and Timpanella in 2019 related to an exceptional quasi-planar power function.
Keywords
Cite
@article{arxiv.2003.13019,
title = {Power Functions over Finite Fields with Low $c$-Differential Uniformity},
author = {Haode Yan and Sihem Mesnager and Zhengchun Zhou},
journal= {arXiv preprint arXiv:2003.13019},
year = {2020}
}