Logistic混沌映射性能分析与改进

陈志刚; 梁涤青; 邓小鸿; 张颖

doi:10.11999/JEIT151039

Logistic混沌映射性能分析与改进

doi: 10.11999/JEIT151039

基金项目:

国家自然科学基金(61272494, 61350011)，江西省教育厅科研项目(GJJ151522)

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- 被引次数: 0
出版历程
- 收稿日期: 2015-09-14
- 修回日期: 2016-02-29
- 刊出日期: 2016-06-19

Performance Analysis and Improvement of Logistic Chaotic Mapping

Funds:

The National Natural Science Foundation of China (612724494, 61350011), Educational Commission Science Foundation of Jiangxi Province of China (GJJ151522)

摘要

摘要: 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。
- 数据加密 /
- Logistic映射 /
- 混沌序列 /
- 安全性
Abstract: 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 windowand 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.
- Data encryption /
- Logistic mapping /
- Chaotic sequence /
- Security

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