E-derivative and derivative were introduced to deeply study internal structure of Boolean function

and analyzed the cryptographic properties of Boolean function

which was a new subject in cryptology.The relationships between correlation-immunity and balanceness was analyzed

and obtain some important results which could not be obtained by analyzing the exterior structure of Boolean function at all.Beyond that

for researching on the correlation immunity of balanced H-Boolean function which play a important role in cryptology

here also give a new research methods to improve the anti-attack ability of cryptosystem.