Certain Cryptographic Functions

This paper deals with two kinds of problems: correlation-immune function and Bent-function. A new description of the two kinds of cryptographic Functions is presented in this paper which take their construction as a combined design.The paper contains of four parts.The first part presents the basic knowledge for the research of cryptographic functions where Walsh transformation is introduced in detail.In the second part correlation-immune function is discussed. After introducing the background briefly and presenting the main results of the research of correlation-immune function, the paper give a new description of correlation-immune function which takes the construction of correlation-immune function as a certain grouping design of n elements .Then the count of correlation-immune functions is discussed. The paper present the count of correlation-immune functions whose Hamming weights are respectively 4 and 6.In the third part Bent-function is discussed. After briefly introducing the background of Bent-function research and presenting its two main properties, the paper give a new description of Bent-function which takes the construction of Bent-function as a certain grouping design of n elements. And then, using this description the paper probeinto the relation between of Bent-function and difference set.In the forth part a method is presented where one property of Bent-function is used to construct correlation-immune functions of two order.