A new fractional two-dimensional quadric polynomial discrete chaotic map (2D-QPDM) with the discrete fractional difference is proposed. Afterwards, the new dynamical behaviors are observed, so that the bifurcation diagrams, the largest Lyapunov exponent plot and the phase portraits of the proposed map are given, respectively. The new discrete fractional map is exploited into color image encryption algorithm and it is illustrated with several examples. The proposed image encryption algorithm is analyzed in six aspects which indicates that the proposed algorithm is superior to other known algorithms as a conclusion.

中文翻译：

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基于二维分数阶多项式映射的图像加密

提出了一种新的具有离散分数差的分数阶二维二次多项式离散混沌映射（2D-QPDM）。然后，观察新的动力学行为，分别给出了分岔图、最大李雅普诺夫指数图和所提出映射的相图。新的离散分数映射被用于彩色图像加密算法，并通过几个例子进行说明。对所提出的图像加密算法进行了六个方面的分析，得出该算法优于其他已知算法的结论。