I guess someone had to ask this question here. Here goes.
Read the above paper by Klinc et al
Extract is below :-
"We consider the problem of compressing encrypted data. Traditionally in communication systems, data from a source is first compressed and then encrypted before it is transmitted over a channel to the receiver. While in many cases this approach is befitting, there exist scenarios where there is a need to reverse the order in which data encryption and compression are performed. Consider for instance a network of low- cost sensor nodes that transmit sensitive information over the internet to a recipient. The sensor nodes need to encrypt data to hide it from potential eavesdroppers, but they do not necessarily want to compress it as that would require additional hardware and thus higher implementation cost. On the other hand, the network operator that is responsible for transferring the data to the recipient wants to compress the data to maximize the utilization of its resources. It is important to note that the network operator is not trusted and hence does not have access to the key used for encryption and decryption of data. If it had the key, it could simply decrypt data, compress and encrypt again. "