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.

Probabilistic model checking is a formal verification technique that has been applied successfully in a variety of domains, providing identification of system errors through quantitative verification of stochastic system models. One domain that can benefit from probabilistic model checking is cloud computing, which must provide highly reliable and secure computational and storage services to large numbers of mission-critical software systems. For real-world domains like cloud computing, external system factors and environmental changes must be estimated accurately in the form of probabilities in system models; inaccurate estimates for the model probabilities can lead to invalid verification results. To address the effects of uncertainty in probability estimates, in previous work we have developed a variety of techniques for perturbation analysis of discrete- and continuous-time Markov chains (DTMCs and CTMCs). These techniques determine the consequences of the uncertainty on verification of system properties. In this paper, we present the first approach for perturbation analysis of Markov decision processes (MDPs), a stochastic formalism that is especially popular due to the significant expressive power it provides through the combination of both probabilistic and nondeterministic choice. Our primary contribution is a novel technique for efficiently analyzing the effects of perturbations of model probabilities on verification of reachability properties of MDPs. The technique heuristically explores the space of adversaries of an MDP, which encode the different ways of resolving the MDP’s nondeterministic choices. We demonstrate the practical effectiveness of our approach by applying it to two case studies of cloud systems.

Distributed storage systems and caching systems are becoming widespread, and this motivates the increasing interest on assessing their achievable performance in terms of reliability for legitimate users and security against malicious users. While the assessment of reliability takes benefit of the availability of well established metrics and tools, assessing security is more challenging. The classical cryptographic approach aims at estimating the computational effort for an attacker to break the system, and ensuring that it is far above any feasible amount. This has the limitation of depending on attack algorithms and advances in computing power. The information-theoretic approach instead exploits capacity measures to achieve unconditional security against attackers, but often does not provide practical recipes to reach such a condition. We propose a mixed cryptographic/information-theoretic approach with a twofold goal: estimating the levels of information-theoretic security and defining a practical scheme able to achieve them. In order to find optimal choices of the parameters of the proposed scheme, we exploit an effective probabilistic model checker, which allows us to overcome several limitations of more conventional methods.

One of the key objectives of distributed denial of service (DDoS) attack on the smart grid advanced metering infrastructure is to threaten the availability of end user's metering data. This will surely disrupt the smooth operations of the grid and third party operators who need this data for billing and other grid control purposes. In previous work, we proposed a cloud-based Openflow firewall for mitigation against DDoS attack in a smart grid AMI. In this paper, PRISM model checker is used to perform a probabilistic best-and worst-case analysis of the firewall with regard to DDoS attack success under different firewall detection probabilities ranging from zero to 1. The results from this quantitative analysis can be useful in determining the extent the DDoS attack can undermine the correctness and performance of the firewall. In addition, the study can also be helpful in knowing the extent the firewall can be improved by applying the knowledge derived from the worst-case performance of the firewall.

Modeling and evaluating the performance of large-scale wireless sensor networks (WSNs) is a challenging problem. The traditional method for representing the global state of a system as a cross product of the states of individual nodes in the system results in a state space whose size is exponential in the number of nodes. We propose an alternative way of representing the global state of a system: namely, as a probability mass function (pmf) which represents the fraction of nodes in different states. A pmf corresponds to a point in a Euclidean space of possible pmf values, and the evolution of the state of a system is represented by trajectories in this Euclidean space. We propose a novel performance evaluation method that examines all pmf trajectories in a dense Euclidean space by exploring only finite relevant portions of the space. We call our method Euclidean model checking. Euclidean model checking is useful both in the design phase—where it can help determine system parameters based on a specification—and in the evaluation phase—where it can help verify performance properties of a system. We illustrate the utility of Euclidean model checking by using it to design a time difference of arrival (TDoA) distance measurement protocol and to evaluate the protocol’s implementation on a 90-node WSN. To facilitate such performance evaluations, we provide a Markov model estimation method based on applying a standard statistical estimation technique to samples resulting from the execution of a system.

Security features are often hardwired into software applications, making it difficult to adapt security responses to reflect changes in runtime context and new attacks. In prior work, we proposed the idea of architecture-based self-protection as a way of separating adaptation logic from application logic and providing a global perspective for reasoning about security adaptations in the context of other business goals. In this paper, we present an approach, based on this idea, for combating denial-of-service (DoS) attacks. Our approach allows DoS-related tactics to be composed into more sophisticated mitigation strategies that encapsulate possible responses to a security problem. Then, utility-based reasoning can be used to consider different business contexts and qualities. We describe how this approach forms the underpinnings of a scientific approach to self-protection, allowing us to reason about how to make the best choice of mitigation at runtime. Moreover, we also show how formal analysis can be used to determine whether the mitigations cover the range of conditions the system is likely to encounter, and the effect of mitigations on other quality attributes of the system. We evaluate the approach using the Rainbow self-adaptive framework and show how Rainbow chooses DoS mitigation tactics that are sensitive to different business contexts.