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

计算机科学 ›› 2015, Vol. 42 ›› Issue (3): 153-157.doi: 10.11896/j.issn.1002-137X.2015.03.032

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

黄景廉,王卓,李娟

西北民族大学电气工程学院兰州730030,西北民族大学电气工程学院兰州730030,西北民族大学电气工程学院兰州730030

出版日期:2018-11-14 发布日期:2018-11-14
基金资助:
本文受国家自然科学基金项目(61262085)资助

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

HUANG Jing-lian, WANG Zhuo and LI Juan

Online:2018-11-14 Published:2018-11-14

摘要/Abstract

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。

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

Abstract: 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.

Key words: H Boolean functions,e-derivative,Derivative,Algebraic degree,Algebraic immunity,Correlation immunity,Relationship

黄景廉,王卓,李娟. 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[J]. 计算机科学, 2015, 42(3): 153-157. https://doi.org/10.11896/j.issn.1002-137X.2015.03.032

HUANG Jing-lian, WANG Zhuo and LI Juan. On Relationship of Algebraic Degree,Correlation Immunity and Algebraic Immunity for a Class of H Boolean Functions[J]. Computer Science, 2015, 42(3): 153-157. https://doi.org/10.11896/j.issn.1002-137X.2015.03.032

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