Relations among E-Derivative, Derivative, Algebraic Degree, Correlation Immunity and Annihilators for H Boolean Functions

Abstract

Using the derivative of the Boolean function and the e-derivative defined by ourselves as research tools, going deep into the internal structure of Boolean functions, we study relationship of algebraic degree, correlation immunity and annihilators for H Boolean functions with a specific Hamming weight. We obtain the algebraic degree of the e-derivative which is a component of H Boolean functions decide the algebraic degree of H Boolean functions. Besides, we describe the characteristics of the algebraic degree of e-derivative for the correlation immune H Boolean functions. We also check the e-derivative of H Boolean functions can put annihilators, correlation immunity and algebraic degree of H Boolean functions together. Meanwhile, we also deduce a formula method to solving annihilators of H Boolean functions. Such researches are important in cryptographic primitive designs, and have significance and role in the theory and application range of cryptosystems.