论文标题
在有限场上的一类功率功能的差分光谱上
On the differential spectrum of a class of power functions over finite fields
论文作者
论文摘要
差异均匀性是密码学中的一个重要概念，因为它量化了针对差异攻击的S盒安全性程度。 $ f（x）= x^d $具有低差异均匀性的功能功能在过去几十年中已经进行了广泛的研究，因为它们对差异攻击的强烈抵抗力和硬件中的实施成本较低。在本文中，我们对Budaghyan，Calderini，Carlet，Davidova和Kaleyski提出的最新猜想给出了肯定的答案，涉及$ f（x）= x^d $ fo $ \ \ \ m athbb {f} _ {2^{2^{4n}} $的差异均匀性，其中$ d = 2^{3n}+2^{2n}+2^{n} -1 $，我们完全确定其差异光谱。
Differential uniformity is a significant concept in cryptography as it quantifies the degree of security of S-boxes respect to differential attacks. Power functions of the form $F(x)=x^d$ with low differential uniformity have been extensively studied in the past decades due to their strong resistance to differential attacks and low implementation cost in hardware. In this paper, we give an affirmative answer to a recent conjecture proposed by Budaghyan, Calderini, Carlet, Davidova and Kaleyski about the differential uniformity of $F(x)=x^d$ over $\mathbb{F}_{2^{4n}}$, where $n$ is a positive integer and $d=2^{3n}+2^{2n}+2^{n}-1$, and we completely determine its differential spectrum.
