Algebraic Immunity Of Boolean Function

Abstract:Boolean functions are the basis of stream ciphers, the attack on stream ciphers which is an important aspect on Boolean functions. So the security of cryptography and cryptographic protocols are affected by the cryptographic properties of Boolean functions. Algebraic immunity is an important cryptographic properties of Boolean functions, which is to put forward for resist algebraic attacks. Algebraic attack is one of the most effective methods to attack, then we must use the Boolean functions with high algebraic immunity to resist algebraic attack. This mainly investigates the algebraic immunity of Boolean functions and construction methods of Boolean functions with optimum algebraic immunity, and analyzes the relationship between algebraic immunity and other cryptographic properties, and obtains main result as follows:The current situation and development home and abroad is analysed.The basic concepts and representation of Boolean functions are introduced, both algebraic immunity and other cryptographic properties , as well as some basic properties and theorems. From these we can conclude that cryptographic properties are interdependent or restrict mutually.Construction methods of Boolean functions with optimum algebraic immunity are introduced intensively,and the other cryptographic properties of Boolean functions constructed were analyzed. Then a new class of Boolean function with optimum algebraic immunity is constructed by a class of Boolean function with optimum algebraic immunity.Study the relationship between algebraic immunity of Boolean functions and its other cryptographic properties. Introduce the relationship between algebraic immunity and the nonlinearity, the most tight lower bound on the nonlinearity of its algebraic immunity. The relationship between linear structure and algebraic immunity is analyzed, and found that if the Boolean functions have the linear structure, then the algebraic immunity is reduced. Some results of algebraic immunity of symmetric Boolean functions are instructed.