Uncertain Wiretap Channels and Secure Estimation

TL;DR

This paper introduces uncertain wiretap channels, defines their zero-error secrecy capacity, and studies secure system estimation ensuring bounded error for the estimator while the eavesdropper's error diverges, based on channel capacities.

Contribution

It introduces the concept of uncertain wiretap channels and derives conditions for secure estimation in dynamical systems with nonstochastic disturbances.

Findings

Secure estimation is possible if the sensor-estimator channel's zero-error capacity exceeds the system's unstable pole logarithm.

Positive zero-error secrecy capacity of the wiretap channel is necessary for security.

The paper provides formulas for calculating capacities when the channel is perfect.

Abstract

Uncertain wiretap channels are introduced. Their zero-error secrecy capacity is defined. If the sensor-estimator channel is perfect, it is also calculated. Further properties are discussed. The problem of estimating a dynamical system with nonstochastic disturbances is studied where the sensor is connected to the estimator and an eavesdropper via an uncertain wiretap channel. The estimator should obtain a uniformly bounded estimation error whereas the eavesdropper's error should tend to infinity. It is proved that the system can be estimated securely if the zero-error capacity of the sensor-estimator channel is strictly larger than the logarithm of the system's unstable pole and the zero-error secrecy capacity of the uncertain wiretap channel is positive.