Relationship between Correlation Immune Order and Algebraic Immunity Order of Boolean Functions

Abstract

Using the derivative of the Boolean function and the e-derivative defined by ourselves as research tools, we go deep into the internal structure of the Boolean function values. Additionally, by the methods of cascade calculations and analytic combinatorics, cryptographic properties such as correlation immune and algebraic immunity of H Boolean functions with Hamming weight of with diffusibility are studied. Then we prove the existing of m order correlation immune H Boolean functions ,and get the result of the sufficient and necessary conditions of algebraic immunity order is 1 of Boolean function with correlation immune order is m.