| 代数免疫度为1的布尔函数 |
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| 引用本文： | 涂自然,邓映蒲.代数免疫度为1的布尔函数[J].系统科学与数学,2011,31(5):512-518. |
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| 作者姓名： | 涂自然 邓映蒲 |
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| 作者单位： | 1. 河南科技大学数学与统计学院,洛阳,471003
2. 中国科学院数学与系统科学研究院数学机械化重点实验室,北京,100190 |
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| 基金项目： | 国家自然科学基金(11071285,61003234,60821002,10971250); 973计划(2011CB302401)资助课题 |
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| 摘 要： | 布尔函数的代数免疫度是在流密码的代数攻击中所产生的重要概念.研究了代数免疫度为1的布尔函数,得到的主要结果有:对代数免疫度为1的布尔函数给出了一个谱刻画,给出了其个数的精确计数公式,最后给出了此类函数的非线性度的紧的上界.
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| 关 键 词： | 代数攻击 代数免疫度 布尔函数 非线性度 |
BOOLEAN FUNCTIONS WITH ALGEBRAIC IMMUNITY ONE |
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| TU Ziran,DENG Yingpu.BOOLEAN FUNCTIONS WITH ALGEBRAIC IMMUNITY ONE[J].Journal of Systems Science and Mathematical Sciences,2011,31(5):512-518. |
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| Authors: | TU Ziran DENG Yingpu |
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| Institution: | TU Ziran (Faculty of Science,Henan University of Science and Technology,Luoyang 471003) DENG Yingpu (Key Laboratory of Mathematics Mechanization,Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing 100190) |
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| Abstract: | Algebraic immunity of Boolean functions is a very important concept in algebraic attacks of stream cipher.In this paper,we have a good understanding for Boolean functions with algebraic immunity one.We give some results about these functions,including a Walsh spectrum characterization,an explicit counting formula and a tight upper bound for nonlinearity of Boolean functions with algebraic immunity one. |
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| Keywords: | Algebraic attack algebraic immunity Boolean functions nonlinearity |
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