Rate-Distortion Theory for Secrecy Systems

TL;DR

This paper develops a rate-distortion framework for secrecy systems, analyzing how secret keys and side information influence the tradeoff between communication efficiency and adversary distortion.

Contribution

It characterizes the optimal tradeoff among rate, key rate, and distortions, highlighting the impact of causal side information at the adversary.

Findings

Causal side information significantly affects the secrecy-distortion tradeoff.

Normalized equivocation measures are encompassed within this framework.

The model provides a comprehensive characterization of secrecy in the presence of side information.

Abstract

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.