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Detecting New Generations of Threats Using Attribute-Based Attack Graphs

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In recent years, the increase of cyber threats has raised many concerns about security and privacy in the digital world. However, new attack methods are often limited to a few core techniques. In this paper, in order to detect new threat patterns, we use an attack graph structure to model unprecedented network traffic. This graph for the unknown attack is matched to a pre-known threat database, which contains attack graphs related to each known threat. The main challenge is to associate unknown traffics to a family of known threats. For this, we utilize random walks and pattern theorem. We utilize the pattern theorem and apply it to a set of proposed algorithms for detecting new generations of malicious traffics. Under the assumption of having a proper threat database, we argue that for each unknown threat, which belongs to a family of threats, it is possible to find at least one matching pattern with high matching rate and sensitivity.
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IET Information Security
Research Article
Detecting new generations of threats using
attribute-based attack graphs
ISSN 1751-8709
Received on 1st August 2018
Revised 19th November 2018
Accepted on 30th January 2019
E-First on 20th February 2019
doi: 10.1049/iet-ifs.2018.5409
www.ietdl.org
Mehran Alidoost Nia1 , Behnam Bahrak1, Mehdi Kargahi1, Benjamin Fabian2
1School of Electrical and Computer Engineering, College of Engineering, University of Tehran, Tehran, Iran
2Information Systems, Hochschule für Telekommunikation Leipzig, Leipzig, Germany
E-mail: alidoostnia@ut.ac.ir
Abstract: In recent years, the increase in cyber threats has raised many concerns about security and privacy in the digital
world. However, new attack methods are often limited to a few core techniques. Here, in order to detect new threat patterns, the
authors use an attack graph structure to model unprecedented network traffic. This graph for the unknown attack is matched to
a pre-known threat database, which contains attack graphs related to each known threat. The main challenge is to associate
unknown traffics to a family of known threats. For this, the authors utilise random walks and pattern theorem. The authors utilise
the pattern theorem and apply it to a set of proposed algorithms for detecting new generations of malicious traffics. Under the
assumption of having a proper threat database, the authors argue that for each unknown threat, which belongs to a family of
threats, it is possible to find at least one matching pattern with high matching rate and sensitivity.
1Introduction
In recent years, computer systems were susceptible and vulnerable
to cyber attacks. A statistical analysis of vulnerability databases
performed by Palo Alto Networks reveals that the number of core
techniques used by attackers is limited to several core techniques
[1]. Compared to the thousands of vulnerabilities recorded in the
National Vulnerability Database (NVD), the number of
unprecedented attack techniques is limited to a dozen [2].
According to NVD results, in 2016, 6000 types of threats were
recorded. Reviewing similar results for recent years reveals that
these threats are mostly categorised as new branches of classic
threat families. These new threats are either implemented using a
new technique or exploit a vulnerability through previously known
attack methods in the system. It is important to detect the
behaviour of new intrusion methods to come up with
corresponding countermeasures. For this, it is necessary to review
intrinsic vulnerability features and the related threats associated
with each of them. In the area of network security, it is necessary to
deal with new generations of threats and to frequently update
protection techniques in security devices. One of the outstanding
examples in the field of network security is the Heartbleed
vulnerability that was caused by a bug in the OpenSSL library [2].
This weakness made it easy for intruders to eavesdrop on the
encrypted data exchange. However, this bug existed in OpenSSL
since 2012; it was not discovered until 2014.
The main question is whether we could detect threats using
such vulnerability from behavioural analysis. Network-traffic
analysis is shown to be an effective method for detecting
unprecedented types of threats [3]. A challenge with detecting
these threats is their unknown nature that makes it difficult to
detect malicious behaviour without any prior knowledge.
In this research, we aim to determine to what extent we can
predict the behaviour of a new class of threats using the known
malicious behaviour of previously detected ones. If all of the
threats were pre-known, established traffic engineering and
analysis methods would be viable to detect malicious behaviour of
an adversary [3]. In this situation, our threat database would be
clairvoyant, and matching each newly sampled traffic to a record
from the database would be simple. If the malicious traffic is
identified, monitoring tools such as firewalls can block it, even
though adversaries have certain techniques to hide malicious traffic
from the external observer, which is done by making fundamental
changes in network flow patterns [4].
However, we have no clairvoyant threat database at hand. When
the security device faces a new traffic sample, it is even-handed to
consider it as either trusted one or malicious traffic. The main goal
of traffic analysis is to match network flows with pre-known traffic
samples using a pessimistic approach. If the matching process fails
to decide on the entry, we should not trust the incoming traffic,
since trust in an unidentified traffic may lead to security defects;
therefore, we must come up with a pragmatic solution for matching
unknown types of network traffic. Addressing this challenge is the
motivation of this research work.
Our proposed method is based on attack graphs. Attack graphs
are a logical description elicited from data related to the threat. In
fact, an attack graph represents a set of paths that the adversary can
adopt to penetrate a host or network [5]. The main application of
attack graphs can be seen in digital forensics where forensic
examiners employ attack graphs to reconstruct a cyber-crime scene
[6]. The attack graph is related to the target application, which
means that an attack graph of the same threat may be different in
various network topologies. Therefore, the first step towards
proposing a solution is to standardise the required specifications of
the environment.
