all scores assigned to vulnerabilities cannot be easily
extended if one wants to consider additional variables
that were not originally taken into account – such as
the age of a vulnerability or the set of IDS rules as-
sociated with it – and do not allow one to change the
relative weights of these variables.
The proposed framework was designed to address
all these limitations, by allowing users and adminis-
trators to control several aspects of the scoring and
ranking process and obtain real-time rankings based
on current vulnerability information. To develop
comprehensive cyber situational awareness (Jajodia
and Albanese, 2017), and in line with more traditional
risk analysis approaches, we also distinguish between
the likelihood that a vulnerability might be exploited
and the impact a successful exploitation would cause.
Furthermore, all details have been disclosed to make
this process reproducible by others.
3 METRICS
In this section, we first briefly review two vulnera-
bility metrics that we introduced in (Iganibo et al.,
2021), namely the exploitation likelihood and the ex-
posure factor and further generalize the definition of
exposure factor compared to its original formulation.
Then, building upon these metrics, we define a com-
mon weakness score that is semantically equivalent
to MITRE’s CWE scores, but presents several key ad-
vantages compared to current solutions.
3.1 Exploitation Likelihood
The exploitation likelihood of a vulnerability is de-
fined as the probability that an attacker will attempt to
exploit that vulnerability when certain preconditions
are met. In our analysis, we identified three main
factors that influence the likelihood that an attacker
will exploit a given vulnerability v: (i) the vulnera-
bility’s exploitability score as determined by CVSS,
Exploitability(v); (ii) the amount of time elapsed
since the vulnerability was made public, t(v); and
(iii) the number of known IDS rules associated with
the vulnerability, |IDS
k
(v)|. Thus, the likelihood of v
is defined by Equation 1, where α, β, and γ are tunable
parameters.
ρ(v) =
1 −e
−α·
√
t(v)
·
1 −e
−β·Exploitability(v)
e
γ·|IDS
k
(v)|
(1)
Intuitively, if a vulnerability has been known for
a long time, it is likely that more exploits have been
developed by the hacker community, making that vul-
nerability easier to exploit. On the other hand, the ex-
istence of know IDS rules associated with a vulnera-
bility may discourage an attacker from exploiting that
vulnerability in favor of less detectable exploits.
The reader can refer to (Iganibo et al., 2021) for a
more detailed discussion about the rationale for this
choice of variables. We argue that these may not
be the only variables influencing the likelihood, and
we have designed this metric to be easily extended
to include any additional variables that administra-
tors deem appropriate. Additionally, by considering
multiple variables, we avoid relying on a single data
source, which might be incomplete or occasionally
unavailable. For instance, as we mentioned earlier, at
any point in time, there might be hundreds or thou-
sands of vulnerabilities that have been reported to
NVD but have not been analyzed yet, therefore they
do not yet have assigned CVSS scores. In such sce-
narios, Equation 1 allows us to ignore the effect of a
variable and assess or compare vulnerabilities based
on any other available data.
Each variable contributes to the overall likelihood
as a multiplicative factor between 0 and 1 that is for-
mulated to account for diminishing returns. A fac-
tor corresponding to a variable x that contributes to
increasing the likelihood is of the form 1 −e
−c·f (x)
,
where f (x) is a monotonically increasing function
7
of x and c is a constant parameter. Similarly, a factor
corresponding to a variable x that contributes to de-
creasing the likelihood is of the form e
−c·f (x)
=
1
e
c·f (x)
.
This formulation provides several practical advan-
tages: (i) the resulting likelihood is normalized be-
tween 0 and 1; (ii) accounting for the effect of addi-
tional independent variables is straightforward; and
(iii) ignoring the effect of a variable simply entails set-
ting the constant c such that the corresponding factor
evaluates to 1 (i.e., c = +∞ for factors increasing the
likelihood and c = 0 for factors decreasing the likeli-
hood).
In summary, this formulation allows administra-
tors to easily add or remove variables in Equation 1
and control the relative weight of each variable by
tuning the corresponding parameter. Note that, based
on the mathematical formulation of each multiplica-
tive factor, the tunable parameters allow us to control
how quickly each factor converges to 1. Once a factor
converges to 1, variables corresponding to the other
factors gain more discriminating power.
7
In most cases, f (x) can be simply defined as the linear
function f (x) = x, but we use f (x) =
√
x for the time since
publication and f (x) = |x| for the set of IDS rules.
Mason Vulnerability Scoring Framework: A Customizable Framework for Scoring Common Vulnerabilities and Weaknesses
217