Security of compressing encrypted sources

When transmitting redundant data over an insecure channel, it is customary to first compress the data and then encrypt it. Johnson et al have investigated a cryptosystem where the order of these steps is reversed, and they have shown that this reversal is possible. We formally study the security of the encrypt-then-compress cryptosystems and show that the compression does not compromise the security of the system in both the information theoretic case (perfectly secure encryption) and the complexity theoretic case (computationally secure encryption).