A new visually meaningful double-image encryption algorithm combining 2D compressive sensing with fractional-order chaotic system

A visually meaningful double-image image encryption algorithm is proposed based on a fractional-order chaotic system combined with 2D compressive sensing (CS). Specifically, in the pre-encryption phase, a 2D discrete wavelet transform (DWT) is performed on two grayscale images followed by a measurement using 2D CS. The measurement matrices are generated by using the fractional-chaotic system and Kronecker product (KP). Then, a Zigzag confusion operation is performed on the two generated measurement matrices after quantization to obtain two secret images. A new measurement matrix optimization algorithm is presented to optimize the high-dimensional measurement matrix. In the embedding phase, a new repairable embedding algorithm is designed which combines matrix encoding and 2 K correction algorithm. The loss of the carrier image quality is effectively reduced while the robustness of the cipher image is enhanced. It is more suitable for practical applications. Numerical simulation and performance analyses show that the average PSNR value of visually meaningful cipher images is 41.7 dB, and the PSNR value of the reconstructed image is 1 ~ 3 dB higher than those in other studies. In addition, the proposed algorithm is also superior to some recently proposed algorithms in efficiency, security, and robustness.