Using a Secret Key to Foil an Eavesdropper

TL;DR

This paper investigates how to optimally use secret keys and limited communication in distributed systems to minimize an eavesdropper's ability to act on signals, considering delayed public information and system actions.

Contribution

It introduces a new value-based secrecy measure, characterizes the optimal rate-payoff region, and proposes non-standard channel synthesis methods for secure communication.

Findings

Optimal system performance depends on which signals are delayed publicly available.

The value function based on system and adversary actions guides secrecy performance.

Optimal communication strategies involve synthesizing a memoryless channel, not standard source coding.

Abstract

This work addresses private communication with distributed systems in mind. We consider how to best use secret key resources and communication to transmit signals across a system so that an eavesdropper is least capable to act on the signals. One of the key assumptions is that the private signals are publicly available with a delay---in this case a delay of one. We find that even if the source signal (information source) is memoryless, the design and performance of the optimal system has a strong dependence on which signals are assumed to be available to the eavesdropper with delay. Specifically, we consider a distributed system with two components where information is known to only one component and communication resources are limited. Instead of measuring secrecy by "equivocation," we define a value function for the system, based on the actions of the system and the adversary, and characterize the optimal performance of the system, as measured by the average value obtained against the worst adversary. The resulting optimal rate-payoff region is expressed with information theoretic inequalities, and the optimal communication methods are not standard source coding techniques but instead are methods that stem from synthesizing a memoryless channel.