Secure Estimation and Zero-Error Secrecy Capacity

TL;DR

This paper investigates secure state estimation for unstable systems over uncertain channels, introducing the zero-error secrecy capacity to quantify the maximum secure transmission rate, and providing conditions for achieving bounded estimation error and security.

Contribution

It introduces the zero-error secrecy capacity for uncertain wiretap channels and derives necessary and sufficient conditions for secure, bounded estimation.

Findings

A sufficient condition for secure estimation over uncertain channels.

Introduction of zero-error secrecy capacity for uncertain wiretap channels.

Analysis of security criteria with numerical examples.

Abstract

We study the problem of securely estimating the states of an unstable dynamical system subject to nonstochastic disturbances. The estimator obtains all its information through an uncertain channel which is subject to nonstochastic disturbances as well, and an eavesdropper obtains a disturbed version of the channel inputs through a second uncertain channel. An encoder observes and block-encodes the states in such a way that, upon sending the generated codeword, the estimator's error is bounded and such that a security criterion is satisfied ensuring that the eavesdropper obtains as little state information as possible. Two security criteria are considered and discussed with the help of a numerical example. A sufficient condition on the uncertain wiretap channel, i.e., the pair formed by the uncertain channel from encoder to estimator and the uncertain channel from encoder to eavesdropper, is derived which ensures that a bounded estimation error and security are achieved. This condition is also shown to be necessary for a subclass of uncertain wiretap channels. To formulate the condition, the zero-error secrecy capacity of uncertain wiretap channels is introduced, i.e., the maximal rate at which data can be transmitted from the encoder to the estimator in such a way that the eavesdropper is unable to reconstruct the transmitted data. Lastly, the zero-error secrecy capacity of uncertain wiretap channels is studied.