The Research Of The Properties Of Boolean Functions

Boolean function is widely used in the structure of Cryptanalysis and password protocol. The property of Boolean functions directly impact on the security of Cryptanalysis and password protocol. In order to resist the best affine approximation attack, people designed Bent functions with the highest degree of nonlinear. Then people have also constructed a class of Bent functions with the higher degree of nonlinear function to compensate for the defects of Bent function.Three representative Bent functions are researched in the paper. Because the relationship between the properties is differenct, such as equivalence, contradiction, compatibility, constraints and so on, the improvement of a property may be lead to others lower. To a certain extent, semi-Bent function, partially Bent functions and extended Bent function enhance their own properties, but they don't satisfy with all the properties. It is significance that researching the relationship, giving a relative balance, then analyzing a class of Bent functions. The main task of this paper is as follows.Firstly, in this paper some basic concepts and theorems of Boolean function are introduced and a briefing on Boolean functions encryption, security, and the research method of the properties are given. From the two aspects of definition and property of the characteristics, we give some conceptions about a class of Bent function.Secondly, in this paper six properties of Bent function are quantified by the Walsh spectrum. The six properties include balancedness, correlation-immunity, nonlinearity, SAC, PC, algebraic. The relationships between the properties are proved by spectrum's technology; Basing on the relationships, this paper analyzed the relationships, and according to their different roles in the Cryptanalysis, we compromise the properties which have constrain relationship. In the end, we give a relative balanced point about the six properties.Finally, in this paper the properties of a class of Bent functions and the advantages and the disadvantages on the aspects of resisting attack are researched. We find the better Boolean function and analyze a class of Bent functions using the relative balanced point.