| 引用本文: | 屈龙江,李强,李超.布尔函数的Walsh谱绝对值分布及其性质研究.[J].国防科技大学学报,2008,30(3):86-89.[点击复制] |
| QU Longjiang,LI Qiang,LI Chao.On the Absolute Values Distribution of the Walsh Spectrums of Boolean Functions and Their Properties[J].Journal of National University of Defense Technology,2008,30(3):86-89[点击复制] |
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| 布尔函数的Walsh谱绝对值分布及其性质研究 |
| 屈龙江1, 李强1, 李超1,2 |
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(1.国防科技大学 理学院，湖南 长沙 410073;2.福建师范大学 网络安全与密码技术重点实验室，福建 福州 350007)
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| 摘要: |
| 提出并研究了布尔函数的Walsh谱绝对值分布。指出布尔函数Walsh谱绝对值分布在仿射变换下的不变性，计算了n(n≤5)元布尔函数的Walsh谱绝对值分布，研究了Walsh谱绝对值分布与Walsh谱支撑和Walsh谱中非零取值个数以及其他一些密码学难题的联系，最后研究了布尔函数的Walsh谱绝对值分布的大小。 |
| 关键词: 布尔函数 Walsh谱绝对值分布 仿射等价类 Walsh谱支撑 Walsh谱非零取值个数 |
| DOI： |
| 投稿日期：2007-11-10 |
| 基金项目:国家自然科学基金资助项目(60573028)；国防科技大学校预研基金资助项目(JC07-02-03)；福建师范大学网络安全与密码技术重点实验室开放课题资助项目(07A0003) |
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| On the Absolute Values Distribution of the Walsh Spectrums of Boolean Functions and Their Properties |
| QU Longjiang1, LI Qiang1, LI Chao1,2 |
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(1.College of Science, National Univ. of Defense Technology, Changsha 410073, China;2.Key Lab of Network Security and Cryptology, Fujian Normal Univ., Fuzhou 350007, China)
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| Abstract: |
| The absolute value distribution of the Walsh spectrums of Boolean functions is presented and studied. The absolute value distribution of the Walsh spectrum is invariant under affine transformations. Then Walsh spectrums' absolute value distributions of all n-variable Boolean functions are obtained for. The relationships of the absolute value distributions of the Walsh spectrums and the support of the Walsh spectrums and the number of nonzero values of the Walsh spectrums and other problems are studied. Finally, the size of the absolute value distribution of the Walsh spectrum of Boolean functions is studied. |
| Keywords: Boolean function the absolute value distribution of Walsh spectrum affine equivalent class Walsh support number of the nonzero values of Walsh spectrum |
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