On Relationship of some Cryptographic Properties for Weight Symmetric H 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,and discuss the relationship of a variety of cryptographic properties of the weight symmetric H Boolean functions in the range of the weight with the existence of H Boolean functions. We get the results of the weight symmetric H Boolean function should have the same algebraic immunity order, correlation immunity order, the degree of diffusion and nonlinearity. The results provide a theoretical basis to reduce nearly half workload for studying the cryptographic properties of H Boolean function, and provides a new research methods for the study of the properties of cryptographic security of Boolean functions.