Abstract The fractional-order chaotic systems have characteristics of the all chaotic systems, however, the improper fractional-order chaotic systems have more complexity random sequences, which more suitable for chaotic cryptosystems. To investigate the application of improper fraction order chaotic system in chaotic cryptography, in this paper, an improper fractional-order laser chaotic system is constructed and applied in image encryption algorithm. The dynamic performances of the system are studied through phase diagrams, Lyapunov exponents spectrum, bifurcation diagrams and C0 complexity. Meanwhile, the improper fractional-order laser chaotic system is realized based on DSP platform. In addition, the performances of the designed encryption scheme are analyzed by key space, correlation coefficients, information entropy, histogram, differential attacks and robustness analysis. The experimental simulation results indicate that the improper fractional-order laser chaotic system not only has the abundant dynamic characteristics, but also has better security when it is used to image encryption algorithm. Therefore, this research would provide theoretical basis for the improper fractional-order laser chaotic system in security communications application.

中文翻译：

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一种不正确分数阶激光混沌系统的动态分析及其图像加密应用

摘要 分数阶混沌系统具有全混沌系统的特点，但不正确分数阶混沌系统具有更复杂的随机序列，更适合于混沌密码系统。为研究假分数阶混沌系统在混沌密码学中的应用，本文构建了一个假分数阶激光混沌系统并将其应用于图像加密算法。通过相图、Lyapunov指数谱、分岔图和C0复杂度研究了系统的动态性能。同时，基于DSP平台实现了不正分阶激光混沌系统。此外，通过密钥空间、相关系数、信息熵、直方图、差分攻击和健壮性分析。实验仿真结果表明，不当分数阶激光混沌系统不仅具有丰富的动态特性，而且在用于图像加密算法时具有较好的安全性。因此，本研究将为安全通信应用中不正确的分数阶激光混沌系统提供理论依据。