| 一类代数免疫度达到最优的布尔函数的构造 |
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| 引用本文： | 孟 强,陈鲁生,符方伟.一类代数免疫度达到最优的布尔函数的构造[J].软件学报,2010,21(7):1758-1767. |
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| 作者姓名： | 孟 强 陈鲁生 符方伟 |
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| 作者单位： | 1. 南开大学,数学科学学院,天津,300071
2. 南开大学,陈省身数学研究所,天津,300071 |
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| 基金项目： | Supported by the National Natural Science Foundation of China under Grant No.60872025 (国家自然科学基金) |
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| 摘 要： | 给出了一种具有最优代数免疫度的偶数元布尔函数的构造,同时还给出了一种具有最优代数免疫度的平衡旋转对称偶数元布尔函数的构造.在构造过程中用到了线性代数和组合计数中的有关结论,这些函数对代数攻击均有很强的抵抗能力.构造的平衡旋转对称布尔函数还可用在Hash算法的轮函数中,增加了算法的安全性.
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| 关 键 词： | 代数攻击 代数免疫度 非线性度 旋转对称 布尔函数 |
| 收稿时间： | 2009/4/14 0:00:00 |
| 修稿时间： | 2009/8/26 0:00:00 |
Construction of Boolean Functions with Maximum Algebraic Immunity |
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| MENG Qiang,CHEN Lu-Sheng and FU Fang-Wei.Construction of Boolean Functions with Maximum Algebraic Immunity[J].Journal of Software,2010,21(7):1758-1767. |
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| Authors: | MENG Qiang CHEN Lu-Sheng and FU Fang-Wei |
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| Abstract: | This paper presents a construction of Boolean functions with the maximum algebraic immunity on even number of variables. It also gives a construction of balanced rotation symmetric Boolean functions with the maximum algebraic immunity on even number of variables. This paper uses some results of linear algebra and enumerative combinatorics in the constructions. These functions have strong resistance against algebraic attacks. The balanced rotation symmetric Boolean functions constructed can also be used in the construction of safer hashing functions. |
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| Keywords: | algebraic attack algebraic immunity nonlinearity rotation symmetric Boolean function |
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