Abstract
Attack graphs are a formalism for capturing the most important ways to compromise a system. They are used for evaluating risks and designing appropriate countermeasures. Analysis of attack graphs sometimes requires computing the optimal attack strategy that minimizes the expected cost of the attacker in case of stochastically failing actions. We point out several results in AI literature that are highly relevant to this problem, but remain unnoticed by security literature. We note the problem has been shown to be NP-hard and we present how the problem can be reduced to the problem of solving an unconstrained influence diagram (UID). We use an existing UID solver to assess the scalability of the approach, showing that it can be used to optimally solve attack graphs with up to 20 attack actions.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Buldas, A., Stepanenko, R.: Upper bounds for adversaries’ utility in attack trees. In: Grossklags, J., Walrand, J. (eds.) GameSec 2012. LNCS, vol. 7638, pp. 98–117. Springer, Heidelberg (2012)
Sarraute, C., Richarte, G., Lucángeli Obes, J.: An algorithm to find optimal attack paths in nondeterministic scenarios. In: Proceedings of the 4th ACM Workshop on Security and Artificial Intelligence, AISec 2011, pp. 71–80. ACM, New York (2011)
Greiner, R., Hayward, R., Jankowska, M., Molloy, M.: Finding optimal satisficing strategies for and-or trees. Artificial Intelligence 170(1), 19–58 (2006)
Jensen, F.V., Vomlelová, M.: Unconstrained influence diagrams. In: Proceedings of the Eighteenth Conference on Uncertainty in Artificial Intelligence, UAI 2002, pp. 234–241. Morgan Kaufmann Publishers Inc., San Francisco (2002)
Ingols, K., Lippmann, R., Piwowarski, K.: Practical attack graph generation for network defense. In: Proceedings of the 22nd Annual Computer Security Applications Conference, ACSAC 2006, pp. 121–130. IEEE Computer Society, Washington, DC (2006)
Ou, X., Boyer, W.F., McQueen, M.A.: A scalable approach to attack graph generation. In: Proceedings of the 13th ACM Conference on Computer and Communications Security, CCS 2006, pp. 336–345. ACM, New York (2006)
Wang, L., Islam, T., Long, T., Singhal, A., Jajodia, S.: An attack graph-based probabilistic security metric. In: Atluri, V. (ed.) DAS 2008. LNCS, vol. 5094, pp. 283–296. Springer, Heidelberg (2008)
Homer, J., Ou, X., Schmidt, D.: A sound and practical approach to quantifying security risk in enterprise networks. Technical report, Kansas State University, Computing and Information Sciences Department (2009)
Luque, M., Nielsen, T.D., Jensen, F.V.: An anytime algorithm for evaluating unconstrained influence diagrams. In: Proc. 4th European Workshop on Probabilistic Graphical Models, pp. 177–184 (2008)
Isa, J., Lisy, V., Reitermanova, Z., Sykora, O.: Unconstrained influence diagram solver: Guido. In: 19th IEEE International Conference on Tools with Artificial Intelligence, ICTAI 2007, vol. 1, pp. 24–27. IEEE Computer Society (2007)
Iša, J., Reitermanová, Z., Sýkora, O.: On the complexity of general solution dags. In: Proceedings of the 2009 International Conference on Machine Learning and Applications, ICMLA 2009, pp. 673–678. IEEE Computer Society, Washington, DC (2009)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Lisý, V., Píbil, R. (2013). Computing Optimal Attack Strategies Using Unconstrained Influence Diagrams. In: Wang, G.A., Zheng, X., Chau, M., Chen, H. (eds) Intelligence and Security Informatics. PAISI 2013. Lecture Notes in Computer Science, vol 8039. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39693-9_5
Download citation
DOI: https://doi.org/10.1007/978-3-642-39693-9_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-39692-2
Online ISBN: 978-3-642-39693-9
eBook Packages: Computer ScienceComputer Science (R0)