Characteristic Matrix In The Logic Function Of The Nature And Tectonic Applications

In this dissertation, we mainly use character matrix to research cryptology characteristic of Boolean function and m-ary logic function.Firstly, by using properties of character matrix's row and column we get an equivalence condition of bent function. Then we have an entirely construct method of 4 variable bent function. Move forward, we have a new recursion construct method, by which we can construct (n+1)(n+2) bent functions with n+2 variable from a n variable bent function.Secondly, we study functions' cryptology characteristics over a set Q, such as correlation immunity, diffusibility etc. Through their character matrixes. We receive an equivalence condition of correlation immune logic function defined on set Q~n, and the number of such correlation immune logic function. Then we concretely give the property of 3-ary bent function character matrixes.Finally, for the first time, we study rotation symmetric(RotS) function's cryptology characteristic by character matrix. And discuss the Walsh spectrum and autocorrelation function of RotS functions, through their character matrixes we discuss and construct a lot of correlation immune RotS function .