随机置换的有关概率问题

Probability problems on random permutation

基于随机选取0,1,…n?1的置换建立了概率模型,求出了这种随机选取意义下置换后Zn中点与原相邻点之间距离(简称距离)的分布律以及距离为a(1≤a≤n?1)的点个数的数学期望与方差,当距离a和置换阶数n互素时,得到了距离为a的点个数的分布律。依据这些结论分析了随机置换的相关密码安全性问题,对在密码设计中采用全距置换的意义提供了新的解释。

Based on selecting permutations on 0,1,…n-lrandomly, a probability model were built. In sense of selecting permutations randomly, the distribution of distance which was between one point and its neighbor in Z. （called distance for short） and the mathematic expectation, the variance of number of the points with distance α（l≤α≤n-1） were presented. When distance a and the permutation order n were prime to each other, the distribution of number of the points with distance a was also given. By these results, the cryptographic security of random permutation is analyzed, and a new explication is presented on the significance of choosing quick trickle permutation in cipher designs,