Secure Lossless Compression with Side Information
  Secure data compression in the presence of side information at both a legitimate receiver and an eavesdropper is explored. A noise-free, limited rate link between the source and the receiver, whose output can be perfectly observed by the eavesdropper, is assumed. As opposed to the wiretap channel model, in which secure communication can be established by exploiting the noise in the channel, here the existence of side information at the receiver is used. Both coded and uncoded side information are considered. In the coded side information scenario, inner and outer bounds on the compression-equivocation rate region are given. In the uncoded side information scenario, the availability of the legitimate receiver's and the eavesdropper's side information at the encoder is considered, and the compression-equivocation rate region is characterized for these cases. It is shown that the side information at the encoder can increase the equivocation rate at the eavesdropper. Hence, the side information at the encoder is shown to be useful in terms of security; this is in contrast with the pure lossless data compression case where side information at the encoder would not help. 
Deniz Gunduz, Elza Erkip, H. Vincent Poor