Performance Analysis and Improvement of Logistic Chaotic Mapping
CHEN Zhigang①③ LIANG Diqing②③④ DENG Xiaohong③⑤ ZHANG Ying⑥
①(College of Software, Central South University, Changsha 410075, China) ②(School of Information Science and Engineering, Central South University, Changsha 410083, China) ③(“Mobile Health” Ministry of Education-China Mobile Joint Laboratory, Central South University, Changsha 410075, China) ④(Informatization Construction and Management Department, Changsha University of Science and Technology, Changsha 410114, China) ⑤(College of Applied Science, Jiangxi University of Science and Technology, Ganzhou 341000, China) ⑥(College of Electrical and Information Engineering, Changsha University of Science and Technology, Changsha 410114, China)
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.
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