一类四项多项式的APN性质的完全刻划
A complete characterization of the APN property of a class of quadrinomials
摘要：
本文利用Hasse-Weil界确定了系数$a_1,a_2,a_3\in\mathbb{F}_{2^n}$与$n=2m$的充要条件，使得$f(x) = {x}^{3\cdot2^m} + a_1x^{2^{m+1}+1} + a_2 x^{2^m+2} + a_3x^3$是$\mathbb{F}_{2^n}$上的APN函数.我们的结果解决了Carlet在International Workshop on the Arithmetic of Finite Fields，83-107，2014中的一个公开问题的上半部分。
英文摘要：
In this paper, by the Hasse-Weil bound, we determine the necessary and sufficient condition on coefficients $a_1,a_2,a_3\in\mathbb{F}_{2^n}$ with $n=2m$ such that $f(x) = {x}^{3\cdot2^m} + a_1x^{2^{m+1}+1} + a_2 x^{2^m+2} + a_3x^3$ is an APN function over $\mathbb{F}_{2^n}$. Our result resolves the first half of an open problem by Carlet in International Workshop on the Arithmetic of Finite Fields, 83-107, 2014.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
