Joint encryption and compression is an ideal solution for protecting security and privacy of image data in a real scenario, e.g. storing them on an existing cloud-based service like Facebook. Recently, some block-wise encryption-then-compression (ETC) schemes compatible with JPEG were proposed to provide a reasonably high level of security without compromising compression ratio much. This paper investigates recovering the block-wise relationship in an ETC scheme exerting on single-color blocks of size $8\times 8$ in the scenarios of ciphertext-only attack, known-plaintext attack and chosen-plaintext attack. Then, the attacking targets are extended to the other conventional ETC schemes exerting on multiple color channels and blocks of various sizes. Especially, an elaborate jigsaw puzzle solver is designed to recover enough visual information from multiple cipher-images encrypted by the same secret key. Moreover, the nice attacking performance was verified over two social media platforms, Facebook and Weibo.

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