| 引用本文: | 杜育松,张方国.关于Tu-Deng函数的一个注记.[J].国防科技大学学报,2012,34(2):18-20,28.[点击复制] |
| DU Yusong,ZHANG Fangguo.A note on the Tu-Deng function[J].Journal of National University of Defense Technology,2012,34(2):18-20,28[点击复制] |
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| 关于Tu-Deng函数的一个注记 |
| 杜育松1,2, 张方国1,3 |
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(1.中山大学 信息科学与技术学院，广东 广州 510006;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;3.中国科学院 软件研究所，北京 100190)
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| 摘要: |
| 2009年，Tu和Deng在一个组合猜想成立的基础上，构造了同时具有最优代数免疫性、最优代数次数和高非线性度的一类偶数元布尔函数。这类函数被称为Tu-Deng函数。基于同一猜想，Tu和Deng又构造了同时具有次最优代数免疫性、最优代数次数和较高非线性度的一类偶数元的1-阶弹性函数。通过研究由Tu-Deng函数导出的两个布尔函数的级联的密码学性质，在Tu-Deng猜想成立的基础上，给出一类奇数元的1-阶弹性布尔函数。这类函数同时具有次最优代数免疫性、最优代数次数和较高非线性度。 |
| 关键词: 流密码 布尔函数 代数免疫度 非线性度 弹性函数 |
| DOI： |
| 投稿日期：2011-07-28 |
| 基金项目:国家自然科学基金资助项目（61070168, 10971246, 61003244, 60803135）；网络安全与密码技术福建省高校重点实验室开放课题资助项目（2011008） |
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| A note on the Tu-Deng function |
| DU Yusong1,2, ZHANG Fangguo1,3 |
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(1.School of Information Science and Technology, Sun Yat-sen University, Guangzhou 510006, China;2.Key Lab of Network Security and Cryptology, Fujian Normal University, Fuzhou 350007, China;3.Institute of Software, Chinese Academy of Sciences, Beijing 100190, China)
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| Abstract: |
| In 2009, based on a combinatorial conjecture, Tu and Deng constructed a class of Boolean functions in even variables with optimal algebraic immunity, optimal algebraic degree and good nonlinearity. This class of functions is called the Tu-Deng function. Based on the same conjecture, they also proposed a class of resilient functions in even variables with suboptimal algebraic immunity, optimal algebraic degree and good nonlinearity. By studying the cryptographic properties of the concatenation of two Boolean functions derived from the Tu-Deng function, based on Tu-Deng's conjecture, a class of resilient Boolean functions in odd variables is proposed. This class of functions has suboptimal algebraic immunity, optimal algebraic degree and good nonlinearity. |
| Keywords: stream cipher Boolean function algebraic immunity nonlinearity resiliency |
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