基于二维耦合映像格子模型的图像加密

为了平衡混沌系统的复杂性和效率之间的关系，将分段Logistic映射（piecewise Logistic map，PLM）引入到二维耦合映像格子（2D coupled map lattices，2DCML）模型中. 采用暂态转换以使模型的输出序列服从均匀分布，进而得到T2DCML模型，基于此模型提出了一类图像加密算法. 在加密算法中，利用模型输出的伪随机序列构造两个初等变换矩阵，对图像进行置乱操作；然后再从模型中提取状态值的比特构造整数序列，对置乱后的图像进行扩散操作；经过若干轮的置乱与扩散操作，产生最后的加密图像. 仿真实验及性能分析表明:该算法的相关系数的绝对平均值为0.001 3，信息熵为7.999 3，像素变化率（number of pixel change rate，NPCR）和统一平均变化强度（unified average change intensity，UACI）分别为99.63%和33.60%，能够有效满足图像在网络中安全传输的需求. 

Image Encryption Based on 2D Coupled Map Lattices

Piecewise Logistic map (PLM) is introduced into 2D coupled map lattices (2DCML) model to face a tradeoff between complexity and efficiency of chaotic systems, and a transformation method based on transient status values is used to make the output sequence of the model obey a uniform distribution. Then, the T2DCML model is built. According to the T2DCML model, an image encryption algorithm is proposed, in which encryption algorithm, the pseudo-random sequence output by the model is used to construct two elementary transformation matrices and the image is scrambled by the matrices. Then, the bits of the state value are extracted from the model to construct an integer sequence and the scrambled image is diffused by the integer sequence. Finally, the encrypted image is produced by multi-rounds of confusion and diffusion. Simulation experiments and performance analysis show that the absolute average correlation coefficient of the algorithm is 0.001 3, the information entropy is 7.999 3, and the number of pixel change rate (NPCR) and the unified average change intensity (UACI) is 99.63% and 33.60%, respectively, revealing that the algorithm can effectively meet the needs of the safe transmission of images in the network.