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Security Decisions for Cyber-Physical Systems based on Solving Critical Node Problems with Vulnerable Nodes

Jens Otto, Niels Grüttemeier, Felix Specht

TL;DR

This work proposes and evaluates a concept for finding the devices to isolate and applies the Critical Node Cut Problem with Vulnerable Vertices (CNP-V) - an NP-hard computational problem originally motivated by isolating vulnerable people in case of a pandemic.

Abstract

Cyber-physical production systems consist of highly specialized software and hardware components. Most components and communication protocols are not built according to the Secure by Design principle. Therefore, their resilience to cyberattacks is limited. This limitation can be overcome with common operational pictures generated by security monitoring solutions. These pictures provide information about communication relationships of both attacked and non-attacked devices, and serve as a decision-making basis for security officers in the event of cyberattacks. The objective of these decisions is to isolate a limited number of devices rather than shutting down the entire production system. In this work, we propose and evaluate a concept for finding the devices to isolate. Our approach is based on solving the Critical Node Cut Problem with Vulnerable Vertices (CNP-V) - an NP-hard computational problem originally motivated by isolating vulnerable people in case of a pandemic. To the best of our knowledge, this is the first work on applying CNP-V in context of cybersecurity.

Security Decisions for Cyber-Physical Systems based on Solving Critical Node Problems with Vulnerable Nodes

TL;DR

This work proposes and evaluates a concept for finding the devices to isolate and applies the Critical Node Cut Problem with Vulnerable Vertices (CNP-V) - an NP-hard computational problem originally motivated by isolating vulnerable people in case of a pandemic.

Abstract

Cyber-physical production systems consist of highly specialized software and hardware components. Most components and communication protocols are not built according to the Secure by Design principle. Therefore, their resilience to cyberattacks is limited. This limitation can be overcome with common operational pictures generated by security monitoring solutions. These pictures provide information about communication relationships of both attacked and non-attacked devices, and serve as a decision-making basis for security officers in the event of cyberattacks. The objective of these decisions is to isolate a limited number of devices rather than shutting down the entire production system. In this work, we propose and evaluate a concept for finding the devices to isolate. Our approach is based on solving the Critical Node Cut Problem with Vulnerable Vertices (CNP-V) - an NP-hard computational problem originally motivated by isolating vulnerable people in case of a pandemic. To the best of our knowledge, this is the first work on applying CNP-V in context of cybersecurity.
Paper Structure (10 sections, 1 theorem, 4 equations, 5 figures, 2 tables, 3 algorithms)

This paper contains 10 sections, 1 theorem, 4 equations, 5 figures, 2 tables, 3 algorithms.

Table of Contents

  1. Introduction
  2. Related Work
  3. Problem Definition
  4. Security Node Problem with Vulnerable Vertices
  5. Solving SNP-V
  6. SNP-V ILP Definition
  7. Solving SNP-V on Instances with a Small Budget
  8. Solving SNP-V with Greedy Algorithm
  9. First Experimental Results
  10. Summary and Future Work

Key Result

Proposition 1

Let $(G=(V,E),A,k)$ be an instance of SNP-V. Furthermore, let $D \subseteq V \setminus A$ be the set of non-attacked degree-one devices. Then, there exists a solution $C$ with $C \cap D = \emptyset$.

Figures (5)

  • Figure 1: Scope of this work: relation between security monitoring, common operational picture and decisions.
  • Figure 2: Example solutions of a CNP-V instance $(G,A,k)$.
  • Figure 3: Example graph of an instance of CNP-V with $k=1$, where the solution is not unique.
  • Figure 4: Synthetic dataset example.
  • Figure 5: SFOWL dataset.

Theorems & Definitions (10)

  • Definition 1
  • Definition 2: Connections
  • Definition 3: $A$-vulnerability
  • Definition 4: CNP-V
  • Definition 5: $A$-healthiness
  • Definition 6: Objective Value
  • Definition 7: SNP-V
  • Definition 8: SNP-V-ILP
  • Proposition 1
  • proof