On algebraic immunity of trace inverse functions on finite fields of characteristic two

doi:10.1007/s11424-016-5208-z

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	On algebraic immunity of trace inverse functions on finite fields of characteristic two
	Feng Xiutao1,2 ; Gong Guang 3
刊名	JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY
	2016-02-01
卷号	29 期号:1 页码:272-288
关键词	Algebraic immunity boolean functions fast algebraic attacks trace inverse functions
ISSN号	1009-6124
DOI	10.1007/s11424-016-5208-z
英文摘要	The trace inverse functions Tr(lambda x (-1)) over the finite field are a class of very important Boolean functions and are used in many stream ciphers such as SFINKS, RAKAPOSHI, the simple counter stream cipher (SCSC) presented by Si W and Ding C (2012), etc. In order to evaluate the security of those ciphers in resistance to (fast) algebraic attacks, the authors need to characterize algebraic properties of Tr(lambda x (-1)). However, currently only some bounds on algebraic immunity of Tr(lambda x (-1)) are given in the public literature, for example, the NGG upper bound and the Bayev lower bound, etc. This paper gives the exact value of the algebraic immunity of Tr(lambda x (-1)) over , that is, , where n a parts per thousand yen 2, lambda a and lambda not equal 0, which shows that Dalai's conjecture on the algebraic immunity of Tr(lambda x (-1)) is correct. What is more, the authors demonstrate some weak properties of Tr(lambda x (-1)) against fast algebraic attacks.
资助项目	National Natural Science Foundation of China[61572491] ; 973 Program[2011CB302401] ; SKLOIS in Institute of Information Engineering, Chinese Academy of Sciences[2015-MS-03]
WOS研究方向	Mathematics
语种	英语
出版者	SPRINGER HEIDELBERG
WOS记录号	WOS:000370162300017
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/22026]
专题	系统科学研究所
通讯作者	Feng Xiutao; Gong Guang
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 3.Univ Waterloo, Dept Elect & Comp Engn, Waterloo, ON N2L 3G1, Canada
推荐引用方式 GB/T 7714	Feng Xiutao,Gong Guang. On algebraic immunity of trace inverse functions on finite fields of characteristic two[J]. JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY,2016,29(1):272-288.
APA	Feng Xiutao,&Gong Guang.(2016).On algebraic immunity of trace inverse functions on finite fields of characteristic two.JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY,29(1),272-288.
MLA	Feng Xiutao,et al."On algebraic immunity of trace inverse functions on finite fields of characteristic two".JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY 29.1(2016):272-288.