Research On Normality Of Boolean Functions

Normality was introduced by Dobbertin in [4]. Since this paper was mainly devoted to the construction of new bent funtions, normality was defined for Boolean functions with an even number m of variables: such a function is normal if it is constant on soma flat of dimension m /2. In this dissertation, some problems on normality are investigated as follows on the basis of recent results on normality of Boolean functions.First, we discuss the normality of Boolean functions and other concering properties systematicly.Second, we focus on some highly nonlinear functions, resilient functions, almost optimal functions and Bent functions, discuss their normality.Third, we discuss the construction of Bent functions, and their applications for construction of normal and non normal Bent functions.Last, we discuss the several algorithms of checking normality, and improve the algorithm of checking normality of Bent functions in [29].