Secure lossy transmission of vector Gaussian sources

We study the secure lossy transmission of a Gaussian vector source to a legitimate user in the presence of an eaves-dropper, where both the legitimate user and the eavesdropper have Gaussian vector side information. The transmitter describes the source to the legitimate user in a way that the legitimate user can reconstruct the source within a certain distortion while the eavesdropper is kept ignorant of the source as much as possible. We obtain an outer bound for the rate, equivocation and distortion region of this secure lossy transmission problem. This outer bound is tight when the transmission rate constraint is removed. In other words, we obtain the maximum equivocation at the eavesdropper when the legitimate user needs to reconstruct the source within a fixed distortion level while there is no constraint on the transmission rate.