On the Differential Spectrum and the APcN Property of a Class of Power Functions Over Finite Fields

作者：Ziran Tu, Nian Li, Yanan Wu, Xiangyong Zeng, Xiaohu Tang, Yupeng Jiang · 发表于：IEEE Transactions on Information Theory · 年份：2022 · DOI：10.1109/tit.2022.3198133 · 被引用次数：23 · 研究领域：Coding theory and cryptography、Cryptographic Implementations and Security、Cellular Automata and Applications

In this paper, we investigate the power function$F(x)=x^{d}$over the finite field$\mathbb {F}_{2^{4n}}$, where$n$is a positive integer and$d=2^{3n}+2^{2n}+2^{n}-1$. We prove that this power function is AP$c\text{N}$with respect to all$c\in \mathbb {F}_{2^{4n}}\setminus \{1\}$satisfying$c^{2^{2n}+1}=1$, and we determine its$c$-differential spectrum. To the best of our knowledge, this is the second class of AP$c\text{N}$power functions over finite fields of even characteristic. By the same proof ideas, we completely determine the differential spectrum of this function, and give an affirmative answer to a recent conjecture proposed by Budaghyan, Calderini, Carlet, Davidova and Kaleyski.