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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