A visually meaningful image encryption scheme with an asymmetric structure based on the discrete wavelet transform (DWT) and Schur decomposition is proposed in this study. First, the RSA algorithm is used to generate the initial values for the chaotic system to produce the random sequence. Then, both scrambling and diffusion operations are performed on the plain image to obtain the preencrypted image. Moreover, the Schur decomposition is applied on the preencrypted plain image to obtain the upper triangular and orthogonal matrices. Second, the cover image is scrambled followed by a DWT operation. Four subbands are then formed, namely, LL, HL, LH, and HH. Finally, the former upper triangular matrix and orthogonal matrix are embedded into subbands LH and HH produced by the cover image. After the application of the inverse DWT and inverse scrambling operation, the final visually meaningful cover image embedded with a secret plain image can be obtained. No one can identify any useful information about the plain image from the final embedded cover image, nor can anybody know that there is any hidden secret image. Experimental simulations show that the normalized correlation values between the original cover image and the final visually meaningful cover image are approximately 0.9997. Therefore, the proposed encryption scheme is imperceptible for secret image communications.

中文翻译：

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基于DWT和Schur分解的视觉有意义的图像加密方案

提出了一种基于离散小波变换（DWT）和Schur分解的具有非对称结构的视觉有意义的图像加密方案。首先，使用RSA算法为混沌系统生成初始值，以生成随机序列。然后，对普通图像执行加扰和扩散操作以获得预加密图像。此外，对预加密的普通图像进行Schur分解以获得上三角矩阵和正交矩阵。其次，对封面图像进行加扰，然后进行DWT操作。然后形成四个子带，即LL，HL，LH和HH。最后，将先前的上三角矩阵和正交矩阵嵌入到由封面图像产生的子带LH和HH中。在应用逆DWT和逆加扰操作之后，可以获得嵌入有秘密普通图像的最终的视觉上有意义的封面图像。没有人可以从最终嵌入的封面图像中识别出有关普通图像的任何有用信息，也没有人知道任何隐藏的秘密图像。实验仿真表明，原始封面图像和最终视觉上有意义的封面图像之间的归一化相关值约为0.9997。因此，所提出的加密方案对于秘密图像通信是不可察觉的。也没有人知道有任何隐藏的秘密图像。实验仿真表明，原始封面图像和最终视觉上有意义的封面图像之间的归一化相关值约为0.9997。因此，所提出的加密方案对于秘密图像通信是不可察觉的。也没有人知道有任何隐藏的秘密图像。实验仿真表明，原始封面图像和最终视觉上有意义的封面图像之间的归一化相关值约为0.9997。因此，所提出的加密方案对于秘密图像通信是不可察觉的。