Visual meaningful image encryption algorithm based on 3D discrete hyperchaotic map and compressive sensing

With the progress of the times, existing compression encryption algorithms have problems such as low compression rate of ciphertext images and easy cracking. In order to solve these problems, this paper first uses Marotto’s theorem to construct a new 3D discrete hyperchaotic map, which has enhanced nonlinearity and sensitivity to initial conditions. Then, a visual meaningful image encryption algorithm based on this map and compressive sensing (VMIEA-DHMC) is proposed. The plaintext image is compressed and encrypted to generate the secret image, which is embedded into a carrier image using the Least Significant Bit (LSB) method, producing a meaningful carrier image with the embedded secret image. To improve reconstruction quality, the algorithm separately extracts the approximate and detail components during compression, applying a higher compression ratio to the approximation and a lower ratio to the details. To address key transmission and management, the RSA algorithm encrypts the secret key, while the hash value of the plaintext image is integrated with the RSA-encrypted keys to generate the initial conditions of the chaotic system, ensuring resistance to known-plaintext attacks.Simulation results show that the proposed algorithm achieves an average NPCR of 99.62% and UACI of 33.47%, which are very close to the ideal values, and delivers a reconstruction PSNR of 33.21 dB at a compression ratio of 0.25. It features a large key space, high sensitivity to decryption keys, and strong imperceptibility, as confirmed by steganalysis and robustness tests. Overall, the scheme provides an effective solution for visually secure image encryption with excellent security and compression performance.