  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.
