A flexible and visually meaningful multi-image compression, encryption and hiding scheme based on 2D compressive sensing

Background: Encrypting plain images into noise-like cipher images is a common method in image encryption. However, when noise-like images appear in public networks, they are more likely to attract attention and suffer more cryptanalysis. To solve this problem, researchers propose the concept of visually meaningful image encryption scheme, which encrypts a plain image into a visually meaningful cipher image. Objective: In order to realize the visual security of cipher image and increase information capacity, this paper proposes a flexible visually secure multi-image compression, encryption and hiding scheme based on two-dimensional compressive sensing (2DCS), which can flexibly complete the compression and encryption of multiple plain images without increasing the amount of ciphertext data. Methods: The scheme is divided into encryption process and embedding process. In the encryption process, the plain image is randomly scrambled and non-linear gray value transformed to obtain a pre-encrypted integer matrix, then 2DCS is used to compress the pre-encrypted integer matrix to get the secret image. Repeat this process for multiple plain images to obtain multiple secret images. In the embedding process, integer wavelet transform and bit-plane decomposition are used to embed multiple secret images into the quantized coefficient matrix of host image to get the modified coefficient matrix, and then the inverse integer wavelet transform is used to transform the modified coefficient matrix into spatial space to get the visually meaningful cipher image. Result: The simulation experiment verifies the feasibility and effectiveness of the visually meaningful multi-image encryption scheme, and users can choose to improve the system's encryption capacity or cipher image's visual security according to their own needs.