Piecewise Linear and Stochastic Models for the Analysis of Cyber Resilience

TL;DR

This paper introduces a combined piecewise linear and stochastic modeling framework to analyze the resilience of autonomous cyber-physical systems against malware attacks, providing methods to approximate system parameters.

Contribution

It develops a novel approach integrating differential equations and stochastic models for cyber-physical resilience analysis, with parameter approximation techniques.

Findings

Stochastic model averages approximate differential equation solutions.

Methodology for parameter estimation in cyber-physical attack models.

Framework applicable to autonomous vehicle cyber-defense systems.

Abstract

We model a vehicle equipped with an autonomous cyber-defense system in addition to its inherent physical resilience features. When attacked, this ensemble of cyber-physical features (i.e., ``bonware'') strives to resist and recover from the performance degradation caused by the malware's attack. We model the underlying differential equations governing such attacks for piecewise linear characterizations of malware and bonware, develop a discrete time stochastic model, and show that averages of instantiations of the stochastic model approximate solutions to the continuous differential equation. We develop a theory and methodology for approximating the parameters associated with these equations.