模2n加整体逼近模2加产生的噪声函数的概率分布研究
doi: 10.3724/SP.J.1146.2008.01307
Research on the Noise Functions Produced by Macrocosm Approximation of XOR with Addition Modulo 2n
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摘要: 该文证明了模2n加变换以6种不同的方式整体逼近模2加时产生的噪声函数取值概率的数值分布相同，给出了6种噪声函数的概率分布之间的相互转化关系，并给出了6种整体逼近所产生的噪声函数的取值概率的计算公式以及概率值平方和的计算公式，并修正了三元模2加整体逼近模2n加时所产生的噪声函数取值概率的平方和的计算公式。这些结论在区分攻击中有一定的应用价值。Abstract: This paper proves that the noise functions produced by six kinds of macrocosm approximations of exclusive or with addition modulo 2n have the same probability distribution values. Then, the relations between the six noise functions are given. Moreover, this paper presents the computing formulas for the probability distributions and the square sums of the probability values, and proposes a correct formula for the square sums of the probability values of noise function produced by macrocosm approximations of addition modulo 2n with exclusive or. The results presented in this paper are useful in some distinguishing attacks.
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