With more and more color images are spread and shared in the untrusted cloud server remotely over the open Internet, some private or confidential information may be contained, it is necessary to develop cryptosystem for these images to free from serious threats. This paper investigates a secure and robust cryptosystem for color image based on discrete trinion Fourier transform and random-multiresolution singular value decomposition. Firstly, a color image is represented into a trinion matrix by precoding and followed by block-wise discrete trinion Fourier transform. Then a mapping from trinion number domain to real number domain is implemented to facilitate random-multiresolution singular value decomposition. To further enhance the randomness of the transformed data, the scrambling based on chaotic sequence is applied to obtain the cipherimage. Experimental results have demonstrated that the proposed color image encryption algorithm is feasible. The adoption of logistic map ensures that the proposed cryptosystem attains high level security. Furthermore, the quality of the retrieved image is better than that of the algorithm based on single color channel processing separately and quaternion matrix based algorithms when it is decrypted correctly or under Gaussian noise and shear attacks. Moreover, employing a trinion matrix to represent a color image is more compact than using quaternion matrix. It would have potential applications in digital image protection.

随着越来越多的彩色图像在开放Internet上远程散布和共享到不受信任的云服务器中，可能会包含一些私有或机密信息，因此有必要开发一种加密系统以使这些图像免受严重威胁。本文研究了一种基于离散的Trinion傅里叶变换和随机多分辨率奇异值分解的彩色图像安全鲁棒密码系统。首先，通过预编码将彩色图像表示为一个Trinion矩阵，然后进行逐块离散Trinion Fourier变换。然后，实现了从Trinion数域到实数域的映射，以促进随机多分辨率奇异值分解。为了进一步增强变换后数据的随机性，基于混沌序列的加扰被应用于获得密文。实验结果表明，提出的彩色图像加密算法是可行的。逻辑映射的采用确保了所提出的密码系统获得高级别的安全性。此外，在正确解密或在高斯噪声和剪切攻击下解密后，检索到的图像的质量要优于分别基于单个彩色通道处理的算法和基于四元数矩阵的算法。此外，使用四维子矩阵表示彩色图像比使用四元数矩阵更紧凑。它将在数字图像保护中具有潜在的应用。正确解密或在高斯噪声和剪切攻击下解密后，检索到的图像的质量要优于分别基于单个彩色通道处理的算法和基于四元数矩阵的算法。此外，使用四维子矩阵表示彩色图像比使用四元数矩阵更紧凑。它将在数字图像保护中具有潜在的应用。正确解密或在高斯噪声和剪切攻击下解密后，检索到的图像的质量要优于分别基于单个彩色通道处理的算法和基于四元数矩阵的算法。此外，使用四维子矩阵表示彩色图像比使用四元数矩阵更紧凑。它将在数字图像保护中具有潜在的应用。