利用Dobbertin指数构造低差分均匀度函数  

Constructing the Low Differentially Uniform Functions from Dobbertin Exponents

作　　者：王彦平[1,2] 

机构地区：[1]西安电子科技大学综合业务网理论及关键技术国家重点实验室,西安710071 [2]西安翻译学院基础课部,西安710105

出　　处：《系统科学与数学》2017年第4期1156-1165,共10页Journal of Systems Science and Mathematical Sciences

基　　金：西安翻译学院重点科研课题(16A03)资助课题

摘　　要：有限域上多项式型的低差分均匀度函数在分组密码的非线性组件S盒中有着重要的作用.为了增强S盒的混淆作用,应用在S盒中的函数应具有较高的非线性度和较高的代数次数.文章通过改变Dobbertin类的单项式函数在有限域F_(2n)的一个子域上的函数值,构造了两类新的多项式型的低差分均匀度函数,并确定了这两类多项式型函数的代数次数和第二类函数的非线性度.Polynomial functions over finite fields with low differential uniformity play an important role in the nonlinear component substitution boxes （S-boxes） of block ciphers. In order to enhance the confusion of S-box, functions used as S-boxes should have high nonlinearity and high algebraic degree. In this paper, we construct two classes of new polynomial functions with low differential uniformity by modifying the image of Dobbertin monomial functions over some subfield of F2n, and determine algebraic degree of these polynomial functions and nonlinearity of the second class functions.

关 键 词：差分均匀度 Dobbertin指数 非线性度 代数次数 

分 类 号：O174[理学—数学]