The Study Of Algebraic Immunity Boolean Function

Boolean function plays a crucial role in digital communication theory, especially in secure communication system with private key.Algebraic immunity is an important norm to measure the ability to resist algebraic attack. If the Boolean function has a low algebraic immunity, then it cannot resist the algebraic attack. According to the algebraic immune degree of a Boolean func-tion with 1-form linear structure is completely determined by the lowest degree of the annihilator for. From the perspective of linear structure, this paper is given Boolean functions with K al-gebraic immunity and the characters of Walsh transform and the nonlinearity of the functions. A series of conclusions reveals the linear structure of Boolean function restricts algebraic immunity. Meanwhile, Special allocation of points of and which can be re-adjusted value of cyclic spectrum and autocorrelation values.In this paper,we also study the existence of low degree annihilators of Boolean function.Meanwhile we get the relations between the algebraic immunity and the degree of Bent functions.