The Annihilators and the Correlation Immunity of H Boolean Functions

Abstract

Using the derivative and the e-derivative defined by ourselves as research tools, we study the compatibility of algebraic immunity and correlation immunity of H Boolean functions with Hamming weight of 2n1  2n2 . We obtain the necessary conditions which the e-derivative satisfies and the necessary and sufficient conditions that the derivative part represents, when H Boolean functions have m-order correlation immunity. We also arrive at the sufficient and necessary condition and the sufficient condition, which are the ones that H Boolean functions satisfy the compatibility of 1st-order algebraic immunity and m-order correlation immunity using e-derivative and derivative. What is more, the main theoretical results are verified through example and are revealed to be correct.