2003, Volume 5, Issue 7
Strategic Study of CAE >> 2003, Volume 5, Issue 7
The Constructions of Cryptographic Functions
Department of Information Research, Information Engineering University, Zhengzhou 450002, China
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Abstract
This paper investigates a decomposition formula of Walsh spectrum for a class of Boolean functions. On the basis of this formula, the constructions of some cryptographic functions, such as resilient functions, Bent functions and H-Boolean function are studied H-Boolean function is a class of Boolean functions of much importance to the applications of coding theory and satisfying the strict Avalanche criterion.
Keywords
Walsh spectrum ; decomposition formula of Walsh spectrum ; Bent function ; resilient function ; strict avalanche criterion
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References
[ 1 ] SiegenthalerT .Correlation—immunityofthecombiningfunctionsforcryptographicapplications[J]. IEEETrans, onInform.Theory, 1984, IT -30 (5) :776～780
[ 2 ] RothausOS .OnBentfunctions[J].JCombinatorialTheory (SerA) , 1976, 20:300～305
[ 3 ] CamionP , CanleautA .Constructionoft resilientfunctionsoverafinitealphabet[M ].AdvancesinCryptology, Eurocrypt96, SpringerVerlag, 1996.283～293
[ 4 ] ZhangXM , ZhengY .Onnonlinearresilientfunctions[M ].AdvancesinCryptology, Eurocrypt95, SpringerVerlag, 1995.274～288
[ 5 ] YarlagaddaR , HersheyJE .AnalysisandsynthesisofBentsequences[A].IEEEProceeding (PartE) [C], 1989, 136:112～123
[ 6 ] 李世取, 曾本胜, 廉玉忠, 等.密码学中的逻辑函数[M].北京:北京中软出版公司, 2003
[ 7 ] 曾本胜, 李世取, 李 坤.一类布尔函数Walsh谱的分解式及其应用[A ].密码学进展—CHINACRYPT’98[M ].北京:科学出版社, 1998.217～220 link1
[ 8 ] 刘文芬.关于具有相关免疫性的多值逻辑函数的性质和构造研究[D].郑州:解放军信息工程学院, 1999
[ 9 ] 李世取, 曾本胜, 廉玉忠.布尔随机向量联合分布的分解式及其应用[J].通信学报, 1998, (11) :61～64 link1
[10] 杨义先, 林须端.编码密码学[M ].北京:人民邮电出版社, 1992 link1
[11] 冯登国.频谱理论及其在密码学中的应用[M ].北京:科学出版社, 2000 link1
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