Algebraic Attacks And Algebraic Immunity Of Boolean Functions

Recently,a special kind of cryptanalysis coined as algebraic attack has gained a lot of attention that can be used for almost all types of cryptographic systems,constructing Boolean functions of high performan-ce can improve algebraic immunity of cryptosystem.According to the theory of algebraic attack that finding the low degree annihilators of Boolean functions to improve the efficient of sloving equations,the paper have analysized the three methods of constructing low degree annihilators of Boolean functions,also taken a exmple tocompare them,then come to the conclusion that the greatest subspace is the best method bec ause the annihilators gained by it is the lowest.Algebraic immunity is the important index to measure algebraic attck,in addition,the ther oem that the algebraic immunity of Boolean functions with n dime nsion is at most[n/2]have been proved,the paper have advanced a kind of Boolean functions of optimization,and illustrated a five di mension Boolean function to give a concret description.The paper have also analysized and compared several kinds of methods of con structing Boolean functions of ciper properties,which including balan ce,nonlinearity,corre-immunity,high algebraic degree and stict-av alance and so on.Recently,most Boolean functions meets the former four properties,strict-avalance put forward new needs for constructin g good Boolean functions.The define of strict-avalance is that if ch oose the opposition of inputing varies,then will alter half of the out put of functions;the use of it is to combining nondegration with av alance.Therefore,Boolean function of good ciper propertise need inc luding stict-avalance,the paper put forword a kind of Boolean functi on of optimal intergration propertise which meet the needs.