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arXiv · 2107.06464

A class of APcN power functions over finite fields of even characteristic

Ziran Tu·Xiangyong Zeng·Yupeng Jiang·Xiaohu Tang
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Abstract

In this paper, we investigate the power functions $F(x)=x^d$ over the finite field $\mathbb{F}_{2^{4n}}$, where $n$ is a positive integer and $d=2^{3n}+2^{2n}+2^{n}-1$. It is proved that $F(x)=x^d$ is APcN at certain $c$'s in $\mathbb{F}_{2^{4n}}$, and it is the second class of APcN power functions over finite fields of even characteristic. Further, the $c$-differential spectrum of these power functions is also determined.

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Ziran Tu, Xiangyong Zeng, Yupeng Jiang, Xiaohu Tang. 2021-07-14. A class of APcN power functions over finite fields of even characteristic. https://arxiv.org/abs/2107.06464

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