Constraints such as limited security investment cost precludes a security decision maker from implementing all possible countermeasures in a system. Existing analytical model-based security optimization strategies do not prevail for the following reasons: (i) none of these model-based methods offer a way to find optimal security solution in the absence of probability assignments to the model, (ii) methods scale badly as size of the system to model increases and (iii) some methods suffer as they use attack trees (AT) whose structure does not allow for the inclusion of countermeasures while others translate the non-state-space model (e.g., attack response tree) into a state-space model hence causing state-space explosion. In this paper, we use a novel AT paradigm called attack countermeasure tree (ACT) whose structure takes into account attacks as well as countermeasures (in the form of detection and mitigation events). We use greedy and branch and bound techniques to study several objective functions with goals such as minimizing the number of countermeasures, security investment cost in the ACT and maximizing the benefit from implementing a certain countermeasure set in the ACT under different constraints. We cast each optimization problem into an integer programming problem which also allows us to find optimal solution even in the absence of probability assignments to the model. Our method scales well for large ACTs and we compare its efficiency with other approaches.
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