Extended algebraic immunity of symmetric Boolean function

Gao-fei WU; Xue-feng LIU; Ye TIAN; Yu-qing ZHANG

doi:10.3969/j.issn.1000-436x.2014.z2.024

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Extended algebraic immunity of symmetric Boolean function

Papers | 更新时间：2024-06-05

- Extended algebraic immunity of symmetric Boolean function
- Journal on Communications Vol. 35, Issue Z2, Pages: 179-183(2014)
- 作者机构：
  
  1. 西安电子科技大学综合业务网理论及关键技术国家重点实验室，陕西西安 710071
  2. 中国科学院大学国家计算机网络入侵防范中心，北京 101408
- 作者简介：
- 基金信息：
  
  The National Natural Science Foundation of China(61272481);The National Natural Science Foundation of China(61402352)
- DOI：10.3969/j.issn.1000-436x.2014.z2.024
  CLC： TN918
- Online First：2014-11，
  
  Published：30 November 2014
- 稿件说明：
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Gao-fei WU, Xue-feng LIU, Ye TIAN, et al. Extended algebraic immunity of symmetric Boolean function[J]. Journal on Communications, 2014, 35(Z2): 179-183.
DOI：

Gao-fei WU, Xue-feng LIU, Ye TIAN, et al. Extended algebraic immunity of symmetric Boolean function[J]. Journal on Communications, 2014, 35(Z2): 179-183. DOI： 10.3969/j.issn.1000-436x.2014.z2.024.

摘要

构造具有最优代数免疫度的布尔函数在流密码中有重要作用，基于布尔函数的单变量多项式表示，构造了一类达到最大扩展代数免疫度的布尔函数。以前的一些函数是这类函数的特例。利用对称布尔函数的基本性质，分析了具有最大代数免疫度的对称布尔函数的扩展代数免疫度。得出结论：共有

个达到最大扩展代数免疫度的n（n是偶数）元对称布尔函数。

Abstract

Boolean functions with optimal algebraic immunity play an important role in stream ciphers.Based on the univariate polynomial representation of Boolean functions

a construction of Boolean functions with maximum extended algebraic immunity (EAI) is proposed

some previous results are special cases of our construction.The EAI of symmetric Boolean functions which have maximum algebraic immunity (AI) are analyzed by using the properties of symmetric Boolean functions.The result shows that there are only

n-variable (n even) symmetric Boolean functions achieve maximum EAI.

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references

COURTOIS N , MEIER W . Algebraic attacks on stream ciphers with linear feedback [A ] . Advances in Cryptology-Eurocrypt 2003,LNCS 2656 [C ] . Berlin , 2003 . 345 - 359 .

MEIER W , PASALIC E , CARLET C . Algebraic attacks and decomposition of Boolean functions [A ] . Advances in Cryptology-Eurocrypt 2004,LNCS 3027 [C ] . Berlin,Springer-Verlag , 2004 . 474 - 491 .

CARLET C . Constructing balanced functions with optimal algebraic immunity [A ] . IEEE ISIT 2007 [C ] . Nice,France , 2007 . 451 - 455 .

CARLET C , FENG K . An infinite class of balanced functions with optimal algebraic immunity,good immunity to fast algebraic attacks and good nonlinearity [A ] . Advances in Cryptology-Asiacrypt 2008,LNCS 5350 [C ] . Berlin : Springer-Verlag , 2008 . 425 - 440 .

DALAI D , MAITRA S , SARKAR S . Basic theory in construction of Boolean functions with maximum possible annihilator immunity [J ] . Des.Codes Cryptogr , 2006 , 40 ( 1 ): 41 - 58 .

WANG Q , PENG J , KAN H , et al . Constructions of cryptographically significant Boolean functions using primitive polynomials [J ] . IEEE Trans Inf Theory , 2010 , 56 ( 6 ): 3048 - 3053 .

TU Z , DENG Y . A conjecture on binary string and its applications on constructing Boolean functions of optimal algebraic immunity [J ] . Des.Codes Cryptogr , 2011 , 60 ( 1 ): 1 - 14 .

TANG D , CARLET C , TANG X . Highly nonlinear Boolean functions with optimal algebraic immunity and good behavior against fast algebraic attacks [J ] . IEEE Trans Inf Theory , 2013 , 59 ( 1 ): 653 - 664 .

李雪莲 , 胡予濮 . 对具有高代数免疫度布尔函数的新型代数攻击 [J ] . 西安电子科技大学学报 , 2009 , 36 ( 4 ): 702 - 707 .

LI X L , HU Y P . Algebraic attack on symmetric Boolean functions with a high algebraic immunity [J ] . Journal of Xidian University , 2009 , 36 ( 4 ): 702 - 707 .

ZHANG X , PIEPRZYK J , ZHENG Y . On algebraic immunity and annihilators [A ] . ICISC 2006,LNCS 4296 [C ] . Berlin,Springer-Verlag , 2004 . 65 - 80 .

WANG C , CHEN X . On extended algebraic immunity [J ] . Des Codes Cryptogr , 2010 , 57 ( 3 ): 271 - 281 .

熊晓雯 , 屈龙江 , 李超 . 布尔函数的扩展代数免疫度 [J ] . 电子与信息学报 , 2011 , 33 ( 2 ): 284 - 288 .

XIONG X W , QU L J , LI C . On extended algebraic immunity of Boolean functions [J ] . Journal of Electronics ＆ Information Technology , 2011 , 33 ( 2 ): 284 - 288 .

CARLET C . Comment on constructions of cryptographically significant Boolean functions using primitive polynomials [J ] . IEEE Trans Inf Theory , 2011 , 57 ( 7 ): 4852 - 4853 .

LI N , QI W . Symmetric Boolean functions depending on an odd number of variables with maximum algebraic immunity [J ] . IEEE Trans Inf Theory , 2006 , 52 ( 5 ): 2271 - 2273 .

QU L , LI C , FENG K . A note on symmetric Boolean functions with maximum algebraic immunity in odd number of variables [J ] . IEEE Trans Inf Theory , 2007 , 53 ( 8 ): 2908 - 2910 .

PENG J , WU Q , KAN H . On symmetric Boolean functions with high algebraic immunity on even number of variables [J ] . IEEE Trans Inform Theory , 2011 , 57 ( 10 ): 7205 - 7220 .

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