Based on this suggested solution, at first, we generate attack
graphs corresponding to each threat. If the sampled traffic belongs
to neither trusted patterns nor malicious ones, we must construct a
new attack graph based on that traffic. Therefore, we need a
similarity measurement for evaluating the similarity of the traffic to
the pre-known threats [7]. It is significant how we define the
similarity measurement. In fact, it is introduced by reviewing the
set of similar subgraphs [8]. In this research, we employ a
customised type of random walk, which is applied to attack graphs
with higher dimensions [9]. To the best of our knowledge, this is
the first research work that uses attack graphs for online traffic
analysis. Another novelty of this work is to apply strong
randomness features of random walk to measuring the similarity of
attack graphs. The main issue is how we apply the random walk to
the structure of attack graphs. Considering the structure of attack
graphs, we need to come up with a customised algorithm for
matching them accurately. We represent implementation details and
proposed algorithms for matching problems in attack graphs.
Concerning our key contributions, we present a number of
achievements in this work:
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293
We put forward traffic-engineering methods to detect
unprecedented network threats.
We argue that the presented method is applicable to online
detection facilities in order to decide about unknown threats in
real time.
We use logical attack graphs to reduce the size of computations
in the presented method. This could help security facilities like
intrusion detection systems (IDSs) to come up with quick
solutions for online decisions.
We apply the random walk to achieve high-precision detection
rates. The results show that the sensitivity of the method is up to
98%. This assures high-level security against new generations of
threats.
We base on strong mathematical foundations such as the pattern
theorem, which enhances the credibility of the proposed system.
The rest of the paper is structured as follows. In Section 2,
preliminaries are reviewed, including prerequisites, definitions,
formulas, applications, and previous work. In Section 3, related
work is discussed. Section 4 reveals the main problem and the idea
of the paper. In Section 5, the proposed algorithms and solution
approach are presented. Section 6 is dedicated to the experimental
result and comparison to previous outstanding research. Finally, the
paper concludes in Section 7.
2Preliminaries
We start with explaining how an attack graph is generated. As
mentioned, an attack graph is a precise path describing how the
attack is executed. In this research, the main purpose is to utilise
the power of matching in graphs in order to detect threats.
However, the generation of attack graphs is not the only challenge,
but paying attention on how they are organised is also important. A
logical representation of attack paths indicates the behaviour of the
adversary [10]. In this research, the main purpose is to utilise the
power of matching in order to detect threats in unknown traffics.
Afterwards, we provide a review on traffic-engineering methods,
random walk, and pattern theorem.
2.1 Attack graph
From a mathematical point of view, attack graphs are directed
graphs, but under some condition, we can also represent them as
undirected [6]. Each vertex of the graph shows an exploit. Each
vertex has a pre-condition and post-condition, which represent
prerequisites before and after an exploit happens. An edge connects
two vertices if the source's post-condition satisfies part of the
destination's pre-condition.
For designing an attack graph, many tool sets have been
proposed. In this research, we employ MulVal, which is an open-
source tool-set for generating attack graphs based on formal
definitions 1–3 [11, 12]. This tool has been designed based on
Prolog and automatically detects vulnerabilities existing in an
enterprise network [13].
Definition 1: A formal attack model is a finite automaton in the
form of M= (S,τ,s0), where S is the set of states, τS×S is the
transition relation, and s0S is the initial state. State space S
represents a triple set of agents denoted by I in the form of
I= {E,D,T}, in which E is the adversary, D represents the
defender, and T indicates the system that is under attack. In this
definition, each agent is indicated by iI and has its own set of
states denoted by Si.
Definition 2: A finite execution of a specific attack model
M= (S,τ,s0) is a sequence of possible states in the form of
α=s0s1sn, where 0 ≤ in,si,si+ 1 τ. An infinite execution
of an attack model is also represented as β=s0s1sn, where
i≥ 0, si,si+1 τ.
Definition 3: Considering Definition 2 and an attack graph with
model M, a series of security properties P is denoted as the set
L(M)/P in which L is the labelling function. It emphasises that the
attack graph encompasses a set of failed executions of model M
under security properties P.
By considering Definition 3, we face a state-space explosion.
Consequently, the construction process of attack graphs involves a
serious challenge. For dealing with the mentioned issue, we have to
reduce the state-space. An attack-graph generator must employ
approximation techniques to simplify the output graph while
preserving its main features.
2.2 Traffic analysis
Traffic analysis is one of the basic approaches to detect network-
level threats. Not only it is useful to determine new threats, but it
also helps to detect certain behaviour of a specific application
according to network-level transactions. To the best of our
knowledge, no perfect approach with 100% correctness has so far
been proposed for detecting new threats. They work best in a
specific environment based on an accurate threat database, which is
ideally filled by pre-known records.
