Compressing encrypted sources using side-information coding

When transmitting a source over an insecure and bandwidth-limited channel, compression (lossy/lossless) precedes encryption. We show that, through the use of side-information coding principles, the order of these operations can be reversed without loss of Wyner-sense perfect secrecy and often with a significant compression ratio. Further, when the source has to be recovered perfectly (with high probability) or is Gaussian (with the mean-squared error fidelity criterion), there is no loss of compression efficiency and the proposed system requires no more randomness in the encryption key compared to systems where compression precedes encryption.