KMS Of Academy of mathematics and systems sciences, CAS
On algebraic immunity of trace inverse functions on finite fields of characteristic two | |
Feng Xiutao1,2; Gong Guang3 | |
2016-02-01 | |
Source Publication | JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY |
ISSN | 1009-6124 |
Volume | 29Issue:1Pages:272-288 |
Abstract | 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. |
Keyword | Algebraic immunity boolean functions fast algebraic attacks trace inverse functions |
DOI | 10.1007/s11424-016-5208-z |
Language | 英语 |
Funding Project | National Natural Science Foundation of China[61572491] ; 973 Program[2011CB302401] ; SKLOIS in Institute of Information Engineering, Chinese Academy of Sciences[2015-MS-03] |
WOS Research Area | Mathematics |
WOS Subject | Mathematics, Interdisciplinary Applications |
WOS ID | WOS:000370162300017 |
Publisher | SPRINGER HEIDELBERG |
Citation statistics | |
Document Type | 期刊论文 |
Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/22027 |
Collection | 系统科学研究所 |
Corresponding Author | Feng Xiutao; Gong Guang |
Affiliation | 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 |
Recommended Citation 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. |
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