Computational Aspects of Attack–Defense Trees

  • Barbara Kordy
  • Marc Pouly
  • Patrick Schweitzer
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7053)

Abstract

Attack–defense trees extend attack trees with defense nodes. This richer formalism allows for a more precise modeling of a system’s vulnerabilities, by representing interactions between possible attacks and corresponding defensive measures. In this paper we compare the computational complexity of both formalisms. We identify semantics for which extending attack trees with defense nodes does not increase the computational complexity. This implies that, for these semantics, every query that can be solved efficiently on attack trees can also be solved efficiently on attack–defense trees. Furthermore, every algorithm for attack trees can directly be used to process attack–defense trees.

Keywords

Boolean Function Defense Tree Computational Aspect Propositional Variable Query Evaluation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Schneier, B.: Attack Trees. Dr. Dobb’s Journal of Software Tools 24(12), 21–29 (1999)Google Scholar
  2. 2.
    Weiss, J.D.: A system security engineering process. In: 14th Nat. Comp. Sec. Conf., pp. 572–581 (1991)Google Scholar
  3. 3.
    Amoroso, E.G.: Fundamentals of Computer Security Technology. Prentice-Hall, Inc., Upper Saddle River (1994)MATHGoogle Scholar
  4. 4.
    Vesely, W.E., Goldberg, F.F., Roberts, N., Haasl, D.: Fault Tree Handbook. Technical Report NUREG-0492, U.S. Regulatory Commission (1981)Google Scholar
  5. 5.
    Mauw, S., Oostdijk, M.: Foundations of Attack Trees. In: Won, D.H., Kim, S. (eds.) ICISC 2005. LNCS, vol. 3935, pp. 186–198. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  6. 6.
    Cervesato, I., Meadows, C.: One Picture Is Worth a Dozen Connectives: A Fault-Tree Representation of NPATRL Security Requirements. IEEE TDSC 4, 216–227 (2007)Google Scholar
  7. 7.
    Edge, K.S., Dalton II, G.C., Raines, R.A., Mills, R.F.: Using Attack and Protection Trees to Analyze Threats and Defenses to Homeland Security. In: MILCOM, IEEE, pp. 1–7 (2006)Google Scholar
  8. 8.
    Morais, A.N.P., Martins, E., Cavalli, A.R., Jimenez, W.: Security Protocol Testing Using Attack Trees. In: CSE (2), pp. 690–697. IEEE Computer Society (2009)Google Scholar
  9. 9.
    Jürgenson, A., Willemson, J.: Serial Model for Attack Tree Computations. In: Lee, D., Hong, S. (eds.) ICISC 2009. LNCS, vol. 5984, pp. 118–128. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  10. 10.
    Bistarelli, S., Peretti, P., Trubitsyna, I.: Analyzing Security Scenarios Using Defence Trees and Answer Set Programming. ENTCS 197(2), 121–129 (2008)Google Scholar
  11. 11.
    Yager, R.R.: OWA trees and their role in security modeling using attack trees. Inf. Sci. 176(20), 2933–2959 (2006)MathSciNetCrossRefMATHGoogle Scholar
  12. 12.
    Kordy, B., Mauw, S., Radomirović, S., Schweitzer, P.: Foundations of Attack–Defense Trees. In: Degano, P., Etalle, S., Guttman, J. (eds.) FAST 2010. LNCS, vol. 6561, pp. 80–95. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  13. 13.
    Kordy, B., Mauw, S., Melissen, M., Schweitzer, P.: Attack–Defense Trees and Two-Player Binary Zero-Sum Extensive Form Games Are Equivalent. In: Alpcan, T., Buttyán, L., Baras, J.S. (eds.) GameSec 2010. LNCS, vol. 6442, pp. 245–256. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  14. 14.
    Kohlas, J.: Information Algebras: Generic Structures for Inference. Springer, Heidelberg (2003)CrossRefMATHGoogle Scholar
  15. 15.
    Davey, B., Priestley, H.: Introduction to Lattices and Order. Cambridge University Press (1990)Google Scholar
  16. 16.
    Pouly, M., Kohlas, J.: Generic Inference: A Unifying Theory for Automated Reasoning. John Wiley & Sons, Inc. (2011)Google Scholar
  17. 17.
    Crama, Y., Hammer, P.: Boolean Functions: Theory, Algorithms and Applications. Cambridge University Press (2011)Google Scholar
  18. 18.
    Wachter, M., Haenni, R.: Multi-state Directed Acyclic Graphs. In: Kobti, Z., Wu, D. (eds.) Canadian AI 2007. LNCS (LNAI), vol. 4509, pp. 464–475. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  19. 19.
    Darwiche, A., Marquis, P.: A Knowledge Compilation Map. J. Artif. Intell. Res. 17, 229–264 (2002)MathSciNetMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Barbara Kordy
    • 1
  • Marc Pouly
    • 1
  • Patrick Schweitzer
    • 1
  1. 1.CSC and SnTUniversity of LuxembourgLuxembourg

Personalised recommendations