Abstract | A new model for intrusion and its propagation through various attack
schemes in networks is considered. The model is characterized by the number of
network nodes n, and two parameters f and g. Parameter f represents the probability
of failure of an attack to a node and is a gross measure of the level of security of
the attacked system and perhaps of the intruder¢s skills; g represents a limit on
the number of attacks that the intrusion software can ever try, due to the danger
of being discovered, when it issues them from a particular (broken) network node.
The success of the attack scheme is characterized by two factors: the number of
nodes captured (the spread factor) and the number of virtual links that a defense
mechanism has to trace from any node where the attack is active to the origin of
the intrusion (the traceability factor). The goal of an intruder is to maximize both
factors. In our model we present four different ways (attack schemes) by which an
intruder can organize his attacks. Using analytic and experimental methods, we first
show that for any 0 < f < 1, there exists a constant g for which any of our attack
schemes can achieve a (n) spread and traceability factor with high probability,
given sufficient propagation time. We also show for three of our attack schemes
that the spread and the traceability factors are, with high probability, linearly related
during the whole duration of the attack propagation. This implies that it will not be
easy for a detection mechanism to trace the origin of the intrusion, since it will have
to trace a number of links proportional to the nodes captured. |