Construction Of Boolean Function With Maximum Algebraic Immunity

Boolean functions are important components of stream ciphers, block ciphers and Hash functions. The cryptographic criteria of Boolean functions are crucial to the security of cryptographic algorithms. The algebraic attack on stream ciphers has become a standard attack, although which has been proposed only a few years. The research on algebraic attacks provides a new necessary cryptographic property: algebraic immunity, for Boolean functions to be used in keystream generators. Possessing optimum algebraic immunity is a necessary criteria for Boolean functions used in stream ciphers against algebraic attacks.This thesis focuses on the construction of Boolean function with maximum algebraic immunity。Firstly an existed construction of Boolean function with maximum algebraic immunity is ameliorated.Then the construction of rotation symmetric Boolean functions with maximum algebraic immunity is discussed.The main results of this thesis are outlined as follows.(1) Utilizing"base exchange"technique, a new method of construction of even n-variable Boolean functions is provided. The functions have high nonlinearity. Compared with the previous methods, their supports do not need sequential powers of the primitive element.(2) Based on"orbit exchange"technique, a construction of rotation symmetric Boolean functions with the maximum algebraic immunity on even number of variables is proposed. These functions have strong resistance against algebraic attacks, and they also have much better nonlinearity and optimal algebraic degree than that of previous constructions.