  Traditional security analyses are often geared towards cryptographic
primitives or protocols. Although such analyses are necessary, they cannot
address a defender's need for insight into {\em which aspects of a networked
system having a significant impact on its security, and how to tune its
configurations or parameters so as to improve security}. This question is known
to be notoriously difficult to answer, and the state-of-the-art is that we know
little about it. Towards ultimately addressing this question, this paper
presents a stochastic model for quantifying security of networked systems. The
resulting model captures two aspects of a networked system: (1) the strength of
deployed security mechanisms such as intrusion detection systems, and (2) the
underlying {\em vulnerability graph}, which reflects how attacks may proceed.
The resulting model brings the following insights: (1) How should a defender
"tune" system configurations (e.g., network topology) so as to improve
security? (2) How should a defender "tune" system parameters (e.g., by
upgrading which security mechanisms) so as to improve security? (3) Under what
conditions is the steady-state number of compromised entities of interest below
a given threshold with a high probability? Simulation studies are conducted to
confirm the analytic results, and to show the tightness of the bounds of
certain important metric that cannot be resolved analytically.
