| 关于高阶e导数性质之研究 |
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| 引用本文： | 邱晓华,陈偕雄.关于高阶e导数性质之研究[J].浙江大学学报(理学版),2013,40(4):424-427. |
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| 作者姓名： | 邱晓华 陈偕雄 |
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| 作者单位： | 1. 金华职业技术学院信息工程学院,浙江金华321017;浙江大学信息工程与电子学系,浙江杭州310027
2. 浙江大学信息工程与电子学系,浙江杭州,310027 |
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| 摘 要： | e导数在组合电路故障检测、揭示H布尔函数的密码学性质和确保密码学系统安全性中具有重要的作用.首先阐述了布尔函数1阶e导数的定义和性质，在此基础上，提出了布尔函数高阶e导数的概念，参照布尔代数2阶及k 阶布尔差分的定义，给出了2阶及k 阶e导数的定义与性质，并给出了证明.将1阶e导数性质推广至n 变量布尔函数任意k 阶e导数，推动与完善了关于e导数的研究.
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| 关 键 词： | style="font-family: 宋体 font-size: 10.5pt mso-bidi-font-family: 宋体 mso-ansi-language: EN-US mso-fareast-language: ZH-CN mso-bidi-language: 布尔函数AR-SA">布尔函数 " target="_blank">lang="EN-US"> e导数 " target="_blank">lang="EN-US"> 高阶 e导数lang="EN-US">e导数 " target="_blank">lang="EN-US"> 特殊运算 |
| 收稿时间： | 2012-03-30 |
Research on properties of high-order e-derivative |
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| QIU Xiao-hua
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CHEN Xie-xiong.Research on properties of high-order e-derivative[J].Journal of Zhejiang University(Sciences Edition),2013,40(4):424-427. |
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| Authors: | QIU Xiao-hua CHEN Xie-xiong |
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| Affiliation: | 1. Information Engineering College of Jinhua Polytechnic, Jinhua 321017, Zhejiang Province, China; 2. Department of Information and Electronic Engineering, Zhejiang University, Hangzhou 310027, China) |
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| Abstract: | The e-derivative of Boolean functions plays an important role on detecting the combinational circuits, revea- ling the cryptographic properties of H-Boolean functions, as well as guaranteeing the security of cryptosystem. The definitions and properties of the first-order e-derivative of Boolean functions are described. Based upon it, the con- ception of high-order e derivative of Boolean functions is proposed, By refering to the definitions of the second-order and k-order Boolean difference on Boolean algebra, it discusses the definitions and properties of the second-order and k-order e-derivative of Boolean functions, and the proofs of the properties are given. The results develope the prop- erties of first-order e-derivative of Boolean functions to arbitrary k-order e-derivative of n-variable Boolean functions, and improve the research of e-derivative of Boolean functions. |
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| Keywords: | Boolean function e-derivative high-order e-derivative special operation |
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