On the significance and function of the Xiao-Massey theorem

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.