Logistic 混沌映射性能分析与改进

摘要

Chaotic system is an important research object in the field of data encryption based on the chaos. The logistic chaotic mapping is the simplest and efficient chaotic system and is usually used by many encryption methods based on the chaos, thus the security of Logistic mapping becomes an important research point. To deal with the issue of attractors and blank area of the presence of the Logistic sequence, an improved Logistic mapping based on the relationship between initial value and the fractal control parameters is proposed. The variables interval of chaotic mapping is reasonable subsection by using this relationship, so the chaos control parameter region can be expanded, and the onto mapping range is extended to the entire control parameter interval. The improved Logistic mapping makes the chaotic sequence distribution more uniform, and solves the problem of“stability window”and the blank area etc. Compared with the improved Logistic and piecewise chaotic Logistic, the experimental results show that the chaotic characteristics of sequence generated by the improved mapping is significantly strengthened, has more uniform distribution, and better random performance index. In addition, the improved Logistic mapping has low computational complexity and is prone to implement. The improved Logistic mapping has broad application prospects in the fields of spread spectrum communication and chaotic cipher.%混沌系统是基于混沌的数据加密领域的一个重要研究对象，Logistic 混沌映射是最简单和有效的混沌系统，被广泛应用在大多数混沌加密算法中，Logistic 映射的安全性成为研究的热点。针对 Logistic 序列存在的吸引子与空白区问题，该文提出一种基于初始值和分形控制参数之间关系的 Logistic 映射改进方法。利用两者之间关系对映射自变量区间进行合理分段，扩大了混沌控制参数区域，将满射范围扩大到整个控制参数区间，使产生的序列分布更均匀，解决了“稳定窗”与空白区等问题。通过将改进 Logistic 与其它分段 Logistic 映射进行仿真对比，实验结果表明改进后的映射产生的序列混沌特性得到显著加强，分布更均匀，具有更好的随机性能测试指标。另外，改进Logistic 映射计算复杂度低，实现简单，在扩频通信与混沌密码等领域有广阔的应用前景。