Design of a Multi-scroll Chaotic System and its Application to Image Encryption
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摘要:
该文提出一种三涡卷混沌系统，首先对系统的李雅普诺夫指数、分岔图、Poincare截面图、功率谱图及平衡点稳定性等动力学特性进行了理论分析和数值仿真，结果表明该系统具有良好的动力学特性和丰富的拓扑吸引子。基于电路仿真软件Multisim研制了实验仿真电路, 该电路结构简单、易于实际制作，且仿真实验与理论分析结论十分吻合，证实了提出的混沌系统电路在物理上是可以实现的，从而验证了该混沌系统的混沌产生能力。最后结合DNA算法设计了一种彩色图像加密算法，利用新系统混沌序列对图像进行加密，重点分析了加密直方图、相邻像素相关性。结果表明，新系统对混沌密钥及明文都非常敏感，密钥空间较大，提出的混沌系统应用于图像加密具有较高的安全性能。
Abstract:A chaotic system with three scrolls is proposed. The dynamics characteristics of the system, such as Lyapunov index, bifurcation diagram, Poincare cross section diagram, power spectrum and equilibrium stability, are studied by numerical simulation. The analysis results show that the system has good dynamics characteristics and rich topological attractors. In addition, an experimental simulation circuit is developed based on the circuit simulation software Multisim, which has a simple structure and is easy to realize in practice. Moreover, the simulation experiment is very consistent with the theoretical analysis conclusion, confirming that the proposed chaotic system circuit can be realized physically, thus verifying the chaos generation capacity of the chaotic system. Finally, a color image encryption algorithm is designed based on DNA algorithm, and the results show that the system has high security performance.Using the new system chaotic sequence to encrypt image, the encryption histogram and correlation between adjacent pixels are analyzed, results show that the new systems are very sensitive to image key and plaintext, key space is large, chaotic system applied to image encryption has higher safety performance.
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Key words:
- Image encryption /
- Multi-scrolls /
- Chaotic system /
- Dynamical behavior /
- Circuit implementation
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