Secure compression in the presence of side information at both the legitimate receiver and the 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 to the compression-equivocation rate region are given. These bounds are shown to match when the receiver also wishes to reconstruct the side information losslessly. The availability of  the legitimate receiver's and the eavesdropper's side information  at the encoder is also considered, and the lossless 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 he pure lossless data compression case where side information a the encoder would not help.