中文摘要：

针对许多基于Logistic图像置乱方法的设计只注重置乱规则和方法,没能很好地给出设计原理这一现象,文章遵循从坚实的数学理论到实际应用这一科学过程,给出了一个全新的具有坚实理论基础的基于Logistic图像置乱算法.依据混沌初值敏感性,密钥空间大这一特性,从混沌映射Logistic着手,结合概率相关理论,设计了基于Logistic映射（0,1）区间上的均匀分布随机变量产生算法,利用这一均匀分布变量生成基于位置互换的随机排列.为了度量该随机排列的置乱强度,设计了置乱强度测试算法.最后,利用这一基于Logistic均匀分布的随机排列驱动图像生成置乱图像.比较Baker算法、Ye算法和Yoon算法,结果显示,文章建议的Logistic图像置乱算法具有很大的密钥空间,很强的密钥敏感性,很强的使结构性数据相关性消失的性能,进而能够增加熵值,很好的抗攻击能力,可以有效地满足图像置乱需求.

英文摘要：

Most algorithms of image scrambling transformation based on Logistic map are currently dedicated to permutation rules and methods without considering design philosophy.In this paper,we propose a new image bit permutation algorithm based on the Logistic map.This algorithm with firmly mathematic theory is designed by following the scientific course from theory to practice.According to the characteristics of chaotic sensitivity to initial condition and large key space,starting from Logistic map,the transformation which can generate uniformly distributed random variable in the interval [0,1] based on Logistic at μ=4 is developed.Utilizing this generated uniform random variable,random permutation algorithm based on interchange position is obtained.For measuring permutation strength of the proposed random permutation algorithm,the corresponding permutation strength testing algorithm is designed.Based on this permutation algorithm,the image bit permutation algorithm is described.When used to image and compared with Baker Ye and Yoon algorithm,the proposed image bit permutation method exhibits large key space,extreme sensitivity to initial condition,effective capability for dissipating high correlation among pixels and increasing information about entropy value.Results show that this proposed scrambling scheme with firmly theoretical foundation can enhance image security significantly.