Abstract
Attack trees are a well-known formalism for quantitative analysis of cyber attacks consisting of multiple steps and alternative paths. It is possible to derive properties of the overall attacks from properties of individual steps, such as cost for the attacker and probability of success. However, in existing formalisms, such properties are considered independent. For example, investing more in an attack step would not increase the probability of success. As this seems counterintuitive, we introduce a framework for reasoning about attack trees based on the notion of control strength, annotating nodes with a function from attacker investment to probability of success. Calculation rules on such trees are defined to enable analysis of optimal attacker investment. Our second result consists of the translation of optimal attacker investment into the associated adversarial risk, yielding what we call adversarial risk trees. The third result is the introduction of probabilistic attacker strategies, based on the fitness (utility) of available scenarios. Together these contributions improve the possibilities for using attack trees in adversarial risk analysis.
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
Similar content being viewed by others
Notes
- 1.
Note that picking argmax may involve nondeterministic choice if multiple arguments produce the maximum. This is one of the issues that the probabilistic attackers in this paper (Sect. 5) help to solve.
References
Arnold, F., Hermanns, H., Pulungan, R., Stoelinga, M.: Time-dependent analysis of attacks. In: Abadi, M., Kremer, S. (eds.) POST 2014 (ETAPS 2014). LNCS, vol. 8414, pp. 285–305. Springer, Heidelberg (2014)
Arnold, F., Pieters, W., Stoelinga, M.I.A.: Quantitative penetration testing with item response theory. In: 2013 Proceedings of Information Assurance and Security (IAS). IEEE (2013)
Bistarelli, S., Fioravanti, F., Peretti, P.: Defense trees for economic evaluation of security investments. In: 2006 The First International Conference on Availability, Reliability and Security, ARES 2006 (2006)
Buldas, A., Laud, P., Priisalu, J., Saarepera, M., Willemson, J.: Rational choice of security measures via multi-parameter attack trees. In: López, J. (ed.) CRITIS 2006. LNCS, vol. 4347, pp. 235–248. Springer, Heidelberg (2006)
Cox Jr, L.A.: Game theory and risk analysis. Risk Anal. 29(8), 1062–1068 (2009)
Cremonini, M., Martini, P.: Evaluating information security investments from attackers perspective: the return-on-attack (ROA). In: 4th Workshop on the Economics on Information Security (2005)
Kordy, B., Kordy, P., Mauw, S., Schweitzer, P.: ADTool: security analysis with attack–defense trees. In: Joshi, K., Siegle, M., Stoelinga, M., D’Argenio, P.R. (eds.) QEST 2013. LNCS, vol. 8054, pp. 173–176. Springer, Heidelberg (2013)
Kordy, B., Piètre-Cambacédès, L., Schweitzer, P.: DAG-based attack and defense modeling: don’t miss the forest for the attack trees. Comput. Sci. Rev. 13–14, 1–38 (2014)
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)
de la Maza, M., Tidor, B.: An analysis of selection procedures with particular attention paid to proportional and Boltzmann selection. In: Proceedings of the 5th International Conference on Genetic Algorithms, pp. 124–131 (1993)
Nulton, J.D., Salamon, P.: Statistical mechanics of combinatorial optimization. Phys. Rev. A 37(4), 1351–1356 (1988)
Pieters, W.: Defining “the weakest link”: comparative security in complex systems of systems. In: 2013 IEEE 5th International Conference on Cloud Computing Technology and Science (CloudCom), vol. 2, pp. 39–44, December 2013
Pieters, W., Lukszo, Z., Hadžiosmanović, D., Van den Berg, J.: Reconciling malicious and accidental risk in cyber security. J. Internet Serv. Inf. Secur. 4(2), 4–26 (2014)
Pieters, W., Van der Ven, S.H.G., Probst, C.W.: A move in the security measurement stalemate: elo-style ratings to quantify vulnerability. In: Proceedings of the 2012 New Security Paradigms Workshop, NSPW 2012, pp. 1–14. ACM (2012)
Schneier, B.: Attack trees: modeling security threats. Dr. Dobb’s J. 24(12), 21–29 (1999)
The Open Group. Risk taxonomy. Technical report C081, The Open Group (2009)
Acknowledgements
The research leading to these results has received funding from the European Union’s Seventh Framework Programme (FP7/2007–2013) under grant agreement number ICT-318003 (TREsPASS). This publication reflects only the authors’ views and the Union is not liable for any use that may be made of the information contained herein.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this paper
Cite this paper
Pieters, W., Davarynejad, M. (2015). Calculating Adversarial Risk from Attack Trees: Control Strength and Probabilistic Attackers. In: Garcia-Alfaro, J., et al. Data Privacy Management, Autonomous Spontaneous Security, and Security Assurance. DPM QASA SETOP 2014 2014 2014. Lecture Notes in Computer Science(), vol 8872. Springer, Cham. https://doi.org/10.1007/978-3-319-17016-9_13
Download citation
DOI: https://doi.org/10.1007/978-3-319-17016-9_13
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-17015-2
Online ISBN: 978-3-319-17016-9
eBook Packages: Computer ScienceComputer Science (R0)