Attack–Defense Trees and Two-Player Binary Zero-Sum Extensive Form Games Are Equivalent

  • Barbara Kordy
  • Sjouke Mauw
  • Matthijs Melissen
  • Patrick Schweitzer
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6442)


Attack–defense trees are used to describe security weaknesses of a system and possible countermeasures. In this paper, the connection between attack–defense trees and game theory is made explicit. We show that attack–defense trees and binary zero-sum two-player extensive form games have equivalent expressive power when considering satisfiability, in the sense that they can be converted into each other while preserving their outcome and their internal structure.


Game Theory Intrusion Detection System Defense Tree Conjunctive Node Attack Modeling 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Schneier, B.: Secrets and lies. Wiley, Indianapolis (2004)Google Scholar
  2. 2.
    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 (2005)CrossRefGoogle Scholar
  3. 3.
    Willemson, J., Jürgenson, A.: 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
  4. 4.
    Rehák, M., Staab, E., Fusenig, V., Pěchouček, M., Grill, M., Stiborek, J., Bartoš, K., Engel, T.: Runtime Monitoring and Dynamic Reconfiguration for Intrusion Detection Systems. In: Kirda, E., Jha, S., Balzarotti, D. (eds.) RAID 2009. LNCS, vol. 5758, pp. 61–80. Springer, Heidelberg (2009)Google Scholar
  5. 5.
    Amenaza: SecurITree,
  6. 6.
  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, pp. 1–7. IEEE, Los Alamitos (2006)Google Scholar
  8. 8.
    Bistarelli, S., Dall’Aglio, M., Peretti, P.: Strategic Games on Defense Trees. In: Dimitrakos, T., Martinelli, F., Ryan, P.Y.A., Schneider, S. (eds.) FAST 2006. LNCS, vol. 4691, pp. 1–15. Springer, Heidelberg (2006)Google Scholar
  9. 9.
    Kordy, B., Mauw, S., Radomirović, S., Schweitzer, P.: Foundations of Attack–Defense Trees. In: FAST. LNCS. Springer, Heidelberg (2010), Google Scholar
  10. 10.
    Kordy, B., Mauw, S., Melissen, M., Schweitzer, P.: Attack–defense trees and two-player binary zero-sum extensive form games are equivalent – technical report with proofs,

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Barbara Kordy
    • 1
  • Sjouke Mauw
    • 1
  • Matthijs Melissen
    • 1
  • Patrick Schweitzer
    • 1
  1. 1.University of LuxembourgLuxembourg

Personalised recommendations