Designing an Efficient Image Encryption-Then- Compression System.In many practical scenarios, image encryption has to be conducted prior to image compression. This has led to the problem of how to design a pair of image encryption and compression algorithms such that compressing the encrypted images can still be efficiently performed. In this paper, we design a highly efficient image encryption-then-compression (ETC) system, where both lossless and lossy compression are considered. The proposed image encryption scheme operated in the prediction error domain is shown to be able to provide a reasonably high level of security. We also demonstrate that an arithmetic coding-based approach can be exploited to efficiently compress the encrypted images.