布尔函数的代数免疫与扩散阶的关系

J4 ›› 2011, Vol. 33 ›› Issue (10): 34-38.

布尔函数的代数免疫与扩散阶的关系

周宇,曹云飞,张文政,祝世雄

(保密通信重点实验室,四川成都 610041)

收稿日期:2011-05-15 修回日期:2011-07-20 出版日期:2011-10-25 发布日期:2011-10-25
作者简介:周宇(1980),男,甘肃庆阳人，博士，工程师，研究方向为布尔函数和流密码。
基金资助:
重点实验室资助项目(9140C11020110C1102)

Relationship Between Algebraic Immunity and Propagation Characteristics of the Boolean Functions

ZHOU Yu,CAO Yunfei,ZHANG Wenzheng,ZHU Shixiong

(Science and Technology on Communication Security Laboratory,Chengdu 610041,China)

Received:2011-05-15 Revised:2011-07-20 Online:2011-10-25 Published:2011-10-25

摘要/Abstract

摘要：

本文利用布尔函数全局雪崩准则得到平方和指标与代数免疫的联系，通过Walsh谱与自相关函数的关系式得到布尔函数满足扩散时自相关值的分布，由此推出了变元数、代数免疫、扩散阶和代数次数之间的不等式，利用计算机搜索得到变元数在4~30之间时这四个指标的简洁表达式。最后得到了扩散阶与线性结构、正规性的关系。

关键词: 布尔函数, 代数免疫, 扩散阶, 全局雪崩准则

Abstract:

Using the relationship between the sum of square and algebraic immunity by GAC, the divisibility properties concerning the autocorrelation coefficient of the Boolean functions with propagation criterion is derived by Walshspectrum and coefficient, and the inequality among variables, algebraic immunity, propagation criteria and algebraic degree is deduced by this divisibility, and by the computer search methods a compactly expression among these four parameters is given from 4 variables to 30 variables. Finally, the relationships between the propagation criterion and the liner structure and normality are discussed.

Key words: Boolean functions;Algebraic immunity;Propagation criteria;GAC

周宇,曹云飞,张文政,祝世雄. 布尔函数的代数免疫与扩散阶的关系[J]. J4, 2011, 33(10): 34-38.

ZHOU Yu,CAO Yunfei,ZHANG Wenzheng,ZHU Shixiong. Relationship Between Algebraic Immunity and Propagation Characteristics of the Boolean Functions[J]. J4, 2011, 33(10): 34-38.

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