Color image encryption based on discrete trinion Fourier transform and random-multiresolution singular value decomposition

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.