Emergent Behavior in Cybersecurity

We argue that emergent behavior is inherent to cybersecurity.Comment: 2 pages, HotSoS'2014 (2014 Symposium and Bootcamp on the Science of Security

A Characterization of Cybersecurity Posture from Network Telescope Data

Data-driven understanding of cybersecurity posture is an important problem that has not been adequately explored. In this paper, we analyze some real data collected by CAIDA's network telescope during the month of March 2013. We propose to formalize the concept of cybersecurity posture from the perspectives of three kinds of time series: the number of victims (i.e., telescope IP addresses that are attacked), the number of attackers that are observed by the telescope, and the number of attacks that are observed by the telescope. Characterizing cybersecurity posture therefore becomes investigating the phenomena and statistical properties exhibited by these time series, and explaining their cybersecurity meanings. For example, we propose the concept of {\em sweep-time}, and show that sweep-time should be modeled by stochastic process, rather than random variable. We report that the number of attackers (and attacks) from a certain country dominates the total number of attackers (and attacks) that are observed by the telescope. We also show that substantially smaller network telescopes might not be as useful as a large telescope

A Stochastic Model of Active Cyber Defense Dynamics

The concept of active cyber defense has been proposed for 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 the techniques we are aware of. We therefore simplify, via mean-field approximation, the Markov process model as a Dynamic System model that is amenable to analysis. This allows us to derive a set of valuable analytical results that characterize the effectiveness of four types of active cyber defense dynamics. Simulations show that the analytical results are inherent to the native Markov process model, and therefore justify the validity of the Dynamic System model. We also discuss the side-effect of the mean-field approximation and its implications

Characterizing the Power of Moving Target Defense via Cyber Epidemic Dynamics

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 {\em 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.Comment: 12 pages; 4 figures; Hotsos 14, 201

Adaptive Epidemic Dynamics in Networks: Thresholds and Control

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 paper we initiate the study of such a perspective, namely that of adaptive defense against epidemic spreading in arbitrary networks. More specifically, we investigate a non-homogeneous 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.Comment: 20 pages, 8 figures. This paper was submitted in March 2009, revised in August 2009, and accepted in December 2009. However, the paper was not officially published until 2014 due to non-technical reason