全局雪崩准则的矩阵表示及其性质

doi:10.6040/j.issn.1671-9352.2.2014.212

山东大学学报（理学版） ›› 2014, Vol. 49 ›› Issue (11): 89-94.doi: 10.6040/j.issn.1671-9352.2.2014.212

• 论文 • 上一篇

全局雪崩准则的矩阵表示及其性质

袁宏博, 杨晓元, 魏悦川, 刘龙飞, 范存洋

武警工程大学电子技术系网络与信息安全武警部队重点实验室, 陕西西安 710086

收稿日期:2014-06-24 修回日期:2014-10-17 出版日期:2014-11-20 发布日期:2014-11-25
作者简介:袁宏博(1989- ),男,硕士研究生,研究方向为密码学、流密码、密码函数. E-mail:402287908@qq.com
基金资助:
国家自然科学基金资助项目(61202492)

Matrix description and properties of global avalanche characteristics

YUAN Hong-bo, YANG Xiao-yuan, WEI Yue-chuan, LIU Long-fei, FAN Cun-yang

Key Laboratory of Network & Information Security of APF, Engineering University of APF, Xi'an 710086, Shaanxi, China

Received:2014-06-24 Revised:2014-10-17 Online:2014-11-20 Published:2014-11-25

摘要/Abstract

摘要： 从研究全局雪崩准则的表达方式出发,提出了全局雪崩准则的矩阵表示方法,并证明了布尔函数f(x)与f(x+α)全局雪崩的绝对值指标和平方和指标相同.依据矩阵表示方法得到了全局雪崩准则与布尔函数Walsh谱值的关系,并给出了一个布尔函数同一个仿射函数的互相关全局雪崩准则绝对指标的上、下限.最后,分析了修改序列中的一位对布尔函数全局雪崩准则指标的影响,结合爬山算法设计了一种修改M-M型Bent函数的优化算法,得到的布尔序列在非线性度和全局雪崩准则指标上优于已有的构造.

关键词: 全局雪崩准则, 爬山算法, 非线性度, 矩阵表示, 布尔函数

Abstract: The global avalanche characteristics matrix representation method was proposed by starting from the expression of global avalanche characteristics.And the same absolute value indicator of Boolean functions f(x) and f(x+α) were proved.The relationship between global avalanche characteristics (GAC) and Walsh spectrum was studied by matrix representation and the GAC absolute indicator's limits between a Boolean function and an affine functions. At last, the influence on GAC indicator by modifying sequence of a Boolean function was analyzed. In combination with hill-climbing algorithm, a large number of Boolean functions with good absolute value indicator were achieved via M-MF Bent functions.

Key words: hill-climbing algorithm, nonlinearity, global avalanche characteristics, matrix, Boolean functions

中图分类号:

TP309

袁宏博, 杨晓元, 魏悦川, 刘龙飞, 范存洋. 全局雪崩准则的矩阵表示及其性质[J]. 山东大学学报（理学版）, 2014, 49(11): 89-94.

YUAN Hong-bo, YANG Xiao-yuan, WEI Yue-chuan, LIU Long-fei, FAN Cun-yang. Matrix description and properties of global avalanche characteristics[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2014, 49(11): 89-94.

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全局雪崩准则的矩阵表示及其性质

Matrix description and properties of global avalanche characteristics

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