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具有最大代数免疫阶的布尔函数的新构造 被引量：2

New Construction of Boolean Function with Maximum Algebraic Immunity
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摘要 针对密码学中布尔函数的构造需求,利用布尔函数的代数标准型,分析了布尔函数不存在次数低于m的非零零化子的充分条件,得到布尔函数达到最大代数免疫阶的条件,从而构造了一类具有最高代数免疫阶的布尔函数,并对所构造函数的平衡性和计数问题进行了分析。 Focusing on algebraic normal form and the construction requirements of Boolean function,the conditions that Boolean function f does not exist annihator with deg（f）≤m are analysed and the sufficient conditions satisfied by Boolean function f with maximum algebraic immunity are obtained.Therefore a class of Boolean functions with optimal algebraic immunity are constructed,and the balanceness and count of the constructed functions are discussed.
作者 曹浩 魏仕民 卓泽鹏 王会歌
机构地区 安徽科技学院理学院 淮北师范大学
出处 《北京大学学报（自然科学版）》 EI CAS CSCD 北大核心 2010年第5期704-708,共5页 Acta Scientiarum Naturalium Universitatis Pekinensis
基金 国家自然科学基金(60573026) 安徽省自然科学研究项目(KJ2010B059) 安徽科技学院引进人才项目(ZRC2008169)资助
关键词 布尔函数 代数标准型 代数免疫阶 Boolean function algebraic normal form algebraic immunity
分类号 TN918 [电子电信—通信与信息系统]
作者简介 E-mail： caohao2000854@ 163. com
  • 相关文献

参考文献11

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二级参考文献28

  • 1张文英,武传坤,于静之.密码学中布尔函数的零化子[J].电子学报,2006,34(1):51-54. 被引量：16
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共引文献14

同被引文献14

  • 1Canteaut A. Invited Talk: Open Problems Related to Algebraic Attacks on Stream Ciphers[C]//Proc. of International Conference on Coding and Cryptography. Berlin, Germany: Springer-Verlag, 2005: 120-134.
  • 2Carlet C, Dalai D K, Maitra S, et al. Cryptographic Properties and Structure of Boolean Functions with Full Algebraic Immunity[C]//Proc. of IEEE International Symposium on Information Theory. [S. l.]: IEEE Press, 2006: 734-738.
  • 3Charpin C. Normal Boolean Functions[J]. Journal of Complexity, 2004, 20(2-3): 245-265.
  • 4Zheng Yuliang, Zhang Xiaomo, Imai H. Restriction, Terms and Nonlinearity of Boolean Functions[J]. Theoretical Computer Science, 1999, 226(1-2): 207-223.
  • 5Rizomiliotis P. On the Resistance of Boolean Functions Against Algebraic Attacks Using Univariate Polynomial Representation[J]. IEEE Trans. on Information Theory, 2010, 56(8): 4014-4024.
  • 6Limniotis K, Kolokotronis N, Kalouptsidis N. Modifying Boolean Functions to Ensure Maximum Algebraic Immu- nity[EB/OL]. (2012-03-01). http://ePrint.iacr.org/2012/046.
  • 7张卫国,丁勇,张宁,肖国镇.代数免疫布尔函数的一个特征[J].北京邮电大学学报,2007,30(5):55-57. 被引量：9
  • 8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. 被引量：4
  • 9莫骄,温巧燕.具有最高代数免疫阶的布尔函数的构造[J].北京邮电大学学报,2009,32(4):73-76. 被引量：5
  • 10陈银冬,陆佩忠.偶数变元代数免疫最优布尔函数的构造方法[J].通信学报,2009,30(11):64-70. 被引量：5

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北京大学学报（自然科学版）
2010年 第5期

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