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Recent Results on Constructing Boolean Functions with (Potentially) Optimal Algebraic Immunity Based on Decompositions of Finite Fields
Liu Zhuojun1; Wu Baofeng2
2019-02-01
Source PublicationJOURNAL OF SYSTEMS SCIENCE & COMPLEXITY
ISSN1009-6124
Volume32Issue:1Pages:356-374
AbstractBoolean 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.
KeywordAdditive decomposition algebraic immunity Boolean function multiplicative decomposition Tu-Deng conjecture
DOI10.1007/s11424-019-8346-2
Language英语
Funding ProjectNational Key Research and Development Program of China[2016YFB0800401]
WOS Research AreaMathematics
WOS SubjectMathematics, Interdisciplinary Applications
WOS IDWOS:000458795500018
PublisherSPRINGER HEIDELBERG
Citation statistics
Cited Times:1[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/32654
Collection系统科学研究所
Affiliation1.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
Recommended Citation
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.
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