Verifiable visually meaningful image encryption algorithm based on compressive sensing and (t, n)-threshold secret sharing

Abstract

Abstract A verifiable visually meaningful image encryption algorithm based on compressive sensing and (t, n)-threshold secret sharing is proposed. Firstly, the plain image is compressed and encrypted by 2D block compressive sensing to obtain the pre-encrypted image. During this process, the enhanced logistic map and the enhanced tent map are used to generate the measurement matrix and the permutation sequence, respectively. Secondly, multiple shadow images of the pre-encrypted image are generated by using the (t, n)-threshold secret sharing scheme, and then each shadow image is further encrypted by using the encryption matrix generated by the chaotic system. Meanwhile, the signatures of the shadow images are obtained by using RSA signature algorithm. Finally, the shadow images and their corresponding signatures are embedded into the carrier image to generate the cipher image with high visual quality by using the LSB method. Additionally, the present algorithm can resist known-plaintext and chosen-plaintext attacks by incorporating the hash value of the plain image as part of the key. Meanwhile, the use of 2D block compressive sensing significantly reduces the reconstruction time. Simulation results demonstrate that the proposed algorithm achieves excellent decryption quality and operational efficiency.