主动网络防御动力学的随机模型

Q3 Mathematics Internet Mathematics Pub Date : 2015-01-02 DOI:10.1080/15427951.2013.830583
Shouhuai Xu, Wenlian Lu, Hualun Li
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引用次数: 69

摘要

近年来,网络主动防御的概念出现在文献中。然而,目前还没有数学模型来表征主动网络防御的有效性。在本文中,我们通过提出一种新的马尔可夫过程模型来填补这一空白,该模型是网络攻击和主动网络防御之间交互的原生模型。不幸的是,本地马尔可夫过程模型不能被我们所知道的技术解决。因此,通过平均场近似,我们将马尔可夫过程模型简化为可用于分析的动力系统模型。这使我们能够得出一组有价值的分析结果,这些结果表征了四种主动网络防御动态的有效性。仿真结果表明,解析结果是固有的马尔可夫过程模型,从而证明了动力系统模型的有效性。我们还讨论了平均场近似的副作用及其含义。
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A Stochastic Model of Active Cyber Defense Dynamics
The concept of active cyber defense has appeared in the literature in recent years. However, there are no mathematical models for characterizing the effectiveness of active cyber defense. In this paper, we fill the void by proposing a novel Markov process model that is native to the interaction between cyber attack and active cyber defense. Unfortunately, the native Markov process model cannot be tackled by techniques of which we are aware. We therefore simplify, via mean-field approximation, the Markov process model as a dynamical system model that is amenable to analysis. This allows us to derive a set of valuable analytic results that characterize the effectiveness of four types of active cyber defense dynamics. Simulations show that the analytic results are intrinsic to the native Markov process model, and therefore justify the validity of the dynamical system model. We also discuss side effects of the mean-field approximation and their implications.
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Internet Mathematics
Internet Mathematics Mathematics-Applied Mathematics
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