In many practical scenarios, image encryption should be implemented before image compression. This leads to the requirement of compressing encrypted images. Compressed sensing (CS), a breakthrough in signal processing, has been demonstrated to be an effective method for compressing encrypted images with robustness. However, for the exiting CS-based image encryption-then-compression (ETC) systems, image encryption is usually performed by using linear operations. When linear operations are used, we cannot achieve low computational complexity and high security in the meantime. To solve this problem, a novel 2D CS (2DCS) based ETC (2DCS-ETC) scheme is proposed in this paper. First, two nonlinear operations, including global random permutation (GRP) and negative-positive transformation (NPT), are utilized to encrypt the original image for high security purpose. Second, the encrypted image is compressed by using 2DCS for low computational complexity purpose. Furthermore, a gray mapping operation is embedded prior to CS encoding. Since gray mapping strategy can reduce the dynamic range of the CS samples, this strategy is also helpful for the rate distortion (R-D) performance improvement. Third, a 2D projected gradient with embedding decryption (2DPG-ED) algorithm is proposed, which can be utilized for the original image reconstruction even if the encrypted image is not sparse anymore. Compared with the previous CS-based ETC methods, the proposed approach can simultaneously achieve high security and low computational complexity with better robustness.

We demonstrate a new approach to chosen-plaintext attack on a general encryption model based on scrambling preprocessing operation and double random phase encoding (DRPE). With this attack, an opponent can access both the scrambling key and two random phase keys. We hope that our work motivates further security analysis of the optical encryption scheme combining the scrambling techniques and DRPE.