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.

翻译：在本文中,我们调查了限定字段的功率函数$F(x)=xd$($mathbb{F)2 ⁇ 4n$,其中美元为正整数,美元=2 ⁇ 3n ⁇ 2 ⁇ 2 ⁇ 2n ⁇ 2 ⁇ 2 ⁇ n}-1美元。事实证明,F(x)=xd$是APN,以美元计,以美元计,以美元计,以美元计,这是APCN对甚至具有特点的限定域的第二类功率函数。此外,还确定了这些功率功能的美元差异范围。