Traffic analysis is useful for security enhancement in an
enterprise network; however, it would endanger privacy and
security of users’ applications [4]. Some methods are able to detect
encrypted network flows using traffic patterns. The hidden Markov
model is one of the outstanding examples that is used to detect
network-level threats [3]. In this context, three features of data
existing in sent packets are considered for traffic analysis. These
are the direction, time, and size of the packets. Depending on the
application, however, it is possible to perform the entire analysis
without some of them [3]. In applications such as Tor, which uses
multi-layered encrypted packets, direction is not accessible [4]. To
perform an accurate analysis, we need to access at least two of the
mentioned features. For generating an attack graph, we employ
these three features in the form of (d,t,s).
Another property in traffic analysis methods is to consider
different security levels. A level states the destructive power of
each attack and their side effects on the system's functionalities
[14]. We have employed a set of levels as a coefficient in the threat
database, which is a metric to show the importance of the same
threat. For example, in matching unprecedented traffics using pre-
known threats, it would be useful to adjust the weight assigned to
each threat and to receive results that are certainly more accurate.
In our proposed method, MulVal gets the provided information
from a set of network flows using the structure described in this
section. The input for MulVal is the same network flows that are
not recognised by the firewall/IDS. So, it is able to generate a
graph that represents the penetration point of the flow. The access
points to the local network are analysed and an attack graph is
generated. The strong point of MulVal is the speed of graph
generation and the reduction in the graph size. By applying a set of
logical methods, it can manage to generate a lightweight and
reduced attack graph that describes the penetration paths very well.
In generating the final attack graphs, some conditions must be
considered. Pre-conditions and post-conditions are two types of the
conditions that refer to a set of penetration/access points in the
graph. The conditions must be fulfilled before/after another
penetration/access point. This depends on the structure of the
network and the behaviour of the adversary.
2.3 Random walk
Consider a salesperson who is walking through a specific path on
the x-axes. He starts the walk from an initial position while he is
able to walk in either −x or +x directions. In each step, he selects
one of his neighbours randomly with equal probability. When he
walks in two directions, it means that the walker has only two
alternatives in each step. He can move either forward or backward.
According to random selections in each step, after walking a
number of steps, we say that the set of steps constructs a random
walk.
Definition 4: Suppose that Xk be a sequence of random
independent vectors. Therefore, Xk can take values ±ei, i = 1,2,…,d
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with probability 1/2d, where d is the number of dimensions. The
main question is to compute the position of the walker after m steps
of random walk. Simply, we need to compute the output value of
the below equation
Rm=
k= 1
m
Xk
(1)
We call this set of random steps that construct a random path a
simple random walk (SRW) [15]. The main application of SRW is
observed in simulation of behaviour in random phenomena. The
outstanding question of Polya divides random walks into two
different categories, transitive and recursive [9]. A random walk is
called recursive if we are sure that the walker will revisit the
previously visited positions. According to Polya's theorem, a
random walk with d ≤ 2 is recursive. It states that we definitely face
the recursion problem in two-dimensional environments [16].
Equation (2) states the same fact using Markov property
xRn= 0 for some n≥ 1 = 1
(2)
According to Markovian properties, if pPd
under d ≤ 2, so p
would be recursive. On the other hand, if we have pPd
x (P in
higher dimensions) and d ≥ 3, therefore, p is transitive [16].
Equation (3) presents the same condition, which is called the
escape probability of q
q= ℙ Rn≠ 0 for all n≥ 1
(3)
We aim to employ higher orders of random walks to our research.
Considering the recursion issue, each type of random walk may
cause some intersections. To come up with a similarity
measurement in attack graphs, we need the same property in a way
to avoid revisiting the nodes through a random walk on vertices of
an attack graph. To deal with this issue, we introduce self-avoiding
random walk (SARW) [17]. Next, we explain how it works.
2.4 Self-avoiding random walk
From a mathematical point of view, the computations based on the
paths related to an SARW are more complicated.
Definition 5: An SARW with length n in the space d is a
sequence ωi defined as ω = (ω0, ω1, …, ωn), where ω0 = 0, ωi∈ℤd,
and ||ωj − ωj-1|| = 1 for each j= 1,…,n under the condition ωi ≠ ωj
where i ≠ j.
Cn is the distance of the random walker after n steps in the
SARW, and it is computed with respect to the limitations imposed
by Definition 5. According to (4), Cn is limited by two values
derived from d through n steps
dnCn≤ 2d(2d− 1)n
(4)
However, the precise computation of Cn is complicated; we can
estimate it via (5). This equation is derived from [18] where the
square distance from the initial point is computed. We have
imposed a further limitation in which the ω parameters are
considered as a vector that belongs to the same lattice [19]. We can
perceive the reason behind this limitation after applying pattern
theorem
ω n n
2=1
Cn
ω:ω=n
ω n 2
(5)
Discussion about SARW is extensive; however, we only talk about
a series of selected topics related to this research scope. It is
obvious that imposing new limitations on a random walk's
behaviour is similar to making some changes in the probability
distribution function. We are changing the random behaviour in
order to make it closer to the reality of a system's behaviour. In
graphs with large sizes like real attack graphs, we must deal with a
greater number of selections. We cannot give up the selection
process and assign similar probabilities to the alternatives.
