Secure source coding with action-dependent side information

We consider a secure lossy source coding problem with the presence of an eavesdropper who has access to the source description. An encoder wants to compress the source in such a way that the intended decoder can reconstruct the source sequence and satisfy a distortion criterion, while revealing only limited knowledge about the source to the eavesdropper. In our system an action sequence is generated based on the source description with some costs to influence the side information available to the legitimate decoder and the eavesdropper. We provide a complete characterization of the rate-distortion-cost-equivocation region for a discrete source with correlated action-dependent side information at the decoders. The result serves as a fundamental limit for example in secure sensor networking.