In this paper, a novel fractional quantum logistic map (FQLM) based on fractional difference is proposed and image encryption algorithm based on it are exploited. First, the FQLM is proposed and its dynamical behaviors are observed with bifurcation diagram, phase portraits and largest Lyapunov exponent plots. After that, the ECC is utilized to cover up the encryption keys and the FQLM is used for the permutation and diffusion process of image encryption. Finally, the cryptosystem is used in image encryption and the algorithm is analyzed in four respects, showing a distinct advantage of the proposed cryptosystem over some of existing ones.

中文翻译：

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分数阶量子逻辑图及其在图像加密技术中的应用

本文提出了一种新的基于分数差分的分数量子逻辑图（FQLM），并开发了基于它的图像加密算法。首先，提出了 FQLM，并通过分岔图、相图和最大 Lyapunov 指数图观察了其动力学行为。之后，ECC 用于隐藏加密密钥，FQLM 用于图像加密的置换和扩散过程。最后，将该密码系统用于图像加密，并从四个方面对该算法进行了分析，显示了所提出的密码系统相对于一些现有密码系统的明显优势。