Secure distributed lossless compression with side information at the eavesdropper

This paper investigates the problem of secure distributed lossless compression in the presence of arbitrarily correlated side information at an eavesdropper. This scenario consists of two encoders (referred to as Alice and Charlie) that wish to reliably transmit their respective (correlated) sources to a legitimate receiver (referred to as Bob) while satisfying some requirement on the equivocation rate at the eavesdropper (referred to as Eve). Error-free rate-limited channels are assumed between the encoders and the legitimate receiver, one of which being perfectly observed by the eavesdropper, which also has access to a correlated source as side information. For instance, this problem can be seen as a generalization of the well-known Slepian-Wolf problem taking into account the security requirements. A complete characterization of the compression-equivocation rates region for the case of arbitrarily correlated sources is derived. It is shown that the statistical differences between the sources can be useful in terms of secrecy.