廣義向量Bent函數(shù)
Generalized Vector Bent Functions
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摘要: 該文完善并拓展了Nyberg(1991)的關(guān)于廣義向量Bent函數(shù)性質(zhì)的結(jié)論,相應(yīng)于Nyberg給出的正則廣義向量Bent函數(shù),提出了負(fù)則的廣義向量Bent函數(shù)的概念:得到有偶數(shù)個(gè)輸入的負(fù)則的廣義向量Bent函數(shù)輸出維數(shù)也不大于輸入維數(shù)的一半;證明了奇數(shù)個(gè)輸入的正則和負(fù)則的廣義向量Bent函數(shù)都不存在,這些結(jié)果的給出,可使密碼設(shè)計(jì)者避免一味去尋找某類不存在的函數(shù).該文還給出了廣義向量Bent函數(shù)的一種遞歸構(gòu)造法.Abstract: This paper generalizes the conclusion of Perfect nonlinear S-boxes by Nyberg(1991), and introduces the conception of inverse regular generalized vector Bent function. It shows that for inverse regular generalized vector Bent function f(m) with even variables, m is no more than half of?. It also shows that when the input dimension n is odd, the regular generalized vector Bent function and the inverse regular generalized vector Bent function do not exist. This may prevent the cryptology designer from seeking the inexistent function. A method for recursively constructing vector generalized Bent function is presented.
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馮登國(guó),吳文玲.分組密碼的設(shè)計(jì)與分析.北京:清華大學(xué)出版社,2000:1-2.[2]丁存生,肖國(guó)鎮(zhèn).流密碼學(xué)及其應(yīng)用.北京:國(guó)防工業(yè)出版社,1994,第六章.[3]Rothaus O S. On Bent functions[J].J. Combinatorial Theory.1976,20 (A):300-[4]Zheng Y, Pieprzyk J, Seberr J Y. HAVAL-A one way hashing algorithm with variable length output, Advances in Cryptology-AUSCRYPT92, Queens land: Springer-Verlag,1993:83 - 104.[5]許成謙,楊義先,胡正名.Bent互補(bǔ)函數(shù)族的性質(zhì)和構(gòu)造方法.電子學(xué)報(bào),1997,25(10):52-56.[6]馮登國(guó).頻譜理論及其在密碼學(xué)中的應(yīng)用.北京:科學(xué)出版社,2000:118-120.[7]Kumar P, Scholtz R, Welch L. Generalized Bent functions and their properties[J].d Combinatorial Theory.1985, 40(A):90-[8]Nyberg K. Perfect nonlinear S-boxes.[J].Advances in CryptologyEurocrypt91, Brighton: Springer-Verlag.1991,:-[9]柯召,孫琦.數(shù)論講義.北京:高等教育出版社,1987,第四章.[10]張文英,滕吉紅,李世取.布爾函數(shù)的譜分解式及其在多維Bent函數(shù)構(gòu)造中的應(yīng)用[A].第三屆中國(guó)信息和通信安全學(xué)術(shù)會(huì)議論文集CCICS 2003,武漢,科學(xué)出版社,2003:290-296. -
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