On Compressing Encrypted Data without the Encryption Key

When it is desired to transmit redundant data over an insecure and bandwidth-constrained channel, it is customary to first compress the redundant data and then encrypt it for security reasons. In this paper, we investigate the novelty of reversing the order of these steps, i.e. first encrypting and then compressing. Although counter-intuitive, we show surprisingly that through the use of coding with side information principles, this reversal in order is indeed possible. In fact, for lossless compression, we show that the theoretical compression gain is unchanged by performing encryption before compression. We show that the cryptographic security of the reversed system is directly related to the strength of the key generator.