Respecting these limitations, we will be able to utilise the pattern
theorem in practice.
2.5 Pattern theorem
Simply, a pattern is a small part of an SARW. According to
Kesten's pattern theorem, if a given pattern is able to happen
several times in an assuming SARW, that pattern must also happen
aN times on the N steps of the same SARW, where a> 0 [19]. This
introduces a new measurement for determining the probability of
repeating a part of SARW in a part of other SARWs.
Statistical analysis of each pattern would be different according
to the target application. When it comes to SARW, many
interesting statistics exist that base on repeating of the same pattern
in the beginning part of an assumed SARW. We refer to the ergodic
feature as one of the most significant analytical properties [17]. It
states that the system's behaviour remains constant in the space
over time. As shown in Fig. 1, two random walks are illustrated,
which have similar patterns in early steps. In the following, we
give a precise definition of a pattern [19].
Definition 6: We say that a pattern in the form of
P= (p(0), …, p(n)), happens in the jth step of an SARW with
specification of ω= (ω(0), …, ω(N)) if a vector v exists in the
space Zd where for each k= 0,…,n; ωj+k=p k +v and v is
computed by ω(j)−p(0).
Assume that RN be a representative for N step of an SARW with
the specified path ω, where ω(0) = 0. For each k 0 and pattern P,
we introduce CN[k,P], the number of steps in which P happens at
most in k steps, and also FN[P], a subset of walks where P happens
in the 0th step. We call P a proper front pattern if FN[P] is a non-
empty set for each large N[19]. In addition, the same pattern can be
a proper internal pattern if for each k, there exists an SARW in
which P happens at least in kth different steps. On the other hand,
this means that the same extracted pattern must be contained in kth
steps to be considered as a proper internal pattern with parameter k.
In this case, P is called a proper internal pattern. Equivalently,
for such a pattern, there exists a cube with specification
Q= {x: 0 ≤ xkb} and an SARW with specification ϕ (e.g.
number of steps and their directions) in which if P happens in some
steps of ϕ, ϕ includes Q. This means that the final points of ϕ are
the corners of Q. In addition, there exists an SARW with
specification ω where P happens in more than three steps of ω.
With this background, we start defining cube and pattern matching
schemas according to Kesten's definitions [19].
Definition 7: A cube Q is a set in the form of (6) where a1,…,ad
and b > 0 are in
Q=xZd:aixiai+bfor all i= 1, …, d
(6)
Definition 8: Consider Q
¯ that, according to (7), is two units in
each direction greater than Q. The outer boundary of Q is shown as
Q in (8) where it is needed to determine a pattern in further steps.
It includes the set of points in Q
¯ that are not in Q
Fig. 1 Comparing two different SARWs with similar patterns
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295
Q
¯=xZd:ai− 2 ≤ xiai+b+ 2, i= 1, …, d
(7)
Q=Q
¯/Q
(8)
It is proved that the whole random path generated by an SARW
exists in Q
¯ [19]. A strong conclusion from the abovementioned
relations is stated in (9). It is the basis for this research, which is
called pattern-matching relation where y(i) is a part of Q. On the
other hand, this fact indicates that expanding the current boundary
with j still includes the same pattern P(i)
i,j 0, …, kand y i ∈ ∂Q:y j +i=P i
(9)
We utilise the patterns in order to work with attribute-based attack
graphs. The attributes of an attack graph refer to the properties that
are extracted from the graph and are able to transfer to the final
patterns in the form of self-avoiding walks. So, the pattern theorem
will be applicable when we are able to generate attribute-based
graphs.
3Related work
In previous sections, we discussed the theoretical and technical
background needed for diving into the design space. In this section,
we are going to have a quick review on outstanding previous
research conducted in this area. We start with research work on
attack graphs. The first and most important application of attack
graph can be seen in digital forensics [6]. In such applications,
examiners come up with an evident graph that consists of digital
evidences of an attack or a cyber-crime. This graph is compared to
the pre-generated attack graphs. Each vertex of the graph
represents evidence and the path of attack is reconstructed using
the corresponding path in attack graph. As new techniques used by
intruders will become more complicated, the analysis of such huge
graphs requires new solutions [13]. We use the attack graphs in our
work with one fundamental difference. Instead of comparing the
graphs directly, we generate patterns from the graphs and match
these patterns together.
The generation of attack graphs is an important issue for
researchers. The large number of paths and vertices in attack
graphs makes it difficult to have an accurate analysis. In addition,
the lack of an existing logical framework in generating such graphs
exacerbates the situations for conducting a proper analysis [10].
Employing tools that take advantage of having a logical and formal
framework, like MulVAL, could help to generate complex attack
graphs in polynomial time [11]. Another issue is graphical
representation of large attack graphs. In a very useful research
conducted in MIT, the required framework for presentation of large
attack graphs has been developed [12]. It is helpful for us to use
such visual tools to represent the final patterns generated from the
graphs, and compare the results visually.
Random walks have many applications in engineering sciences.
