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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. More notably, the proposed compression approach applied to encrypted images is only slightly worse, in terms of compression efficiency, than the state-of-the-art lossless/lossy image coders, which take original, unencrypted images as inputs. In contrast, most of the existing ETC solutions induce significant penalty on the compression efficiency.