Analysis Of Algebraic Immunity Of Boolean Function

Boolean functions play a central role in security of block ciphers andstream ciphers.To withstand several known attacks on the cryptosystem,Boolean funcions should possess several criterias, including:balancedness, a high algebraic degree, a high nonlinearity and a high correlation immunity etc.In recent years,,algebraic attacks has posed a severe threat on stream ciphers as well as block cipher systems and have received a lot of attention in the cryptographic literatuer.This attack recover the secret key by solving an overdefined system of multivariate algebraic equations. To resist this kind of attack,A new critere which measures the security of Boolean function called algebraic immunity has been introduced .Because of algebraic attacks, a high algebraic immunity is now necessary for Boolean functions.This paper mainly investigate the algebraic immunity of Boolean functions and associative cryptographic properties.In this paper we show several construction methods of Boolean functions with optimum algebraic immunity and research symmetric Boolean functions accordingly.At last,we analyze the relationship between algebraic immunity and other cryptographic properties, and obtains main result as follows:The current situation and development both here and abroad is analysed.The basic concepts and representation of Boolean functions are introduced,both algebraic immunity and some basic properties and theorems.Other cryptographic properties are presented,we can conclude that cryptographic properties are interdependent .Construction methods of Boolean functions with optimum algebraic immunity are introduced intensively.Then we study algebraic immunity of symmetric Boolean functions and present construction methods of them accordingly.Simultaneously, the other cryptographic properties of Boolean functions constructed were analyzed.At last, we study the relationship between algebraic immunity of Boolean functions and other cryptographic properties,specialy the relationship between algebraic immunity and the nonlinearity, the relationship between algebraic immunity and linear structure,we also study the relations between the algebraic immunity and the Hamming weight of Boolean functions...