In this talk, we consider a problem of lossy source coding with side information under a constraint that the reconstruction sequence at a decoder should be kept secret, to a certain extent, from another terminal in the network. We are interested in how the new privacy constraint affects the existing tradeoff between rate and distortion. We propose the use of randomized decoder, and characterize inner and outer bounds to the rate-distortion-equivocation region for different cases. In the special case, the complete rate-distortion-equivocation region is given. A binary example illustrating a new tradeoff due to the new secrecy constraint, and a potential gain from the use of randomized decoder is also provided.