Abstract
We introduce infeasibility certificates, compact and easily verifiable proofs that no profitable attacks exist in the considered system model. We introduce computational methods for generation and validation of such proofs using an enhanced weight reduction technique. A new method for obtaining adversarial expenses by approximating an interval within which this value resides, is an interesting approach to tackle NP-complete tasks and allows to obtain values that require extensive computations in reasonable time.
The research leading to these results has received funding from the European Regional Development Fund through Estonian Centre of Excellence in ICT Research (EXCITE) and the Estonian Research Council under Institutional Research Grant IUT27-1.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Ahmadi, A.A., Olshevsky, A., Parrilo, P.A., Tsitsiklis, J.N.: NP-hardness of deciding convexity of quartic polynomials and related problems. Math. Program. 137(1), 453–476 (2013)
Buldas, A., Laud, P., Priisalu, J., Saarepera, M., Willemson, J.: Rational choice of security measures via multi-parameter attack trees. In: Lopez, J. (ed.) CRITIS 2006. LNCS, vol. 4347, pp. 235–248. Springer, Heidelberg (2006). doi:10.1007/11962977_19
Buldas, A., Lenin, A.: New efficient utility upper bounds for the fully adaptive model of attack trees. In: Das, S.K., Nita-Rotaru, C., Kantarcioglu, M. (eds.) GameSec 2013. LNCS, vol. 8252, pp. 192–205. Springer, Cham (2013). doi:10.1007/978-3-319-02786-9_12
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). doi:10.1007/978-3-642-34266-0_6
Blekherman, G., Parrilo, P.A., Thomas, R.R.: Semidefinite Optimization and Convex Algebraic Geometry. Society for Industrial and Applied Mathematics, Philadelphia (2012)
Boyd, S., Vandenberghe, L.: Convex Optimization. Cambridge University Press, New York (2004)
Corbineau, P.: A declarative language for the Coq proof assistant. In: Miculan, M., Scagnetto, I., Honsell, F. (eds.) TYPES 2007. LNCS, vol. 4941, pp. 69–84. Springer, Heidelberg (2008). doi:10.1007/978-3-540-68103-8_5
De Loera, J.A., Lee, J., Malkin, P.N., Margulies, S.: Computing infeasibility certificates for combinatorial problems through hilbert’s nullstellensatz. J. Symb. Comput. 46(11), 1260–1283 (2011)
Helton, J.W., Nie, J.: Semidefinite representation of convex sets. Math. Program. 122(1), 21–64 (2010)
Hillar, C., Lim, L.-H.: Most tensor problems are np-hard. J. ACM 60(6), 4:51–45:39 (2013)
Jürgenson, A., Willemson, J.: Computing exact outcomes of multi-parameter attack trees. In: Meersman, R., Tari, Z. (eds.) OTM 2008. LNCS, vol. 5332, pp. 1036–1051. Springer, Heidelberg (2008). doi:10.1007/978-3-540-88873-4_8
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). doi:10.1007/978-3-642-14423-3_9
Jürgenson, A., Willemson, J.: On fast and approximate attack tree computations. In: Kwak, J., Deng, R.H., Won, Y., Wang, G. (eds.) ISPEC 2010. LNCS, vol. 6047, pp. 56–66. Springer, Heidelberg (2010). doi:10.1007/978-3-642-12827-1_5
Lenin, A.: Reliable and Efficient Determination of the Likelihood of Rational Attacks. TUT Press, Tallinn (2015)
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). doi:10.1007/11734727_17
de Moura, L., Bjørner, N.: Z3: an efficient SMT solver. In: Ramakrishnan, C.R., Rehof, J. (eds.) TACAS 2008. LNCS, vol. 4963, pp. 337–340. Springer, Heidelberg (2008). doi:10.1007/978-3-540-78800-3_24
Prajna, S., Papachristodoulou, A., Seiler, P., Parrilo, P.A.: Sostools: Sum of squares optimization toolbox for matlab (2004)
Schneier, B.: Attack trees. Dr. Dobb’s J. Softw. Tools 24(12), 21–22, 24, 26, 28–29, December 1999
Smith, K.E., Kahanpää, L., Kekäläinen, P., et al.: An Invitation to Algebraic Geometry. Universitext. Springer Science + Business Media, New York (2000)
Stengle, G.: A nullstellensatz and a positivstellensatz in semialgebraic geometry. Math. Ann. 207, 87–98 (1974)
Stengle, G.: A nullstellensatz and positivstellensatz in semialgebraic geometry. Math. Ann. 207, 87–97 (1994)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2017 Springer International Publishing AG
About this paper
Cite this paper
Buldas, A., Lenin, A., Willemson, J., Charnamord, A. (2017). Simple Infeasibility Certificates for Attack Trees. In: Obana, S., Chida, K. (eds) Advances in Information and Computer Security. IWSEC 2017. Lecture Notes in Computer Science(), vol 10418. Springer, Cham. https://doi.org/10.1007/978-3-319-64200-0_3
Download citation
DOI: https://doi.org/10.1007/978-3-319-64200-0_3
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-64199-7
Online ISBN: 978-3-319-64200-0
eBook Packages: Computer ScienceComputer Science (R0)