The Importance of Study Cryptographic Properties of H Boolean Function with Hamming Weight of 2n-1 + 2n-2

Abstract

In this paper, using the derivative of the Boolean function and the e-derivative defined by ourselves as research tools, we discuss the cryptographic properties of H Boolean function with Hamming weight of 2n1 2n2  . We get the result that studying the algebraic immunity and the correlation immunity of this class of H Boolean functions has critical influence on the study of a large number of H Boolean functions within all Hamming weight range, which is a essential basis of studying cryptographic properties of Balanced H Boolean functions, Bent functions and other H Boolean functions.