Description of global avalanche characteristics and constructions of Boolean functions

Hong-bo YUAN; Xiao-yuan YANG; Li-xian WEI; Long-fei LIU

doi:10.3969/j.issn.1000-436x.2014.z2.035

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Description of global avalanche characteristics and constructions of Boolean functions

Correspondences | 更新时间：2024-06-05

- Description of global avalanche characteristics and constructions of Boolean functions
- Journal on Communications Vol. 35, Issue Z2, Pages: 251-255(2014)
- 作者机构：
  
  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
- 作者简介：
- 基金信息：
  
  The National Natural Science Foundation of China(61272492)
- DOI：10.3969/j.issn.1000-436x.2014.z2.035
  CLC： TP309
- Online First：2014-11，
  
  Published：30 November 2014
- 稿件说明：
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Hong-bo YUAN, Xiao-yuan YANG, Li-xian WEI, et al. Description of global avalanche characteristics and constructions of Boolean functions[J]. Journal on Communications, 2014, 35(Z2): 251-255.
DOI：

Hong-bo YUAN, Xiao-yuan YANG, Li-xian WEI, et al. Description of global avalanche characteristics and constructions of Boolean functions[J]. Journal on Communications, 2014, 35(Z2): 251-255. DOI： 10.3969/j.issn.1000-436x.2014.z2.035.

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刻画方法，为研究全局雪崩准则提供了新的工具。根据全局雪崩准则平方和指标的性质，提出了一种改造 M-M 型函数的奇数元几乎最优函数，其满足多个密码学性质，具有较小的平方和指标。构造全局雪崩准则性质优良的密码函数是当前研究的一个难点，利用构造新的映射的方法来改造M-M型函数是一种行之有效的办法。

Abstract

Global avalanche characteristics matrix representation method starting from the expression of global avalanche characteristics was proposed and a new tool for research global avalanche characteristics was provided.According to properties of sum-of-square indicator

an odd almost optimal Boolean functions which meet savariety of properties of cryptography was constructed and hold slower sum-of-square indicator via M-M Boolean functions.It is a problem that how to construct a kind of functions satisfying GAC.There is a effecint way that modifying M-M functions with designing new mapping.

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references

ZHANG X M , ZHENG Y L . GAC—the criterion for global avalanche characteristics of cryptographic functions [J ] . Journal for Universal Computer Science , 1995 , 1 ( 5 ): 316 - 333 .

ADAMS C M , TAVARES S E . Generating and counting binary bent sequences [J ] . IEEE Transactions on Information Theory , 1995 , 36 ( 5 ): 1170 - 1173 .

周宇 . 布尔函数的密码学性质研究 [D ] . 西安电子科技大学 , 2009 .

ZHOU Y . Research on Cryptographic Properties of Boolean Functions [D ] . Xi’an University of Electronic Science and Technology , 2009 .

CARLET C . Generalized partial spreads [J ] . IEEE Trasactions on Informatiom Theory , 1995 , 41 ( 5 ): 1482 - 1487 .

BIHAM E , SHAMIR A . Differential cryptanalysis of DES-like cryptosystems [J ] . Journal of Cryptology , 1991 , 4 ( 1 ): 3 - 72 .

ZHOU J , CHEN W , GAO F . Best linear approximation and correlation immunity of functions over Z m [J ] . IEEE Transaction on Information Theory , 1999 , 45 ( 1 ): 303 - 308 .

ZENG X , CARLET C , SHAN J , 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 . 6310 - 6320 .

ROTHAUS O S . On `bent' functions [J ] . J Combin Theory A , 1976 , 20 : 300 - 305 .

XIAO G Z , MASSEY J L . A Spectral characterization of correlation immune combining functions [J ] . IEEE Transaction on Information Theory , 1988 , 34 ( 3 ): 569 - 571 .

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 , 23 - 27 .

ZHANG W , YANG X Y , HAN Y L . Cryptography Based Theory and Agreement [M ] . Beijing : Tsinghua University Press , 2012 , 23 - 27 .

ZHENG Y , ZHANG X M . Plateaued functions [A ] . advances in cryptology-ICIC'99,lecture notes in computer science [C ] . Heidelberg,Ed,Springer-verlag,1999 , 1726 : 284 - 300 .

常志文 , 张杰 , 李红霞 . 由已知Bent序列构造新的Bent序列 [J ] . 哈尔滨理工大学学报 , 2010 , 15 : 78 - 81 .

CHANG Z W , ZHANG J , LI H X . Constructing Bent sequence form given bent sequence [J ] . Journal of Harbin University of Science and Technology , 2010 , 15 : 78 - 81 .

张恭庆 . 高维哈达玛矩阵理论与应用 [M ] . 北京 : 科学出版社 , 2010 . 66 - 92 .

ZHANG G Q . High-dimensional Hadamard Matrix Theory and Application [M ] . Beijing : Science PressPress , 2010 . 66 - 92 .

张卫国 . 密码函数及其构造 [D ] . 西安电子科技大学 , 2006 .

ZHANG W G . Research on Boolean Function and Construction [D ] . Xi’an University of Electronic Science and Technology , 2006 .

MAITRA S . Highly nonlinear balanced Boolean functions with good local and global avalanche characteristics [J ] . Inform Process Lett , 2002 , 83 : 281 - 286 .

LI N , QU L , QI W , et al . On the construction of Boolean functionswith optimal algebraic immunity [J ] . IEEE Transaction on Informations Theory , 2008 , 54 : 1330 - 1334 .

CARLET C , DALAI D K , GUPTA K C , et al . Algebraic immunity for cryptographically significant Boolean functions:analysis and construction [J ] . IEEE Transactions on Information Theory , 2006 , 52 : 3105 - 3121 .

DILLON J F . Elementary hardamard difference sets [A ] . Proceeding of 6th S E Conference of Combinatorics,Graph Theory,and Computing [C ] . Utility Mathematics,Winnipeg , 1975 . 237 - 249 .

MAITRA S , SARKAR P . Modifications of pattterson-wiedemann functions for cryptographic applications [J ] . IEEE Transactions on Information Theory , 2002 , 48 ( 1 ): 278 - 284 .

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