Further properties of several classes of Boolean functions with optimum algebraic immunity
文献类型：期刊论文
| 作者 | Carlet, Claude2,3,4; Zeng, Xiangyong1,5; Li, Chunlei1; Hu, Lei6 |
| 刊名 | DESIGNS CODES AND CRYPTOGRAPHY
 |
| 出版日期 | 2009-09-01 |
| 卷号 | 52期号:3页码:303-338 |
| 关键词 | Boolean function Algebraic immunity Nonlinearity Balancedness Krawtchouk polynomial |
| ISSN号 | 0925-1022 |
| DOI | 10.1007/s10623-009-9284-0 |
| 英文摘要 | Based on a method proposed by the first author, several classes of balanced Boolean functions with optimum algebraic immunity are constructed, and they have nonlinearities significantly larger than the previously best known nonlinearity of functions with optimal algebraic immunity. By choosing suitable parameters, the constructed n-variable functions have nonlinearity 2(n-1) - (n-1 n/2 -1) + 2(n - 2 n/2 -2) / (n - 2) for even n >= 8 and 2(n-1) - (n - 1 n - 1/2) + Delta(n) for odd n, where Delta(n) is a function increasing rapidly with n. The algebraic degrees of some constructed functions are also discussed. |
| 资助项目 | National Science Foundation of China (NSFC)[60603012] ; National Science Foundation of China (NSFC)[60773134] ; State Key Laboratory of Information Security ; National 863 Project of China[2006AA01Z416] ; National Basic Research (973) Program of China[2007CB311201] |
| WOS研究方向 | Computer Science ; Mathematics |
| 语种 | 英语 |
| WOS记录号 | WOS:000266007400005 |
| 出版者 | SPRINGER |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/8322]  |
| 专题 | 中国科学院数学与系统科学研究院 |
| 通讯作者 | Zeng, Xiangyong |
| 作者单位 | 1.Hubei Univ, Fac Math & Comp Sci, Wuhan 430062, Peoples R China 2.Univ Paris 08, Dept Math, LAGA, F-93526 St Denis, France 3.Univ Paris 13, Dept Math, LAGA, F-93526 St Denis, France 4.CNRS, F-93526 St Denis, France 5.Chinese Acad Sci, State Key Lab Informat Secur, Grad Sch, Beijing 100049, Peoples R China 6.Chinese Acad Sci, Key Lab Math Mechanizat, Inst Syst Sci, AMSS, Beijing 100190, Peoples R China |
| 推荐引用方式 GB/T 7714 | Carlet, Claude,Zeng, Xiangyong,Li, Chunlei,et al. Further properties of several classes of Boolean functions with optimum algebraic immunity[J]. DESIGNS CODES AND CRYPTOGRAPHY,2009,52(3):303-338. |
| APA | Carlet, Claude,Zeng, Xiangyong,Li, Chunlei,&Hu, Lei.(2009).Further properties of several classes of Boolean functions with optimum algebraic immunity.DESIGNS CODES AND CRYPTOGRAPHY,52(3),303-338. |
| MLA | Carlet, Claude,et al."Further properties of several classes of Boolean functions with optimum algebraic immunity".DESIGNS CODES AND CRYPTOGRAPHY 52.3(2009):303-338. |
入库方式： OAI收割
来源：数学与系统科学研究院
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