In computer science, the main application of random walks is
observed in modelling of complex networks [20]. One of the other
applications of random walks are PCS networks [21]. In such
networks, in order to update distance metrics dynamically, random
walks are deployed. Another important application of random walk
is traffic-engineering [4]. Not only it is used in order to detect
cyber-threats, but it is also applied to network-based applications to
improve the privacy of users through the Internet [14]. In our
previous work that is highly related to the current research, we
deployed random walks in order to directly analyse the network
flows. However, in the current research work, we aim to use
random walks for extracting the patterns from the attack graphs.
Then we can match the patterns instead of comparing the graphs. It
helps out to remove some limitations of classic approaches that do
not have the ability to represent large network structures. In our
previous work, we had the same limitations that decrease the scope
of analysis.
One of the popular applications of random walk is similarity
measurement between two given graphs [9]. Similarity
measurement is a technique through which an observer can decide
if two or more graphs are similar. The similarity is evaluated based
on a set of pre-defined metrics. If we aim to match two graphs, the
best idea is to extract some elements in graphs that are in common.
The first element that comes to mind is subgraphs. Similarity
measurement among subgraphs is the subject of a dedicated
research direction [22]. Furthermore, we divide the main problem
of similarity measurement of graphs to similarity measurement of
subgraphs. Mainly, this type of research is based on distance
computation in all maximal common subgraphs. The main concern
about this research, comparing to our work, is the ability to analyse
large network structures.
Similarity measurement is an important feature in the
development of matching techniques. Doing that, random walk has
special abilities related to similarity measurement between nodes
that in a previous work, it is deployed in recommender systems
[23]. In this approach, two random variables are defined on two
different graph structures. Based on the maximum degree of the
graph, the dimension and other features of random walk are
determined. So, as a gaming model, two variables play an
interactive game by walking on the graphs. The similarity level is
evaluated based on the similarity of the walks on two graphs.
Finally, one can decide if two graphs are similar to each other. The
approach helps to improve the precision of decision-making by
walking through the graph edges. Another application of this
measurement can be seen in parsed texts, which is related to
natural-language applications [24]. As an application for random
walk in machine learning, we refer to natural-language processing.
Through a random walk, the walker/agent can learn many aspects
that are used for further evaluations. For example, if the agent has
the experience of walking on a ring graph, he can learn to
distinguish walking on this type of graphs in the near future. This
can be considered as a common point between pattern theorem and
random walk where we learn from patterns to determine the similar
walks in unprecedented graphs. In our work, in each random walk,
the walker collects a set of experiences and utilises them in its
future walks to discover and learn new patterns
Fault-tolerant graph matching is a fundamental concept in the
reliability of the results [8]. To this end, we must ensure that our
matching technique is accurate in terms of similarity metrics. The
final result of the matching technique should lead to reliable
decisions. This feature is costly, and therefore, it requires a precise
strategy in security-related applications. Applying each matching
technique must ensure the reliability of the result by an acceptable
level of accuracy. For example, if the accuracy of the result is
evaluated 98%, we should expect 98 accurate matching results
among 100 matching operations.
Detecting unprecedented threats is one of the main goals of this
research. Considering this feature, we need to enhance accuracy
and integrity of the detection process. This is not the first work in
this area [3, 14, 25]; however, we propose a new solution to deal
with this issue. Academic and business implementations for threat-
detection systems are applied in two different ways. The first is
online detection of threats that suffers many limitations [26, 27]. It
is difficult to apply detection, recognition, and making decision in
real time when the traffic is considered as unknown. The second
approach is to conduct some parts of the detection process offline.
These techniques have some applications in tracking and
monitoring. They focus more on prevention instead of detection/
recognition. One of the most significant products designed in Palo
Alto Company is exploit prevention module (EPM) [1]. Such
prevention techniques concentrate more on penetration techniques
for exploiting the entire system. They try to secure a specific
system using a set of security policies. This approach decreases the
ability to detect threats in real time. Therefore, we focus on the first
group of techniques that preserve the ability for detecting threats in
real time.
4Problem statement and solution idea
As discussed earlier, the main problem is detecting new
generations of cyber-threats. In this section, we provide a detailed
overview on the main problem and the solution idea.
The input of the problem is an unprecedented network flow,
which is not identified by network security tools like firewall and
IDS. A finite sequence of network packets is sampled in the form
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© The Institution of Engineering and Technology 2019
of (d,t,s), where d, t, and s are representatives for direction, time,
and size of the packets, respectively. Further information, including
encryption status, application-level features, employed protocols,
requested ports, and accessed network paths, is attached to the
sample. Afterwards, all input/output flows associated with the
same path will be continuously analysed in order to model its
behaviour in an attack graph.
For each unprecedented network flow, we consider a
pessimistic scenario in which all unprecedented flows are assumed
malicious until our analysis determines whether it belongs to a
threat family or not. Therefore, we can come up with a
corresponding attack graph. We assign the flow's attributes to
vertices of the attack graph G that must be compared to other pre-
known attack graphs existing in our threat database denoted by DB.
The quantity of samples in threat database is not the main topic of
our study. We aim to propose a systematic approach to cope with
the matching problem of unprecedented attack graphs.
