Biblio
Probabilistic model checking is a useful technique for specifying and verifying properties of stochastic systems including randomized protocols and reinforcement learning models. However, these methods rely on the assumed structure and probabilities of certain system transitions. These assumptions may be incorrect, and may even be violated by an adversary who gains control of some system components. In this paper, we develop a formal framework for adversarial robustness in systems modeled as discrete time Markov chains (DTMCs). We base our framework on existing methods for verifying probabilistic temporal logic properties and extend it to include deterministic, memoryless policies acting in Markov decision processes (MDPs). Our framework includes a flexible approach for specifying structure-preserving and non structure-preserving adversarial models. We outline a class of threat models under which adversaries can perturb system transitions, constrained by an ε ball around the original transition probabilities. We define three main DTMC adversarial robustness problems: adversarial robustness verification, maximal δ synthesis, and worst case attack synthesis. We present two optimization-based solutions to these three problems, leveraging traditional and parametric probabilistic model checking techniques. We then evaluate our solutions on two stochastic protocols and a collection of Grid World case studies, which model an agent acting in an environment described as an MDP. We find that the parametric solution results in fast computation for small parameter spaces. In the case of less restrictive (stronger) adversaries, the number of parameters increases, and directly computing property satisfaction probabilities is more scalable. We demonstrate the usefulness of our definitions and solutions by comparing system outcomes over various properties, threat models, and case studies.
Real-time situational awareness (SA) plays an essential role in accurate and timely incident response. Maintaining SA is, however, extremely costly due to excessive false alerts generated by intrusion detection systems, which require prioritization and manual investigation by security analysts. In this paper, we propose a novel approach to prioritizing alerts so as to maximize SA, by formulating the problem as that of active learning in a hidden Markov model (HMM). We propose to use the entropy of the belief of the security state as a proxy for the mean squared error (MSE) of the belief, and we develop two computationally tractable policies for choosing alerts to investigate that minimize the entropy, taking into account the potential uncertainty of the investigations' results. We use simulations to compare our policies to a variety of baseline policies. We find that our policies reduce the MSE of the belief of the security state by up to 50% compared to static baseline policies, and they are robust to high false alert rates and to the investigation errors.