This work investigates three aspects:

(a) a network vulnerability as the non-uniform vulnerable-host distribution
(b) threats, i.e., intelligent malwares that exploit such a vulnerability
(c) defense, i.e., challenges for fighting the threats. 

We first study five large data sets and observe consistent clustered
vulnerable-host distributions. We then present a new metric,
referred to as the non-uniformity factor, which quantifies the
unevenness of a vulnerable-host distribution. This metric is
essentially the Renyi information entropy and better characterizes
the non-uniformity of a distribution than the Shannon
entropy. Next, we analyze the propagation speed of networkaware
malwares in view of information theory. In particular, we
draw a relationship between Renyi entropies and randomized
epidemic malware-scanning algorithms.We find that the infection
rates of malware-scanning methods are characterized by the
Renyi entropies that relate to the information bits in a nonunform
vulnerable-host distribution extracted by a randomized
scanning algorithm. Meanwhile, we show that a representative
network-aware malware can increase the spreading speed by
exactly or nearly a non-uniformity factor when compared to
a random-scanning malware at an early stage of malware
propagation. This quantifies that how much more rapidly the
Internet can be infected at the early stage when a malware
exploits an uneven vulnerable-host distribution as a networkwide
vulnerability. Furthermore, we analyze the effectiveness of
defense strategies on the spread of network-aware malwares. Our
results demonstrate that counteracting network-aware malwares
is a significant challenge for the strategies that include host-based
defense and IPv6.