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In general, JPEG2000 code streams have marker codes in the header, which define particular meanings such as start of packet and end of code stream. Marker codes do not exist in the data part of code streams. The selective encryption of the data part has been considered to avoid generating marker codes. Such encryption is effective in business content exchange. To handle this issue, some schemes have been proposed. However, the security of these schemes has not been evaluated yet. This paper shows that an existing scheme can be broken by cryptanalysis. We describe a secure encryption scheme and mode against cipher-text attacks, known plain-text attacks and chosen plain-text attacks.