Treating Scalability and Modelling Human Countermeasures against Local Preference Worms via Gradient Models

Abstract.

A network worm is a specific type of malicious software that self propagates by exploiting application vulnerabilities in network-connected systems. Worm propagation models are mathematical models that attempt to capture the propagation dynamics of scanning worms as a means to understand their behaviour. It turns out that the emerged scalability in worm propagation plays an important role in order to describe the propagation in a realistic way. On the other hand human-based countermeasures also drastically affect the propagation in time and space. This work elaborates on a recent propagation model that makes use of Partial Differential Equations in order to treat correctly scalability and non-uniform behaviour (e.g., local preference worms). The aforementioned gradient model is extended in order to take into account human-based countermeasures that influence the propagation of local-preference worms in the Internet. Certain aspects of scalability emerged in random and local preference strategies are also discussed by means of random field considerations. As a result the size of a critical network that needs to be studied in order to describe the global propagation of a scanning worm is estimated. Finally, we present simulation results that validate the proposed analytical results and demonstrate the higher propagation rate of local preference worms compared with random scanning worms.

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