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星对偶
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     star
    
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     Star
     展台
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     On Antithesis
     浅谈对偶
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     ) antithesis is in (L, (?)
     )对偶于(L,(?)
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     The Dual Star Semimodules and the Reflexive Star Semimodules
     对偶幺半模与自反幺半模
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The algorithm of AES is restated on exponential domain to reveal its properties. The unique nonlinear operation of AES, i.e., the inverse of multiplication becomes linear. However, the linear operation XOR induces a nonlinear operation ∨ on exponential domain. Moreover,the operation ∨ is represented by star-dual operation and addition modulo 255,the law of star-dual operation is obtained, and the randomness of ∨-operation and star-dual operation is limited and put into a subset including nine elements. A new...

The algorithm of AES is restated on exponential domain to reveal its properties. The unique nonlinear operation of AES, i.e., the inverse of multiplication becomes linear. However, the linear operation XOR induces a nonlinear operation ∨ on exponential domain. Moreover,the operation ∨ is represented by star-dual operation and addition modulo 255,the law of star-dual operation is obtained, and the randomness of ∨-operation and star-dual operation is limited and put into a subset including nine elements. A new framework is given for advanced cryptanalysis.

在指数域上重述AES算法 ,以揭示其性质 AES惟一的非线性运算 (即乘法逆元运算 )在指数域上变成线性运算 ,而线性运算按位异或诱导了指数域上的非线性运算∨ ,并且 ,运算∨被表示为星对偶运算与模 2 5 5加法 获得了星对偶运算的规律 ,并将星对偶运算和∨运算的“随机性”限制于 9个数的子集之内 为深入的密码分析提供了新的框架

The ith chord-integrals of star bodies are introduced,and some inequalities and propositions for the chord-integrals of star bodies established.As an application,the Brunn-Minkowski inequality for star duality of intersection bodies is obtained.

首先引入星体弦长积分的概念,研究了其性质并建立了有关星体弦长积分的不等式.作为应用,给出相交体的星对偶的Brunn-Minkowski型不等式.

 
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