| 一种广义Bent函数非存在性证明 |
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| 引用本文： | 张风雨,;张习勇,;王春铭,;李玉娟.一种广义Bent函数非存在性证明[J].郑州大学学报(自然科学版),2014(3):32-35. |
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| 作者姓名： | 张风雨 ;张习勇 ;王春铭 ;李玉娟 |
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| 作者单位： | [1]国家数字交换系统工程技术研究中心,河南郑州450002; [2]信息保障技术重点实验室,北京100072 |
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| 基金项目： | 基金项目：国家自然科学基金资助项目,编号61372121,60803154,信息保障技术重点实验室开放基金,编号KJ-13-108. |
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| 摘 要： | 广义Bent函数具有良好的组合学和密码学性质,在通信、密码学等领域具有重要的应用价值.将Z2p上的广义Bent函数等价地转换为一种分裂型相对差集,通过集合分解,证明了这类相对差集的不存在性,从而用一种新方法证明了Z2p上不存在广义Bent函数.
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| 关 键 词： | 广义Bent函数 相对差集 群环 |
A Non-existence Proof of a Generalized Bent Function |
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| Institution: | ZHANG Feng-yu, ZHANG Xi-yong , WANG Chun-ming, LI Yu-juan (1. National Digital Switching System Engineering ＆ Technological R＆D Center, Zhengzhou 450002, China) (2. Science and Technology on Information Assurance Laboratory, Beijing 100072, China) |
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| Abstract: | Generalized Bent functions had good combination and cryptography properties. Thus this kind of functions could be used in the field of communication, cryptography and other fields. The equivalent relationship between Bent functions on Z2p and a kind of splitting relative difference sets was established. The non-existence of this kind of relative difference sets by means of factoring the RDS was thus proven, which gave a different method of proving the non-existence of such Bent functions. |
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| Keywords: | generalized Bent functions relative difference sets group ring |
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