Recent Results on Constructing Boolean Functions with (Potentially) Optimal Algebraic Immunity Based on Decompositions of Finite Fields

doi:10.1007/s11424-019-8346-2

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	Recent Results on Constructing Boolean Functions with (Potentially) Optimal Algebraic Immunity Based on Decompositions of Finite Fields
	Liu Zhuojun1 ; Wu Baofeng 2
	2019-02-01
发表期刊	JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY
ISSN	1009-6124
卷号	32 期号:1 页码:356-374
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.
关键词	Additive decomposition algebraic immunity Boolean function multiplicative decomposition Tu-Deng conjecture
DOI	10.1007/s11424-019-8346-2
语种	英语
资助项目	National Key Research and Development Program of China[2016YFB0800401]
WOS研究方向	Mathematics
WOS类目	Mathematics, Interdisciplinary Applications
WOS记录号	WOS:000458795500018
出版者	SPRINGER HEIDELBERG
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/32654
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.