Moving Target Defense (MTD) can enhance the resilience of cyber systems against attacks. Although there have been many MTD techniques, there is no systematic understanding and quantitative characterization of the power of MTD. In this paper, we propose to use a cyber epidemic dynamics approach to characterize the power of MTD. We define and investigate two complementary measures that are applicable when the defender aims to deploy MTD to achieve a certain security goal. One measure emphasizes the maximum portion of time during which the system can afford to stay in an undesired configuration (or posture), without considering the cost of deploying MTD. The other measure emphasizes the minimum cost of deploying MTD, while accommodating that the system has to stay in an undesired configuration (or posture) for a given portion of time. Our analytic studies lead to algorithms for optimally deploying MTD.
We will use the cyber epidemic dynamics model in @cite_2 as the starting point of our study. This model @cite_2 describes reactive adaptive defense (i.e., the defender aims to adjust its defense to control contain the global security state). We extend this model to accommodate MTD, a kind of proactive defense , and the resulting model is analyzed using different skills @cite_51 @cite_9 . We mention that the effect of dynamic structures in cyber epidemic models is studied in @cite_34 , where the structure dynamics however follows a deterministic and periodic process, rather than adaptively scheduled by using (for example) MTD. We also mention that the effect of dynamic semi-heterogeneous structures (i.e., clustered networks), rather than arbitrary heterogeneous structures, is studied in @cite_19 . These studies @cite_34 @cite_19 consider static parameters only and do not have any of the measures we propose to use.
@cite_9 @cite_19 @cite_2 @cite_34 @cite_51
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Theoretical modeling of computer virus worm epidemic dynamics is an important problem that has attracted many studies. However, most existing models are adapted from biological epidemic ones. Although biological epidemic models can certainly be adapted to capture some computer virus spreading scenarios (especially when the so-called homogeneity assumption holds), the problem of computer virus spreading is not well understood because it has many important perspectives that are not necessarily accommodated in the biological epidemic models. In this article, we initiate the study of such a perspective, namely that of adaptive defense against epidemic spreading in arbitrary networks. More specifically, we investigate a nonhomogeneous Susceptible-Infectious-Susceptible (SIS) model where the model parameters may vary with respect to time. In particular, we focus on two scenarios we call semi-adaptive defense and fully adaptive defense, which accommodate implicit and explicit dependency relationships between the model parameters, respectively. In the semi-adaptive defense scenario, the model’s input parameters are given; the defense is semi-adaptive because the adjustment is implicitly dependent upon the outcome of virus spreading. For this scenario, we present a set of sufficient conditions (some are more general or succinct than others) under which the virus spreading will die out; such sufficient conditions are also known as epidemic thresholds in the literature. In the fully adaptive defense scenario, some input parameters are not known (i.e., the aforementioned sufficient conditions are not applicable) but the defender can observe the outcome of virus spreading. For this scenario, we present adaptive control strategies under which the virus spreading will die out or will be contained to a desired level. The spread of epidemics and malware is commonly modeled by diffusion processes on networks. Protective interventions such as vaccinations or installing anti-virus software are used to contain their spread. Typically, each node in the network has to decide its own strategy of securing itself, and its benefit depends on which other nodes are secure, making this a natural game-theoretic setting. There has been a lot of work on network security game models, but most of the focus has been either on simplified epidemic models or homogeneous network structure. We develop a new formulation for an epidemic containment game, which relies on the characterization of the SIS model in terms of the spectral radius of the network. We show in this model that pure Nash equilibria (NE) always exist, and can be found by a best response strategy. We analyze the complexity of finding NE, and derive rigorous bounds on their costs and the Price of Anarchy or PoA (the ratio of the cost of the worst NE to the optimum social cost) in general graphs as well as in random graph models. In particular, for arbitrary power-law graphs with exponent β > 2, we show that the PoA is bounded by O(T2(β -1))), where T = γ α is the ratio of the recovery rate to the transmission rate in the SIS model. We prove that this bound is tight up to a constant factor for the Chung-Lu random power-law graph model. We study the characteristics of Nash equilibria empirically in different real communication and infrastructure networks, and find that our analytical results can help explain some of the empirical observations. Understanding the dynamics of computer virus (malware, worm) in cyberspace is an important problem that has attracted a fair amount of attention. Early investigations for this purpose adapted biological epidemic models, and thus inherited the so-called homogeneity assumption that each node is equally connected to others. Later studies relaxed this often unrealistic homogeneity assumption, but still focused on certain power-law networks. Recently, researchers investigated epidemic models in arbitrary networks (i.e., no restrictions on network topology). However, all these models only capture push-based infection, namely that an infectious node always actively attempts to infect its neighboring nodes. Very recently, the concept of pull-based infection was introduced but was not treated rigorously. Along this line of research, the present article investigates push- and pull-based epidemic spreading dynamics in arbitrary networks, using a nonlinear dynamical systems approach. The article advances the state-of-the-art as follows: (1) It presents a more general and powerful sufficient condition (also known as epidemic threshold in the literature) under which the spreading will become stable. (2) It gives both upper and lower bounds on the global mean infection rate, regardless of the stability of the spreading. (3) It offers insights into, among other things, the estimation of the global mean infection rate through localized monitoring of a small constant number of nodes, without knowing the values of the parameters. Due to deep automation, the configuration of many Cloud infrastructures is static and homogeneous, which, while easing administration, significantly decreases a potential attacker's uncertainty on a deployed Cloud-based service and hence increases the chance of the service being compromised. Moving-target defense (MTD) is a promising solution to the configuration staticity and homogeneity problem. This paper presents our findings on whether and to what extent MTD is effective in protecting a Cloud-based service with heterogeneous and dynamic attack surfaces - these attributes, which match the reality of current Cloud infrastructures, have not been investigated together in previous works on MTD in general network settings. We 1) formulate a Cloud-based service security model that incorporates Cloud-specific features such as VM migration snapshotting and the diversity compatibility of migration, 2) consider the accumulative effect of the attacker's intelligence on the target service's attack surface, 3) model the heterogeneity and dynamics of the service's attack surfaces, as defined by the (dynamic) probability of the service being compromised, as an S-shaped generalized logistic function, and 4) propose a probabilistic MTD service deployment strategy that exploits the dynamics and heterogeneity of attack surfaces for protecting the service against attackers. Through simulation, we identify the conditions and extent of the proposed MTD strategy's effectiveness in protecting Cloud-based services. Namely, 1) MTD is more effective when the service deployment is dense in the replacement pool and or when the attack is strong, and 2) attack-surface heterogeneity-and-dynamics awareness helps in improving MTD's effectiveness. The systematic study of large-scale networks has unveiled the ubiquitous presence of connectivity patterns characterized by large-scale heterogeneities and unbounded statistical fluctuations. These features affect dramatically the behavior of the diffusion processes occurring on networks, determining the ensuing statistical properties of their evolution pattern and dynamics. In this article, we present a stochastic computational framework for the forecast of global epidemics that considers the complete worldwide air travel infrastructure complemented with census population data. We address two basic issues in global epidemic modeling: (i) we study the role of the large scale properties of the airline transportation network in determining the global diffusion pattern of emerging diseases; and (ii) we evaluate the reliability of forecasts and outbreak scenarios with respect to the intrinsic stochasticity of disease transmission and traffic flows. To address these issues we define a set of quantitative measures able to characterize the level of heterogeneity and predictability of the epidemic pattern. These measures may be used for the analysis of containment policies and epidemic risk assessment.