The matching process is applied on graphs using the generation
of a random path from an SARW. Instead of matching subgraphs,
we aim to match elicited patterns π from SARW with patterns
existing in our database Π. From now on, pattern theorems on
SARWs would help us to address the matching problem in attack
graphs. Matching rate MR is the output of this step for each attack
graph existing in our threat database. We assign each attack graph
in the database a weight according to its destructive effects in the
system. Determining this coefficient requires experimental results
that are discussed in the next section. So, the problem is
summarised to find out the matching rate between a set of pre-
known patterns in our database Π and a set of unknown patterns
extracted from the given network flow π. The former is computed
based on the knowledge in the threat database, and the latter is
determined by applying SARW to online traffic. Equation (10)
describes the entire problem formally: its output gives the matching
rate
i∈ 1…n. MRi= MatchiΠDB,γ
(10)
Here, n shows the number of pattern types that should be compared
in the database. One can easily measure the similarity between the
patterns according to the output of the matching rate.
The threat database stores an information related to pre-known
vulnerabilities that support our pattern matching technique. This
includes name and the family of the threat, behavioural coefficient,
sample network flow f in the form of di,ti,sif for all i∈ ℕ,
generated attack graph G corresponding to f, and finally a set of
extracted patterns P in the form of (p1,p2,p3,p4) ∈ P.
Based on Definition 3, the structure of G(V,E) is just like other
ordinary graphs with the difference that V is a representative for
penetration points into the network and E denotes a set of
penetration paths between each two nodes of the graph. Formally,
an attack graph is employed to illustrate the behaviour of the threat/
adversary. As discussed earlier, the patterns are actually a subset of
a walk on the attack graph. So, to represent a pattern, it is
necessary to store it by a special data structure. In our model, we
store a pattern/walk by a multi-dimensional array. Depending on
the graph density and its maximum degree, the dimension is
determined. This fact is fully discussed in the next sections.
We give an overview of the solution idea in the form of a set of
steps. As shown in Fig. 2, decisions about unknown traffics are
made with at most six consequent steps. At first, the firewall tries
to detect an incoming network flow, but cannot evaluate it properly.
In this part (I), incoming traffic is investigated by monitoring tools,
which sample the required data from the incoming flow. In part
(II), an attack graph is generated, which helps to provide an
accurate evaluation about an unprecedented flow.
Considering Fig. 2, in part (III), we generate a set of random
walks from the graph. The main algorithm in this section is SARW,
which is fully discussed in the next section. According to part (IV),
we need to compare the random walk to the existing ones from our
database. If we could not find any 100% match, it is proved that the
flow is unprecedented, and, respectively, we need to come up with
a pattern-matching technique in part (V). At the end of this life
cycle, the final decision is sent to the firewall (or any other security
tool of the network).
5Steps of the solution approach
In this section, we are going to review the implementation process
and the proposed algorithms. We can improve the precision of the
whole process using proper parameter selection in the network
environment. Next, we look at the tools and implementation
process.
5.1 Solution approach
To implement the proposed system, we need to integrate a set of
tools and modules. We have indicated them in Fig. 3. The
implementation step is divided into two independent parts: the first
is associated with the attack graph, which is generated using the
MulVAL tool set. After generating an attack graph, a set of
dedicated modules cooperate in order to final decision about that
flow is made.
At first, the SARW module converts the graph to the random
walk. At the same time, the required patterns are generated using
the PatG module. As a result, we have a set of generated patterns
that must be matched to random walks existing in the database.
This work is performed using the module PatM. At the end, the
final decision is made whether we consider the unprecedented flow
Fig. 2 Overview of the solution approach; it shows the life cycle of the system using analysis of attack graphs
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297
as malicious or not. In the next sections, we discuss the special
abilities of each module.
The tool chain that we have presented helps the network
security devices to decide about unknown network flows. Pattern
matching, which is the basis of this research, is equivalent to
matching subgraphs in two given attack graphs. It comes from
Definition 6 that a pattern is a subset of an SARW. On the other
hand, each set of random steps belongs to a specific attack graph,
which reflects a unique behaviour.
5.2 Generation SARW from attack graph
The primary mechanism for utilisation of pattern matching is a
random walk. Therefore, it is important to pay special attention to
details of the SARW module. Self-avoiding walk has been applied
to many research; however, we have customised it according to
attack graph model. It depends on the graph size to determine in
what dimension the random walk must be implemented. We have
to set a threshold for the number of directions in the random walk.
It is determined according to the maximum degree of the graph's
vertices. In each dimension, we have two selections. This metric is
selected by maximum output degree (Δ) of the graph. For example,
if Δ = 6, we must set dimensions to three in order to reach six
directions in the random walk. We use (11) to calculate the number
of dimensions
d=Δ(G)
2
(11)
Our investigations show that attack graphs generated by the
MulVAL tool contain no considerable bottleneck. It is due to the
logical operations performed in MulVAL [13]. The maximum
number of dimensions used in this work does not exceed five. It
has been proved that the pattern theorem is applicable for higher
dimensions [19]. Imposing such constraints to the system does not
affect the strength of our proposed approach.
