Rate-Distortion Theory for Secrecy Systems
This work addresses secure communication design for systems where adversaries may have side information, providing a foundational theoretical framework.
The paper tackles the problem of characterizing the optimal tradeoff between communication rate, secret key rate, distortion at an adversary, and distortion at a legitimate receiver in secrecy systems, showing that causal side information at the adversary is pivotal and that normalized equivocation measures are a special case.
Secrecy in communication systems is measured herein by the distortion that an adversary incurs. The transmitter and receiver share secret key, which they use to encrypt communication and ensure distortion at an adversary. A model is considered in which an adversary not only intercepts the communication from the transmitter to the receiver, but also potentially has side information. Specifically, the adversary may have causal or noncausal access to a signal that is correlated with the source sequence or the receiver's reconstruction sequence. The main contribution is the characterization of the optimal tradeoff among communication rate, secret key rate, distortion at the adversary, and distortion at the legitimate receiver. It is demonstrated that causal side information at the adversary plays a pivotal role in this tradeoff. It is also shown that measures of secrecy based on normalized equivocation are a special case of the framework.