一类H布尔函数的代数次数、相关免疫性与代数免疫性的关系

以布尔函数的导数和自定义的e-导数为研究工具,研究了一类特定Hamming重量的H布尔函数的代数次数、代数免疫性、相关免疫性之间的关联问题.得出H布尔函数的组成部分e-导数的代数次数决定了H布尔函数的代数次数;H布尔函数的e-导数与H布尔函数的代数免疫阶的大小紧密关联;H布尔函数的e-导数可将H布尔函数的代数免疫性、零化子、相关免疫性、代数次数联系到一起等.同时,导出了公式法和级联法两类求解H布尔函数最低代数次数零化子的不同方法.

On Relationship of Algebraic Degree,Correlation Immunity and Algebraic Immunity for a Class of H Boolean Functions

Using the derivative of the Boolean function and the e-derivative defined by ourselves as research tools,we studied the relationship of algebraic degree,algebraic immunity and correlation immunity for H Boolean functions with a specific Hamming weight.We obtained the algebraic degree of the e-derivative which is a component of H Boolean functions deciding the algebraic degree of H Boolean functions.Besides,we determined the e-derivative of H Boolean functions which is closely related to the order of the algebraic immunity of H Boolean functions.We also checked the e-derivative of H Boolean functions which can put algebraic immunity,annihilators,correlation immunity and algebraic degree of H Boolean functions together.Meanwhile,we also deduced two kinds of methods which are formula method and cascade method.By using these two methods we could solve annihilators of the lowest algebraic degree of H Boolean functions.