recentresultsonconstructingbooleanfunctionswithpotentiallyoptimalalgebraicimmunitybasedondecompositionsoffinitefields

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	recentresultsonconstructingbooleanfunctionswithpotentiallyoptimalalgebraicimmunitybasedondecompositionsoffinitefields
	Liu Zhuojun1 ; Wu Baofeng 2
	2019
发表期刊	journalofsystemsscienceandcomplexity
ISSN	1009-6124
卷号	32 期号:1 页码:356
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.
语种	英语
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/47853
专题	系统科学研究所
作者单位	1.中国科学院数学与系统科学研究院 2.中国科学院信息工程研究所
推荐引用方式 GB/T 7714	Liu Zhuojun,Wu Baofeng. recentresultsonconstructingbooleanfunctionswithpotentiallyoptimalalgebraicimmunitybasedondecompositionsoffinitefields[J]. journalofsystemsscienceandcomplexity,2019,32(1):356.
APA	Liu Zhuojun,&Wu Baofeng.(2019).recentresultsonconstructingbooleanfunctionswithpotentiallyoptimalalgebraicimmunitybasedondecompositionsoffinitefields.journalofsystemsscienceandcomplexity,32(1),356.
MLA	Liu Zhuojun,et al."recentresultsonconstructingbooleanfunctionswithpotentiallyoptimalalgebraicimmunitybasedondecompositionsoffinitefields".journalofsystemsscienceandcomplexity 32.1(2019):356.