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 2n1 2n2 . 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.
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