In recent years, both sophistication and harm potential of Internet worms have increased tremendously. To perceive their threat, we want to seem into their payload for signatures as well as propagation pattern for Internet-scale behavior. An accurate analytical propagation model permits us to comprehensively study how a worm propagates beneath various conditions, that is often computationally too intensive for simulations. More importantly, it offers us an insight into the impact of every worm/ network parameter on the propagation of the worm. Traditionally, most modeling work in this space concentrates on the relatively simple random-scanning worms. But, modeling the permutation- scanning worms, a class of worms that are fast nevertheless stealthy, has been a challenge thus far. This paper proposes a mathematical model that precisely characterizes the propagation patterns of the general permutation-scanning worms. The analytical framework captures the interactions among all infected hosts by a series of interdependent differential equations, that are then integrated into closed-type solutions that together gift the general worm behavior. We have a tendency to use the model to study how each worm/network parameter affects the worm propagation. We tend to conjointly investigate the impact of dynamic network conditions on the correctness of the model.
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