论文标题
四类四级属性的APN特性的完整表征
A complete characterization of the APN property of a class of quadrinomials
论文作者
论文摘要
在本文中，通过hasse-weil限制，我们确定了系数上的必要条件$ a_1，a_2，a_3 \ in \ mathbb {f} _ {2^n} $，$ n = 2m $，使$ f（x）= {x} = {x} = {x） a_2 x^{2^m + 2} + a_3x^3 $是$ \ mathbb {f} _ {2^n} $的APN函数。我们的结果解决了在2014年有限领域的算术算术的国际研讨会上的一个公开问题的上半年，2014年。
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.
