几类具有低c-差分均匀度的幂函数和置换多项式  

Several Classes of Power Functions and Permutation Polynomials with Low c-Differential Uniformity

作　　者：王聪慧 郑大彬 袁木 王小强 WANG Cong-Hui;ZHENG Da-Bin;YUAN Mu;WANG Xiao-Qiang(Hubei Key Laboratory of Applied Mathematics,Faculty of Mathematics and Statistics,Hubei University,Wuhan 430062,China)

机构地区：[1]湖北大学数学与统计学学院应用数学湖北省重点实验室,武汉430062

出　　处：《密码学报》2023年第3期597-608,共12页Journal of Cryptologic Research

基　　金：国家自然科学基金(11971156,12001175)。

摘　　要：S盒是分组密码算法中的核心部件.为了抵抗差分密码攻击,S盒应具有较低的差分均匀度.低差分密码函数在密码学、编码学、组合设计等领域中有着广泛的应用.Ellingsen等人提出c-差分均匀度的概念,且一些具有低c-差分均匀度的函数被构造出来.本文运用有限域上的二次特征和迹函数提出三类具有低c-差分均匀度的单项式函数,证明了两类已知置换多项式具有低c-差分均匀度.特别地,两类幂函数的c-差分均匀度不超过2.Sbox is one of the core components of block ciphers.In order to resist differential attacks,an Sbox is required to have low differential uniformity.The study on cryptographic functions with low differential uniformity is a hot topic due to their wide applications in cryptography,coding theory,combinatorial design and so on.Recently,a new concept called c-differential uniformity was introduced by Ellingsen et al.,and some low c-differential uniform functions are constructed.This paper further proposes three classes of power functions with low c-differential uniformity.By employing the quadratic character and trace functions,the c-differential uniformity of two classes of the constructed functions with known permutations are proved to be at most 2.

关 键 词：S盒 c-差分均匀度 二次特征 置换多项式 

分 类 号：TP309.7[自动化与计算机技术—计算机系统结构]