| 具有最优代数免疫阶的一类新布尔函数的构造 |
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| 引用本文： | 董新锋,张文政,谯通旭,赵伟. 具有最优代数免疫阶的一类新布尔函数的构造[J]. 计算机工程与应用, 2010, 46(27): 85-87. DOI: 10.3778/j.issn.1002-8331.2010.27.023 |
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| 作者姓名： | 董新锋 张文政 谯通旭 赵伟 |
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| 作者单位： | 现代通信国家重点实验室，成都 610041 |
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| 基金项目： | 国防科技保密通信重点实验室基金 |
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| 摘 要： | 构造了一类至少具有次优代数免疫阶的布尔函数f，并利用级联的方法构造了一类具有最优代数免疫阶的布尔函数h。这类函数h不同于以前相关文献中所提出的最优代数免疫的布尔函数，给出了f的数目，并进一步讨论了h（偶数个变元的情况下）的非线性度，发现利用择多函数Fn构造的一类函数h非线性度达到Lobanov界。
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| 关 键 词： | 最优（次优）代数免疫阶 布尔函数 Walsh谱 非线性度 |
| 收稿时间： | 2009-11-20 |
| 修稿时间： | 2010-3-18 |
Construction of Boolean functions with optimal algebraic immunity |
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| DONG Xin-feng,ZHANG Wen-zheng,QIAO Tong-xu,ZHAO Wei. Construction of Boolean functions with optimal algebraic immunity[J]. Computer Engineering and Applications, 2010, 46(27): 85-87. DOI: 10.3778/j.issn.1002-8331.2010.27.023 |
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| Authors: | DONG Xin-feng ZHANG Wen-zheng QIAO Tong-xu ZHAO Wei |
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| Affiliation: | State Key Laboratory for Modern Communications，Chengdu 610041，China |
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| Abstract: | A class of Boolean functions f with suboptimal（or optimal） algebraic immunity is presented,by means of the second construction methods, a new class of Boolean functions h with optimal immunity is gotten.The h is different from what have been constructed before.The number of the functions f is given, the nonlinearity of the function h is discussed in the case of even number variables.Finally, the nonlinearity is discussed and that the nonlinearity of the function h constructed by means of the majority function Fn can make the Lobanov bound tight is found. |
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| Keywords: | （sub） optimal algebraic immunity Boolean functions walsh spectral nonlinearity |
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