As the number of dimensions increases, the process of
generating SARW would be simpler. This is due to the reduction in
previously visited points in higher dimensions. The more the
number of dimensions increases, the more the alternatives rise.
Consequently, the number of intersections occurring in a random
walk will be decreased [14]. As a result, using higher dimensions
will decrease the cost of the entire system.
Algorithm 1 (see Fig. 4) indicates how a random walk is
constructed on a given graph. The input of this algorithm is a set of
information associated with the attack graph. We need to get
adjacency matrix, graph size, and maximum degree of the graph.
According to the properties of that graph, it generates the random
walk in the form of a two-dimensional array. Lines 1–4 show the
initialisation process and auxiliary variables. Lines 5–14 indicate
the main functionalities of the algorithm. The random walk starts
from an arbitrary vertex of the attack graph. It is the first vertex in
the adjacency matrix. At first, a set of accessible nodes is
determined as alternatives for the next step. As we have selected
self-avoiding walk, it cannot intersect the previously visited nodes.
To this end, among the neighbours, a set of vertices that
guarantee this rule is selected and put in List. In the next round, it
selects from the same list at random, and according to the set of
paths dir, the next random step would be selected. In each step of
the algorithm, the selected node and the direction of the walk are
stored. Visited vertices are added to pv in order to be imposed as
further limitation in the next rounds. The algorithm is executed
recursively until we cannot select any vertex according to set of
visited nodes. It is not necessary to cover all the edges of the graph
because we need subsets of the random walk. According to the
pattern theorem, apart from behaviour of a complete graph, we can
match a specific part of it to the other graphs.
5.3 Pattern generation from random walk
We need to extract proper patterns from the output of Algorithm 1.
We have previously mentioned the module patG, which is
indicated in Fig. 3. This is the most sensitive part of the research.
Generating precise patterns from random walks leads to accurate
decisions in the matching process. Algorithm 2 (see Fig. 5)
illustrates the criteria required for implementation of the patG
module.
As shown in Algorithm 2, we search for four different patterns
that lead us towards the generation of unique patterns. P is the set
of the four types of patterns that we have proposed to facilitate the
matching process and it is the output of the algorithm. They are
proposed based on the uniqueness of random walk and the
behaviour of the patterns. Actually, we have discovered these types
of patterns by empirical analysis of the threat database. In our
database, a set of patterns is generated for each threat family. By
analysing these patterns, we found out that even if the number of
patterns increases we are still able to categorise them into the same
types of patterns. Note that if we plan to generate patterns for more
than four dimensions, the analysis process should be applied again,
and some new types of patterns may be discovered.
According to our analysis on the threat database, the four types
of patterns are categorised as follows, in which each index
indicates the pattern's priority in the given SARW.
Fig. 3 Review on pattern generation and matching modules in our proposed system
Fig. 4 Algorithm 1: SARW algorithm for attack graph
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Paths that have no two consequent steps in the same dir (P1).
Paths where all steps happen in the same dir (P2).
Paths that form unclosed squares and rectangles; this means that
the beginning and the end of paths happen in the same dim with
different dir, while the steps between them have the same dir
(P3).
Paths that construct a part of a cube (P4).
After generation of a random path, it is possible to select a variety
of subpaths as pattern. The four abovementioned cases are selected
according to the pattern theorem and the behaviour of the attack
graphs. We have tried to select types of patterns that reflect more
contrasts in the matching process. For example, P1 has the most
contrast level and shows tendencies to change the behaviour in
attack graphs performed by the adversary. In addition, patterns P3
and P4 illustrate patterns in two and three dimensions. To match
similar behaviours in two or three dimension, we employ
geometric matching techniques.
5.4 Pattern matching process
In this section, we are going to match generated patterns to the
ones existing in our threat database. To do so, we need to another
algorithm, which is illustrated in Fig. 3 as patM module. Note that
the system covers four types of predefined patterns where each
type is only comparable to the same type. The output for matching
is shown with a number between zero and one. The output
indicates to what extent patterns have similar behaviours. An
interesting feature of this approach is that it is independent of the
initial point. This means that it is not important where the patterns
are selected from the SARW. The only feature that we are
interested in is similarity in behaviour.
Algorithm 3 (see Fig. 6) shows the matching of subpatterns
associated with attack graphs. To measure the similarity of two
attack graphs, we need to compare the similarity between two sets
of patterns. We say that two sets of patterns, P and Q, are matched
if and only if there exists two patterns PNP and QNQ, where
QN and PN are matched together. Note that some graphs may not
include a type of patterns. This is due to their behaviour and the
topology of attack graph. For example, P4 happens only in attack
graphs with complex structures. In order to observe such patterns,
the walk must be generated in at least three dimensions. However,
some patterns like P3 are susceptible to occur in all walks.
Illustrated in Algorithm 3, sets of generated patterns are given
to the algorithm as input. In addition, a set of selected patterns is
picked from the threat database for which we should test whether
they match or not. Matching processes for each type of patterns are
performed separately. According to the algorithm, matching more
than one pattern is not important to us. On the other hand,
matching only one pattern suffices for making any decision. In the
context, functions entitled Matching are responsible for deciding
about the matching process. If we do not reach 100% matching
rate, the results are given to another algorithm to estimate the
similarity level using a set of thresholds M. In this situation, we
may force to recalculate the random walk. Algorithm 3 generates
the final decision if it reaches one matching for each type of
pattern.
