A visually meaningful image encryption algorithm based on P-tensor product compressive sensing and newly-designed 2D memristive chaotic map

The noise-like visual feature of cipher images produced by using the traditional image encryption technology explicitly reflects the presence of secret information. To overcome this issue, a visually meaningful image encryption algorithm is proposed based on a newly designed 2D memristive chaotic map, P-tensor product compressive sensing (PTP-CS) and discrete Hartley transform (DHT). For concreteness, a new two-dimensional discrete memristive chaotic map is first designed to provide highly unpredictable secret code streams while maintaining low time consumption. Second, the threshold processing and zigzag confusion operations are performed on the discrete wavelet coefficients of the plain image to meet the prerequisites for effective compression. Third, the intermediate secret information is obtained by utilizing PTP-CS in the compression layer. Information entropy and edge entropy are employed to adaptively identify the complex regions that are suitable for embedding due to inconspicuous visual degradation in the carrier image. Finally, the embedding of the secret information in the DHT domain of these regions is accomplished. Security test and performance analysis confirm that our algorithm has the advantage of a high balance between the encryption security and the decryption recovery, and exhibits excellent performance in important indicators such as visual quality, robustness and timeliness.