基于改进 Logistic 混沌映射的图像自适应加密算法

摘要

针对一维Logistic混沌映射迭代序列分布非均匀，处于混沌状态的参数空间较小等问题，在映射原型基础上，增加非线性调节项和控制参数构造改进映射，经过分析证明改进映射具有更大的混沌范围，更均匀的序列分布，更多正的Lyapunov指数。设计一种基于改进映射的自适应图像加密策略，使改进映射的初值随明文信息自适应改变，且对明文的各种细微改变均非常敏感。通过理论分析和仿真实验表明，算法的安全性较高，能够抵御统计性分析和攻击性操作。%In order to solve the problem that the iterative sequences produced by the one -dimension(1D) Logistic chaotic map are uneven distribution and the parameter space of chaos is smaller , an improved Logistic map was constructed by increasing the con-trol parameter and nonlinear adjustment in the Logistic chaotic map , which has a wider chaotic range and more uniform distribu-tion than its prototype by analyzing bifurcation diagram and Lyapunov exponent .A self-adaptive image encryption scheme based on improved Logistic chaotic map was introduced , and the initial value of improved Logistic chaotic map is adaptive change with the plain image , and the scheme is sensitive to all sorts of subtle change of the plain image .Experiments and security analysis in-dicate that the algorithm has high security , and can resist statistical analysis and attack operation.