三元模2~n加与模2加的相容概率分析

Analysis on the Consistent Probability of Triple Addition Modulo 2~n With XOR

深入分析了三元模2~n加与模2加两种运算的相容概率对密码算法安全性的影响,并采用减差分这种形式使三元模2~n加整体逼近模2加,目前还没有公开文献对这种逼近方式进行分析。计算了减差分形式整体逼近的噪声函数的概率分布及概率分布取值平方和,通过对差分和减差分两种逼近方法进行比较,结果显示:减差分整体逼近的噪声函数概率分布取值是均匀的,且整体逼近无论是差分还是减差分其相容概率都为2^(1-n)。

This paper deeply analyzed the impact on the security of cryptographic algorithm by the consistent probability of triple addition modulo 2^nand exclusive OR（ XOR）. It adopted the reduction of difference to realize macrocosm approximation of triple addition modulo 2^nto XOR,which hadn＇t been researched before. Based on reduction of difference,this paper calculated the probability distribution and its value square of the Noise Function of macrocosm approximation of triple addition modulo 2^nto XOR,then carried on the comparison on the two ways of reduction of difference and difference. The result showed that the value square of the probability distribution of the Noise Function of reduction of difference was homogeneous,and the consistent probability of the Noise Function of macrocosm approximation for the two ways was the same,which was 2^1-n.