布尔函数的扩展代数免疫度

熊晓雯; 屈龙江; 李超

doi:10.3724/SP.J.1146.2010.00470

布尔函数的扩展代数免疫度

doi: 10.3724/SP.J.1146.2010.00470

熊晓雯^{*① 屈龙江,},
屈龙江,
李超

基金项目:

国家自然科学基金(60803156)和移动通信国家重点实验室开放研究基金(W200807)资助课题

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- 被引次数: 0
出版历程
- 收稿日期: 2010-05-11
- 修回日期: 2010-09-14
- 刊出日期: 2011-02-19

On Axtended Algebraic Immunity of Boolean Functions

Xiong Xiao-Wen^{*① 屈龙江
,},
Qu Long-Jiang,
Li Chao

摘要

摘要: 该文研究了布尔函数的扩展代数免疫度，首先给出了布尔函数的扩展代数免疫度与其代数免疫度相等的一个充分必要条件；然后讨论了两类具有最大代数免疫度的布尔函数的扩展代数免疫度，给出了其扩展代数免疫度也达到最大值的充分必要条件；最后基于代数补元素的思想，给出了布尔函数零化子结构的一种新刻画。
- 密码学 /
- 布尔函数 /
- 零化子 /
- 代数攻击 /
- 代数免疫度
Abstract: Extend algebraic immunity of Boolean functions are investigated in this paper. Firstly, a sufficient and necessary condition is presented that algebraic immunity of a Boolean function equals to its extended algebraic immunity. Secondly, it is proved that two classes of Boolean functions with maximum algebraic immunity also have optimal extended algebraic immunity. Finally, it is analyzed that the structure of the annihilators of Boolean functions with the algebraic complement.
- Cryptography /
- Boolean functions /
- annihilators /
- Algebraic attacks /
- Algebraic immunity

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参考文献(1)

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