  In a system that performs both encryption and lossy compression, the
conventional way is to compress first and then encrypt the compressed data.
This separation approach proves to be optimal. In certain applications where
sensitive information should be protected as early as possible, it is
preferable to perform encryption first and then compress the encrypted data,
which leads to the concept of the reversed system. Johnson et al. proposed an
achievability scheme for the reversed system that has a modulo-sum encryption
followed by a compression using Wyner-Ziv distributed source coding with side
information. However, this reversed system performs worse than the conventional
system in the sense that it requires more compression rate and secrecy key
rate. In this paper, we propose a new achievability scheme for the reverse
system where encryption is conducted by a permutation cipher and then the
encrypted data is compressed using the optimal rate-distortion code. The
proposed scheme can achieve the optimal compression rate and secret key rate,
and therefore shows that reversing the order of encryption and compression does
not necessarily compromise the performance of an encryption-compression system.
The proposed system attains weak secrecy, and we show that the information
leakage is mainly contributed by the type information of the sequence, which is
not concealed by the permutation cipher. Given the type of the sequence, the
rest of the information leakage vanishes exponentially.
