Asymmetric color cryptosystem based on compressed sensing and equal modulus decomposition in discrete fractional random transform domain

In this paper, we propose an asymmetric encryption and compression method for a color image based on compressed sensing and equal modulus decomposition in the discrete fractional random transform (DFrRT) domain. In this scheme, a color image is firstly encrypted into a single channel image, which is divided into low-frequency image and high-frequency image by the discrete wavelet transform. Subsequently, the high-frequency image is compressed into two matrices by compressed sensing. One of the matrices is combined with the low-frequency image into one input of DFrRT. The other acts as another input of DFrRT. Finally, the output result of DFrRT is encrypted by the equal modulus decomposition in DFrRT domain to create an effective trapdoor one-way function. Compared to the other transformations, the private key of DFrRT is the high-frequency component related to the plaintext in this paper. Thus, the proposed cryptosystem is able to resist various types of attacks and maintain the asymmetric characteristics of the cryptosystem. Numerical simulations are presented to demonstrate the feasibility and robustness of the proposed method.