Compressing encrypted data: A permutation approach

In a system where it is necessary to perform both encryption and lossy compression, the conventional way is to compress first and then encrypt the compressed data. Furthermore, this separation 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. We call this the reversed system. Johnson et al. proposed an achievability scheme for the reversed system that utilizes modulo-sum encryption followed by compression using Wyner-Ziv distributed source coding with side information. However, the scheme requires more compression rate and secrecy key rate than the conventional system that first compresses and then encrypts. In this paper, we propose a new achievability scheme for the reversed system where encryption is done using 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 lead to performance loss of an encryption-compression system.