Robust and hierarchical watermarking of encrypted images based on Compressive Sensing

•An encryption method with the data embedding feature based on Compressive Sensing.•The watermark can be detected into encrypted domain or decrypted domain.•The operations of watermark extraction and image decryption are commutative.•It has the properties of robustness against noise and hierarchical security.•It has flexible data embedding capacity and high correct bit extraction rate.

We propose a method that allows watermarking encrypted image and detecting the watermark in encrypted domain or decrypted domain. First, image is divided into blocks and transformed to wavelet coefficients, and then scrambled with Arnold map and encrypted with Compressive Sensing. Next, watermark is embedded into the encrypted image using the Scalar Costa Scheme. The operations of watermark extraction and image decryption are commutative. The watermark can be extracted in the compressed encrypted domain and then the original image can be decrypted and reconstructed. In the other case, the image can be decrypted and the watermark can be extracted in the decrypted domain. The proposed method is compared with the-state-of-art methods, where its superiority in terms of robustness, high correct bit extraction rate, flexible data embedding capacity and hierarchical security are highlighted.