On the separation of encryption and compression in secure distributed source coding

We study a secure distributed source coding problem. Two terminals with correlated observations would like to send their observations securely to a receiver using minimal transmission rates and key rates. By providing a converse, we show the optimality of a natural structure, in which Slepian-Wolf distributed compression is followed by an application of a onetime pad for encryption. Hence, in contrast to many multiuser setting, the separation of compression and encryption is optimal for this particular case. The optimality of the separation can simplify practical algorithm design. In addition, we constructively demonstrate that switching the order of compression and encryption does not incur any performance loss. Finally, we show that if one requires perfect secrecy and zero error probability, the required rates increase significantly and data compression becomes unnecessary.