Secure lossy source coding with side information

We study the problem of secure lossy source coding with side information. In all works on this problem, either the equivocation of the source at the eavesdropper or the equivocation of the legitimate user´s reconstruction of the source at the eavesdropper is used as the measure of secrecy. In this work, we propose a new secrecy measure, namely, the relative equivocation of the source at the eavesdropper with respect to the legitimate user. We argue that this new secrecy measure is the one that corresponds to the natural generalization of the equivocation in a wiretap channel to the context of secure lossy source coding, and discuss its advantages over the other two secrecy measures. Once we adopt the relative equivocation as the measure of secrecy, we provide a single-letter description of the rate, relative equivocation and distortion region. We specialize this single-letter description to the degraded and reversely degraded cases. Moreover, we investigate the relationships between the optimal scheme that attains this region and the Wyner-Ziv scheme.