Some Classes of Cryptographic Power Functions and Permutation Polynomials with Low (-1)-Differential Uniformity in Cyber Security

Cryptographic functions with low differential uni-formity have wide applications in cryptography and cyber security. In this paper, we further investigate c-differential uniformity proposed by Ellingsen et al. (IEEE Transactions on Information Theory. 2020, 66(9): 5781–5789). Specifically, two classes of power functions with low (-1)-differential uniformity over finite fields with odd characteristic are obtained. In addition, a class of permutation polynomials and
$\mathrm{P}_{-1}\mathrm{N}$
or
$\text{AP}_{-1}\mathrm{N}$
functions over
$\mathbb{F}_{3^{n}}$
are proposed. These functions with low
$c$
-differential uniformity are utilized to resist against
$c$
-differential attacks in cyberspace from those with the usual low differential uniformity.