Generating visually secure encrypted images by partial block pairing-substitution and semi-tensor product compressed sensing

Abstract

Recently visually secure image encryption scheme attracts more and more researchers' attention on the grounds that it will not stimulate the attackers' curiosity. Generally, four aspects should be paid great attention in visually meaningful encryption schemes, including the similarity between the cipher image and carrier image, the large embedding capacity which can embed the secret image, the satisfactory recovered quality and the robustness to resist various attacks. To improve the visual quality of the meaningful cipher image and the embedding capacity, this paper proposes a novel visually secure image encryption scheme by combining semi-tensor product compressed sensing and partial block pairing-substitution technique. The blocks of two images which have similar Standard Deviation values are selected to execute the block pairing-substitution. This makes the cipher image more similar to the carrier image, and the secret is more difficult to detect. The metric MSSIM values are all exceeding 0.91, and a close value for two-dimensional detrended fluctuation (2D-DFA), which verifies the high similarity between the cipher image and the carrier image to a greater extent. The embedding capacity can reach four times of the plain image in theory, when the compression ratio is 0.25, which demonstrates the large embedding capacity of the proposed scheme. Furthermore, less computational and spatial resources are required since the incorporation of semi-tensor product compressed sensing and cellular automata. Importantly, the embedding capacity increases as the embedding is performed on the spatial domain. Both the simulation results and theoretical analysis demonstrate the high quality of the cipher images and the high security of the proposed scheme.