Harnessing the Power of Deception in Attack Graph-Based Security Games

Abstract

We study the use of deception in attack graph-based Stackelberg security games. In our setting, in addition to allocating defensive resources to protect important targets from attackers, the defender can strategically manipulate the attack graph through three main types of deceptive actions. We show that finding the optimal deception and defense strategy is at least NP-hard. We provide two techniques for efficiently solving this problem: a mixed-integer linear program for layered directed acyclic graphs (DAGs) and neural architecture search for general DAGs. We empirically demonstrate that using deception on attack graphs gives the defender a significant advantage, and the algorithms we develop scale gracefully to medium-sized problems.

Appendix

We modify the DE [61] variant DE/rand/1/bin [42]. To initialize the population, we randomly choose the sequence of deceptive actions to consider. For each type, we determine the maximum number of components that can be altered (e.g., edges to add) for this individual. If allowed, we then modify the graph with randomly-selected modifications of that type. We also add a new termination condition based on the known optimal utility (0) for the defender if the defender has infinite protective and deceptive budgets. If any solution yields this utility, then we stop early and select it as the final solution. We also use a more compact solution representation: the full solution takes space $m_e (2 |N| + 1) + |N| + 2 |E|$, where $m_e$ indicates the maximum number of edges that can be added to the graph given $B^d$. Each edge to be added takes space 2|N|. To indicate that an edge is to be added, we take the ${{\,\mathrm{arg\,max}\,}}$ over the effort allocated in the first N and last N slots. The resulting indices i, j indicate the endpoints of the edge. If the summed effort at i, j is greater than a threshold, the edge is added. We further compact the representation when the defender cannot add or hide any edges without violating constraints by removing these parts of the solution, so each strategy uses space $|E| + |N|$.