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  

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

作　　者：黄景廉[1] 王卓[1] 李娟[1] 

机构地区：[1]西北民族大学电气工程学院,兰州730030

出　　处：《计算机科学》2015年第3期153-157,共5页Computer Science

基　　金：国家自然科学基金项目(61262085)资助

摘　　要：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。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.

关 键 词：H布尔函数 e-导数 导数 代数次数 代数免疫 相关免疫 关系 

分 类 号：TP309[自动化与计算机技术—计算机系统结构]