Functional Forms of Optimum Spoofing Attacks for Vector Parameter Estimation in Quantized Sensor Networks

TL;DR

This paper analyzes optimal spoofing attack strategies in quantized sensor networks, providing conditions for guaranteed attack performance and demonstrating how attackers can effectively compromise estimation accuracy.

Contribution

It introduces a generalized attack model with arbitrary functional forms and derives necessary and sufficient conditions for optimal attacks in quantized sensor networks.

Findings

Highly desirable attacks can be constructed with sufficiently large attack vectors.

Under such attacks, attacked data does not reduce the CRB.

Conditions for guaranteed attack performance are established regardless of estimation processing.

Abstract

Estimation of an unknown deterministic vector from quantized sensor data is considered in the presence of spoofing attacks which alter the data presented to several sensors. Contrary to previous work, a generalized attack model is employed which manipulates the data using transformations with arbitrary functional forms determined by some attack parameters whose values are unknown to the attacked system. For the first time, necessary and sufficient conditions are provided under which the transformations provide a guaranteed attack performance in terms of Cramer-Rao Bound (CRB) regardless of the processing the estimation system employs, thus defining a highly desirable attack. Interestingly, these conditions imply that, for any such attack when the attacked sensors can be perfectly identified by the estimation system, either the Fisher Information Matrix (FIM) for jointly estimating the desired and attack parameters is singular or that the attacked system is unable to improve the CRB for the desired vector parameter through this joint estimation even though the joint FIM is nonsingular. It is shown that it is always possible to construct such a highly desirable attack by properly employing a sufficiently large dimension attack vector parameter relative to the number of quantization levels employed, which was not observed previously. To illustrate the theory in a concrete way, we also provide some numerical results which corroborate that under the highly desirable attack, attacked data is not useful in reducing the CRB.