模2加整体逼近二元和三元模2^n加的噪声函数分析

Analysis of the Noise Functions of Macrocosm Approximation of Binary Addition and Triple Addition Modulo 2^n with XOR

整体逼近就是用一个弱密码函数替代一个强密码函数的攻击方法,这两个函数的模2和称为该整体逼近的噪声函数。该文研究了模2加整体逼近二元模2^n加和三元模2^n加时噪声函数的概率分布,给出了噪声函数的概率分布的计算公式以及噪声函数的概率值的平方和的计算公式。这些结果有助于掌握二元模2^n加和三元模2^n加对抗模2加的整体逼近攻击的能力。

Macrocosm approximation is a class of attacks to weak cipher function. The XOR of the two functions is called ciphers by replacing a strong cipher function with a the noise function of this macrocosm approximation. This paper studies the probability distributions of the noise functions produced by macrocosm approximation of binary addition and triple addition modulo 2- with XOR, and gives the computation formulae of the probability distributions of the corresponding noise functions and the square sums of the probabilities, which is helpful to recognize the ability of resistance to macrocosm approximation of binary addition and triple addition modulo 2- with XOR,