Scalable min-max multi-objective cyber-security optimisation over probabilistic attack graphs

Mhr. Khouzani, Zhengliang Liu and Pasquale Malacaria

European Journal of Operational Research, 2019, vol. 278, issue 3, 894-903

Abstract: We present a framework to efficiently solve a multi-objective optimisation problem for cyber-security defence. Facing an attacker who can mount a multi-stage attack (modelled using attack graphs), the defence problem is to select a portfolio of security controls which minimises the security risk and the (direct and indirect) costs of the portfolio of controls. The main challenges for the optimisation are: (a) the effect of the security controls is in general probabilistic, for example, the effect of staff anti-phishing training; moreover, some controls like taking regular back-ups do not have an attack-preventing effect, but rather, mitigate the losses of a successful attack; (b) each control may affect multiple vulnerabilities; and each vulnerability may be affected by multiple controls; (c) there can be a prohibitively large number of attack paths, each involving exploitation of different vulnerabilities. Our mathematical framework deals with all these problems. In particular, we model the problem as a min-max multi-objective optimisation. Using techniques such as ILP conversion, exact LP relaxation and dualisation, we convert the problem into a very efficient MILP. For instance, it returns the optimal solution for attack graphs with 20,000 nodes in less than four minutes typically.

Keywords: Computing science; Multi-objective optimisation; Cyber-security; Probabilistic attack graph (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (6)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:ejores:v:278:y:2019:i:3:p:894-903

DOI: 10.1016/j.ejor.2019.04.035

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