Recent Results on Constructing Boolean Functions with (Potentially) Optimal Algebraic Immunity Based on Decompositions of Finite Fields
文献类型：期刊论文
| 作者 | Liu Zhuojun1 ; Wu Baofeng2
|
| 刊名 | JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY
 |
| 出版日期 | 2019-02-01 |
| 卷号 | 32期号:1页码:356-374 |
| 关键词 | Additive decomposition algebraic immunity Boolean function multiplicative decomposition Tu-Deng conjecture |
| ISSN号 | 1009-6124 |
| DOI | 10.1007/s11424-019-8346-2 |
| 英文摘要 | Boolean functions with optimal algebraic immunity (OAI functions) are important cryptographic primitives in the design of stream ciphers. During the past decade, a lot of work has been done on constructing such functions, among which mathematics, especially finite fields, play an important role. Notably, the approach based on decompositions of additive or multiplicative groups of finite fields turns out to be a very successful one in constructing OAI functions, where some original ideas are contributed by Tu and Deng (2012), Tang, et al. (2017), and Lou, et al. (2015). Motivated by their pioneering work, the authors and their collaborators have done a series of work, obtaining some more general constructions of OAI functions based on decompositions of finite fields. In this survey article, the authors review our work in this field in the past few years, illustrating the ideas for the step-by-step generalizations of previous constructions and recalling several new observations on a combinatorial conjecture on binary strings known as the Tu-Deng conjecture. In fact, the authors have obtained some variants or more general forms of Tu-Deng conjecture, and the optimal algebraic immunity of certain classes of functions we constructed is based on these conjectures. |
| 资助项目 | National Key Research and Development Program of China[2016YFB0800401] |
| WOS研究方向 | Mathematics |
| 语种 | 英语 |
| WOS记录号 | WOS:000458795500018 |
| 出版者 | SPRINGER HEIDELBERG |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/32653]  |
| 专题 | 系统科学研究所 |
| 通讯作者 | Wu Baofeng |
| 作者单位 | 1.Chinese Acad Sci, Acad Math & Syst Sci, Key Lab Math Mechanizat, Beijing 100190, Peoples R China 2.Chinese Acad Sci, Inst Informat Engn, State Key Lab Informat Secur, Beijing 100093, Peoples R China |
| 推荐引用方式 GB/T 7714 | Liu Zhuojun,Wu Baofeng. Recent Results on Constructing Boolean Functions with (Potentially) Optimal Algebraic Immunity Based on Decompositions of Finite Fields[J]. JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY,2019,32(1):356-374. |
| APA | Liu Zhuojun,&Wu Baofeng.(2019).Recent Results on Constructing Boolean Functions with (Potentially) Optimal Algebraic Immunity Based on Decompositions of Finite Fields.JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY,32(1),356-374. |
| MLA | Liu Zhuojun,et al."Recent Results on Constructing Boolean Functions with (Potentially) Optimal Algebraic Immunity Based on Decompositions of Finite Fields".JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY 32.1(2019):356-374. |
入库方式： OAI收割
来源：数学与系统科学研究院
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