您的位置:山东大学 -> 科技期刊社 -> 《山东大学学报(理学版)》

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   

  1. 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   

  1. 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: 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
[1] ZHANG Xianmo, ZHENG Yuliang. GAC—the criterion for global avalanche characteristics of crytographic functions[J]. Journal for Universal Computer Science, 1995, 1(5):316-333.
[2] ADAMS C M, TAVARES S E. Generating and counting binary Bent sequences[J]. IEEE Transactions on Information Theory, 1995, 36(5):1170-1173.
[3] 周宇.布尔函数的密码学性质研究[D].西安:西安电子科技大学,2009. ZHOU Yu. Research on cryptographic properties of Boolean functions[D]. Xi'an: Xidian University, 2009.
[4] CARLET C. Generalized partial spreads[J]. IEEE Transactions on Information Theory, 1995, 41(5):1482-1487.
[5] BIHAM E, SHAMIR A. Differential cryptanalysis of DES-like cryptosystems[J]. Journal of Cryptology, 1991, 4(1):3-72.
[6] ZHOU Jinjun, CHEN Weihong, GAO Fengxiu. Best linear approximation and correlation immunity of functions over Zm*[J]. IEEE Transactions on Information Theory, 1999, 45(1):303-308.
[7] ZENG Xiangyong, CARLET C, SHAN Jinyong, et al. More balanced Boolean functions with optimal algebraic immunity and good nonlinearity and resistance to fast algebraic attacks[J]. IEEE Transactions on Information Theory, 2011, 57:6310-6320.
[8] SHANNON C. Excommunication theory of secrecy systems[J]. Bell Systems Technical Journal, 1949, 28(4):656-715.
[9] 张薇,杨晓元,韩益亮.密码基础理论与协议[M].北京:清华大学出版社,2012. ZHANG Wei,YANG Xiaoyuan, HAN Yiliang. Based theory and cryptography protocol[M]. Beijing: Tsinghua University Press, 2012.
[10] DILLON J F. Elementary hadamard difference sets[D]. Maryland: University of Maryland, 1974.
[11] MCELIECE R L. A family of noncyclic difference sets[J]. Journal of Combinatorial Theory, 1973, 15:1-10.
[12] ST?NIC? P. Nonlinearity, local and global avalanche characteristics of balanced Boolean functions[J]. Discret Math, 2002, 248:181-193.
[13] ST?NIC? P, SUNG S H. Improving the nonlinearity of certain balanced Boolean functions with good local and global avalanche characteristics[J]. Information Processing Letter, 2001, 79:167-172.
[14] MAITRA S. Highly nonlinear balanced Boolean functions with good local and global avalanche charac-teristics[J]. Information Processing Letter, 2002, 83:281-286.
[15] CANTEAUT A, CARLET C, CHARPIN P, et al. Propagation characteristics and correlation immunity of highly nonlineaar Boolean functions[J]. Lecture Notes in Computer Sceince, 2000, 1807:507-522.
[16] ST?NIC? P, SUNG S H. Boolean functions with five controllable cryptographic properties[J]. Des Codes Cryptogr, 2004, 31:147-157.
[17] TANG Deng, ZHANG Weiguo, TANG Xiaohu. Construction of balanced Boolean functions with high nonlinearity and good autocorrelation properties[J]. Springer Science Des Codes Cryptogr, 2013, 67:77-91.
[1] 卓泽朋, 崇金凤, 魏仕民. bent-negabent函数的构造[J]. 山东大学学报(理学版), 2015, 50(10): 47-51.
[2] 卓泽朋,崇金凤,魏仕民. Nega-Hadamard变换和negabent 函数[J]. J4, 2013, 48(7): 29-32.
[3] 焦玉娟,张申贵. 斜Hurwitz级数环的三角矩阵表示[J]. J4, 2011, 46(2): 105-109.
[4] 张丽梅1,2. 分配格上矩阵的M-P逆和加权M-P逆[J]. J4, 2010, 45(12): 33-39.
[5] 傅丽. 均匀逻辑公式的基本性质及其真度的分布[J]. J4, 2010, 45(11): 59-62.
Viewed
Full text


Abstract

Cited

  Shared   
  Discussed   
No Suggested Reading articles found!