Based on selecting permutations on 0

1

…n?1randomly

a probability model were built.In sense of selecting permutations randomly

the distribution of distance which was between one point and its neighbor in Zn（called distance for short）and the mathematic expectation

the variance of number of the points with distance a（1≤a≤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.