  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.
