| PS 类Bent函数的一种构造方法 |
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| 引用本文： | 常祖领,陈鲁生,符方伟.PS 类Bent函数的一种构造方法[J].电子学报,2004,32(10):1649-1653. |
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| 作者姓名： | 常祖领 陈鲁生 符方伟 |
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| 作者单位： | 1. 北京邮电大学理学院,北京 100876;2. 南开大学数学科学学院,天津 300071 |
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| 基金项目： | 国家自然科学基金，教育部跨世纪优秀人才培养计划，教育部优秀青年教师资助计划 |
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| 摘 要： | PS 类bent函数类是所有2(n/2)-1或2(n/2)-1+1个Fn2的"不交的" n 2 维子空间的指示函数的模2和所组成的函数的集合.这些函数具有很好的代数结构并在密码学中有很多应用.如何来刻画 PS bent函数的代数范式一直是公开的难题.构造 PS 类bent函数关键在于如何将Fn2划分为2n/2+1个 n 2 维子空间.本文给出一种划分的方法,从而构造出 PS 类bent函数,并给出了对应的代数范式.
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| 关 键 词： | Bent函数 代数范式 Galois域 线性化多项式 |
| 文章编号： | 0372-2112(2004)10-1649-05 |
| 收稿时间： | 2002-12-17 |
One Method for Constructing Bent Functions of Class PS |
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| CHANG Zu-ling ,CHEN Lu-sheng,FU Fang-wei.One Method for Constructing Bent Functions of Class PS[J].Acta Electronica Sinica,2004,32(10):1649-1653. |
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| Authors: | CHANG Zu-ling CHEN Lu-sheng FU Fang-wei |
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| Affiliation: | 1. Scholl of Science,Beijing University of Posts and Telecommunications,Beijing 100876,China;2. College of Mathematical Science,Nankai University,Tianjin 300071,China |
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| Abstract: | The class of PS bent functions is one interesting class of bent functions,they have good algebraic structure and have many applications in cryptography.They are also useful for studying the general structure of bent functions.Unfortunately,the construction of PS bent functions is theoretic,it is still an open problem to characterize the algebraic normal forms of PS bent functions.In this paper we study the properties of such functions,and one method to construct PS bent functions and the corresponding algebraic normal forms are provided. |
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| Keywords: | bent function algebraic normal form Galois field linearized polynomial |
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