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As a result of potential damage to our national infrastructure due to cyber attacks, a number of cyber-security bills have been introduced in Congress and a National Strategy for Trusted Identities in Cyber-space has been developed by the White House; a component of this strategy is the development of models to assess risks due to cyber incidents. A worm attack on a network is one type of attack that is possible. The simulation of rare events, such as the occurrence of a catastrophic worm attack, is impractical without special simulation techniques. In this paper we present an application of splitting methods to estimate rare-event probabilities associated with the propagation of a worm through a network. We explore the sensitivity of the benefits of splitting methods, as compared to standard simulation, to the rarity of the event and the level function used.