浅析Xiao-Massey定理的意义和作用

On the significance and function of the Xiao-Massey theorem

分别征服相关攻击是一类重要的序列密码分析方法,是设计序列密码时必须要防御的分析方法之一。抵抗分别征服相关攻击常用的防御策略是使得序列密码中所采用的密码函数具有一定的相关免疫阶,将这类密码函数称为相关免疫函数。相关免疫布尔函数的沃尔什频谱特征刻画是构造和分析这类函数的理论基础,最早由肖国镇(G.Z.Xiao)教授和梅西(J.L.Massey)教授提出,国际上称之为Xiao-Massey定理。Xiao-Massey定理的提出为序列密码研究开辟了一个新的研究方向。主要回顾了Xiao-Massey定理,简述了Xiao-Massey定理的意义,阐释了Xiao-Massey定理的作用。

Divide-and-conquer correlation analysis is an important stream cipher analytical method,which is one of the analytical methods that must be defended when designing the stream cipher.The frequently-used defense strategy is to make the cryptographic function used in the stream cipher have a certain correlation immune order.This kind of cryptographic function is called the correlation immune function.The characterization of correlation immune functions is the theoretical basis for constructing and analyzing such functions.Professor G.Z.Xiao and Professor J.L.Massey first gave the characterization of the Walsh spectrum of correlation immune Boolean functions(called Xiao-Massey theorem),which opened up a new research direction for the study of stream ciphers.This paper mainly reviews the Xiao-Massey theorem,sketches the significance of the Xiao-Massey theorem,and explains the function of the Xiao-Massey theorem.