Logistic混沌映射性能分析與改進(jìn)
doi: 10.11999/JEIT151039 cstr: 32379.14.JEIT151039
基金項(xiàng)目:
國家自然科學(xué)基金(61272494, 61350011)，江西省教育廳科研項(xiàng)目(GJJ151522)
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)
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摘要: 混沌系統(tǒng)是基于混沌的數(shù)據(jù)加密領(lǐng)域的一個(gè)重要研究對(duì)象，Logistic混沌映射是最簡單和有效的混沌系統(tǒng)，被廣泛應(yīng)用在大多數(shù)混沌加密算法中，Logistic映射的安全性成為研究的熱點(diǎn)。針對(duì)Logistic序列存在的吸引子與空白區(qū)問題，該文提出一種基于初始值和分形控制參數(shù)之間關(guān)系的Logistic映射改進(jìn)方法。利用兩者之間關(guān)系對(duì)映射自變量區(qū)間進(jìn)行合理分段，擴(kuò)大了混沌控制參數(shù)區(qū)域，將滿射范圍擴(kuò)大到整個(gè)控制參數(shù)區(qū)間，使產(chǎn)生的序列分布更均勻，解決了穩(wěn)定窗與空白區(qū)等問題。通過將改進(jìn)Logistic與其它分段Logistic映射進(jìn)行仿真對(duì)比，實(shí)驗(yàn)結(jié)果表明改進(jìn)后的映射產(chǎn)生的序列混沌特性得到顯著加強(qiáng)，分布更均勻，具有更好的隨機(jī)性能測試指標(biāo)。另外，改進(jìn)Logistic映射計(jì)算復(fù)雜度低，實(shí)現(xiàn)簡單，在擴(kuò)頻通信與混沌密碼等領(lǐng)域有廣闊的應(yīng)用前景。
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關(guān)鍵詞:
- 數(shù)據(jù)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.-
Key words:
- Data encryption /
- Logistic mapping /
- Chaotic sequence /
- Security
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