combined with Markov graphs. Invented for use
within the safety and reliability area (Bouissou and
Bon, 2003) it was later applied to the security industry
by (Pietre-Cambacedes and Bouissou, 2010) in 2010.
Its goal is to find a better trade off between readabil-
ity, modelling power and quantification capabilities
with respect to the existing solutions particularly at-
tack trees. BDMP’s advantages over the traditional
attack trees are its ability to use what they call trig-
gers. Triggers allow modelling of sequences and sim-
ple dependencies by conditionally “activating” sub-
trees of the global structure. Because BDMP is based
on fault trees there is an array of connections avail-
able such as AND, OR and PAND gates, this also
gives the model the advantage that it is easy to un-
derstand and read. In (Kriaa et al., 2012) Kriaa mod-
els Stuxnet using BDMP. Quantification for BDMP is
dependent on how the fault tree is modelled, and this
allows for a very versatile set of metrics. Typical met-
rics include: overall mean-time to success, probabil-
ity of success in a given time, ordered list of attack se-
quences leading to the objective, cost of attacks, han-
dling of boolean indicator and so on. It is also pos-
sible to model defence-centric attributes which reflect
the detection and prevention of the system already in
place, this allows for a more realistic prediction of at-
tack path. There is one tool (KB3-BDMP
1
) capable
of developing BDMP models and performing analy-
sis of the model, development and implementation of
the tool was detailed in (Pietre-Cambacedes and Def-
lesselle, 2011).
3.3 CoPNet
CoPNet is a hybrid threat model which combines at-
tack trees and coloured Petri nets. It was partially de-
fined by (Bouchti and Haqiq, 2012), in this informal
specification their case study is based on a SCADA
network. The case study is a simple SCADA network
with a 3-bus power grid which contains a HMI mon-
itoring the three generators, they model the network
and a range of possible threats then identify the most
likely attack path using their quantification method. It
uses attack trees to model the attack to help in simpli-
fying the development and allow for importing exist-
ing models. Once an attack is modelled using attack
trees, CoPNet has detailed a method which can con-
vert attack trees into coloured Petri nets where they
can then perform the threat analysis. The authors
provide partially working tools available to develop
a CoPNet model. When testing we we’re unable to
generate a usable results from the tools.
1
http://researchers.edf.com/software/kb3-80060.html
3.4 Attack Trees with Sequential
Conjunction
Attack trees with sequential conjunction (SAND) is
an enhancement of attack trees, which were popular-
ized by Schneier (Schneier, 1999). SAND enhances
Attack Trees by defining the use of a sequential AND
operator. This allows for the child nodes to be com-
pleted in sequence adding another level of complexity
without losing the simplicity of attack trees and main-
taining the advantages. SAND was defined in 2015
and has formally been described in (Jhawar et al.,
2015), though this is the most formal definition of
the operator it has been used by other formalisations
previously. There is one primary tool which supports
SAND, called ATSyRA (Pinchinat et al., 2014), a tool
built on top of the Eclipse IDE.
3.5 Problems with Current Threat
Modelling Approaches
To effectively model the Duqu 2.0 malware it was
necessary to identify some requirements upon which
to chose a formalisation. It needs to be easy to un-
derstand in both the raw and visual form. An effec-
tive formalisation must be able to represent sequential
events or dependencies to be able to model a complex
process such as Duqu 2.0. A practical formalisation
also needs to support some form of quantification so
the model can be used for analysis of the malware.
It is also desirable to have a formal specification of
the formalisation to ensure that our model is built to a
correct standard.
Time Dependent attack trees upon first glance ap-
pear to meet all the requirements. They have been
formally defined, support sequential operations and
a working tool is available to help generate models.
Though as the name suggests, the only quantification
which it supports is based on time, and that the model
has to be built using acyclic phase-type distribution
(APH) expressions which abstracts the model, thus
losing information, and reduces the readability of the
model. These two points make it unsuitable for our
application as we wish to develop a model which can
be easily understood and provide a base for further
quantification metrics to be applied.
BDMP has a similar ability to represent sequen-
tial operations by using triggers. It has been formally
defined, though it lacks the readability of traditional
attack trees. BDMP is a hybrid formalisation com-
bining attack trees and Markov graphs, this combina-
tion requires the model designer to have a solid under-
standing of BDMP before they can start working on
a model, as well as the modelling tool being depen-
Modelling Duqu 2.0 Malware using Attack Trees with Sequential Conjunction
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