Trinion discrete cosine transform with application to color image encryption

This paper introduces trinion discrete cosine transform that can process color image holistically, it can be computed by combination of single-channel discrete cosine transform. Compared with quaternion discrete cosine transform, trinion discrete cosine transform is more efficient and compact to represent color image. Moreover, it is used for developing a robust color image encryption algorithm jointing with quantum logistic map and Josephus traversing. Firstly, color components are precoded into a trinion matrix, which is performed trinion discrete cosine transform. Then three parts of the transformed result are pairwisely combined into complex matrices and the synthesized spectrums satisfying symmetry are established. Followed by Josephus scrambling with variable steps on magnitudes, the ciphertext image can be acquired. The plaintext image can be ideally restored with the granted keys, where the average value of PSNR is close to 300.00 dB. Moreover, the proposed algorithm has high-level security. It also shows better resistance against Gaussian noise and shearing in comparison with some existing algorithms.