满足严格雪崩准则相关免疫函数的代数免疫阶

计算机科学 ›› 2013, Vol. 40 ›› Issue (4): 147-151.

满足严格雪崩准则相关免疫函数的代数免疫阶

黄景廉,王卓,张志杰

西北民族大学计算机科学与信息工程学院兰州730030;西北民族大学计算机科学与信息工程学院兰州730030;辽宁工程技术大学软件学院阜新123000

出版日期:2018-11-16 发布日期:2018-11-16
基金资助:
本文受国家自然科学基金项目(61262085),中央高校基本科研业务费专项资金项目(ZYZ2011055)资助

Algebraic Immune Order of Correlation Immune Functions Satisfying Strict Avalanche Criterion

HUANG Jing-lian,WANG Zhuo and ZHANG Zhi-jie

Online:2018-11-16 Published:2018-11-16

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,讨论满足严格雪崩准则、具有相关免疫性、重量为2n－1+2n－2的H布尔函数的代数免疫问题。得出这类函数奇数(n≥17)元、偶数(n≥16)元的最优代数免疫函数及其构造方法,给出了代数免疫阶AI(f)≥8的n元代数免疫函数的构造方法；还给出了零化子及最低代数次数零化子的求法及其与布尔函数的导数的关系等结果。

关键词: H布尔函数,相关免疫性,子函数,最优代数免疫,代数免疫阶

Abstract: Using the derivative of Boolean functions and custom e-derivative as a research tool,we discussed the issue of algebraic immunity of H Boolean function with correlation immunity and weight of 2n－1+2n－2 which meets the strict avalanche criterion. We got the optimal algebraic immunity function and its construction method of these functions with odd(n≥17)variables and even(n≥16)variables and gave the construction method of algebraic immunity function with n variables that the algebraic immunity order is AI(f)≥8,also gave the method of solving the annihilator and the minimum algebraic degree annihilators and the derivative relations of annihilator and the Boolean function．The derivative of the Boolean function and the e-derivative defined with derivative can directly and explicitly depict the weight of the Boolean functions as research tools,in-depth to the internal structure of the value of the Boolean function.

Key words: H Boolean function,Correlation immune,Subfunction,Optimal algebraic immunity,Algebraic immunity order

黄景廉,王卓,张志杰. 满足严格雪崩准则相关免疫函数的代数免疫阶[J]. 计算机科学, 2013, 40(4): 147-151. https://doi.org/

HUANG Jing-lian,WANG Zhuo and ZHANG Zhi-jie. Algebraic Immune Order of Correlation Immune Functions Satisfying Strict Avalanche Criterion[J]. Computer Science, 2013, 40(4): 147-151. https://doi.org/

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