Color image encryption scheme based on quaternion discrete multi-fractional random transform and compressive sensing

A color image compression-encryption algorithm by combining quaternion discrete multi-fractional random transform with compressive sensing is investigated, in which the chaos-based fractional orders greatly improve key sensitivity. The original color image is compressed and encrypted with the assistance of compressive sensing, in which the partial Hadamard matrix adopted as a measurement matrix is constructed by iterating Chebyshev map instead of utilizing the entire Guassian matrix as a key. The sparse images are divided into 12 sub-images and then represented as three quaternion signals, which are modulated by the quaternion discrete multi-fractional random transform. The image blocking and the quaternion representation make the proposed cryptosystem avoid additional data extension existing in many transform-based methods. To further improve the level of security, the plaintext-related key streams generated by the 2D logistic-sine-coupling map are adopted to diffuse and confuse the intermediate results simultaneously. Consequently, the final ciphertext image is attained. Simulation results reveal that the proposed cryptosystem is feasible with high security and has strong robustness against various attacks.