Abstract Due to the insufficient visual security of encrypted images generated by conventional image encryption algorithms, it is easily recognized and decrypted or attacked by attackers in public channels. To solve this problem, this paper proposes a visually meaningful image encryption (VMIE) method based on a new chaotic map to improve the encryption complexity and unpredictability. Moreover, we design a two-way intertwine scrambling and deep embedding algorithm to protect the content of the image, and the encrypted image also has visual security. Firstly, a new one-dimensional chaotic map combining sine and tangent functions is designed to construct the measurement matrix, and then a new two-way intertwine scrambling algorithm is used to scramble the sparse matrix of the encrypted image. Secondly, the chaotic system generates measurement matrix and diffusion matrix for compressing and diffusing the scrambled image. Finally, a new embedding strategy is adopted to retain more information of the plain image and reduce information loss. The experimental results show that the average PSNR of the encrypted image is 38.96dB and that of the decrypted image is 34.59dB. Compared with the existing schemes, this algorithm has better visual quality and reconstruction quality.
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