Double-image encryption and authentication scheme based on compressed sensing and double random phase encoding

To enhance the security of image information, a double-image encryption and authentication scheme combining compressive sensing (CS) and double random phase encoding (DRPE) is proposed. First, two plaintext images are taken as real and imaginary parts to form a complex-valued image, which is then encoded using DRPE. Next, extract the phase of the encrypted complex-valued image and encode it into authentication information. Simultaneously, the complex-valued image is sampled using the measurement matrix, which is optimized by Schmidt orthogonalization, and then quantized to form a compressed image. Subsequently, the authentication information is embedded into the compressed image, and by applying the permutation and diffusion algorithm to it, the ciphertext image is obtained. At the receiving end, the ciphertext is decrypted using inverse permutation and inverse diffusion algorithms, and the authentication information is decoded to acquire the authentication image. Finally, synchronous authentication of the two reconstructed images is achieved using a nonlinear cross-correlation method. Additionally, the keys in the proposed scheme are generated using high-dimensional chaotic systems, effectively reducing the required storage space and transmission bandwidth. Simulation results demonstrate that the proposed scheme has high image reconstruction performance at different compression ratios and possesses outstanding security and authentication capabilities.