As mentioned earlier, the main goal of this project is to detect
new generations of attacks. For example, consider that the input
attack graph is a representative for a DoS attack. We expect to
receive positive result when comparing it to the attack graphs in
our database that belong to the family of DoS attacks. The output
indicates whether the current traffic has a similar behaviour
comparing to the other family members. If the positive result is
confirmed, we store it as a new generation of the same family.
According to Algorithm 3, if the matching result is calculated as
100%, we have already detected the unknown traffic. Consider
now that the matching rate is lower than 100%. In this situation, we
must store it in the database with a probability for further
utilisation. Assume that a matching has resulted in vector
P= {0.6, 0.8, 0.92, 0.73}. According to Algorithm 3, it needs
further analysis because the rates in the vector are higher than the
given threshold (0.5). We have ten different results from this family
in the database in the form of P1,P2, …, P10. According to (12),
we calculate the average amounts. If the result is higher than a
given threshold γ, we store it in the database with probability ϕ
Pi, 1 ≤ inpi1,pi2,pi3,pi4>γϕ=i= 1
nPi
n
(12)
The probabilistic coefficient ϕ is calculated by (11) and can be
updated in the future. It is not possible to assign it with certainty to
a family of threats. However, we have shown that with probability
ϕ, its behaviour is similar to the assigned family. We call ϕ the
behavioural coefficient. Previously known threats have the same
coefficient in the database that is set to one. In further comparisons,
the newly added records to the database will also participate, but
their final effect is multiplied by their behavioural coefficient.
5.5 Details of the algorithms
At the end of this section, we are going to review all the algorithms
via a simple scenario. Assume that a new incoming network flow is
not detected by the firewall. However, it is blocked (e.g. by IPS) by
applying network policies, and the analysis process is started by
sampling the network traffic. So, the traffic is sent to the MulVal
analysis tool plus some information on the network structure.
Fig. 5 Algorithm 2: Pattern generation algorithm (patG module)
Fig. 6 Algorithm 3: Pattern-matching algorithm (patM module)
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MulVal generates the attack graph corresponding to the same
network flow. At the moment, Algorithm 1 is applied to the graph
and the random walk is generated. The output of Algorithm 1 is
sent to Algorithm 2 in order to generate behavioural patterns.
Based on four pre-defined types of patterns, we expect to receive a
set of patterns for each type separately. Finally, these patterns are
sent to Algorithm 3, and the pattern-matching process is conducted
according to the threat database. Based on the matching result, the
security mechanism can decide if the flow is trusted or malicious.
The final decision depends on the probability ϕ that is calculated
according to (12).
6Experimental results and discussion
In this section, we discuss the details of our implementations and
results. We start by a real example and extend the same approach to
other experiments.
6.1 Implementation and example
Here, we are going to present a sample of our method and explain
it step by step. As shown in Fig. 7, two attack graphs are generated
by MulVAL. Note that attack graphs are directed graphs and may
contain several sinks and sources. Apart from the real meaning of
each node, we have numbered each vertex sequentially, reflecting
the dependencies of network structure on local policies. Since we
are interested in modelling the behaviour of the adversary using
random walks, we do not need any further information about
network architecture. We have generated ten attack graphs labelled
by AG1–AG10.
After the extraction of graphs, it is time to determine the data
structure. Since we have to execute random walks on attack graphs,
we select the adjacency matrix as data structure. While the graphs
are directed, the matrix would not be symmetric. Random walks
are applied independently from the number of vertices and other
parameters of the graph. Therefore, matching graphs with different
sizes does not negatively affect our method.
Each pair indicates coordinates in two dimensions. In
calculations related to AG2, we faced an exception. Exceptions are
thrown when self-avoiding rules associated with SARW are
violated. In this situation, we must roll back and modify the
conflicts. The exceptions do not belong to the calculated path and
must be removed at the end. In order to reduce the number of
exceptions, we must use higher dimensions of random walk.
In the next step, we generate patterns from random walks.
According to Algorithm 2, each type of pattern is detected. The
result of this step is sent to Algorithm 3 in order to compute the
matching rate. We are seeking for the greatest random subpath that
contains four specified subpatterns in the patterns vector. Based on
Algorithm 2, vector P is computed for each random walk
(illustrated in Fig. 8) as follows:
AG2 => PAG2 = p1ω0ω5,p2→ Null, p3→ Null,
p4→ Null
AG3 => PAG3 = p1ω0ω4,p2→ Null, p3→ Null,
p4→ Null
According to the results, we can guess that the two random
walks are matched. Since the vectors have some similarities in
common, they would be comparable. Then it is time to calculate
matching rates. In this example, we assume that AG3 belongs to
the threat database, and we should decide about AG2. The length
of the paths for AG2 is greater than for AG3. Therefore, AG2
dominates AG3 and we receive 100% matching rate.
We must pay special attention to each subpattern p1 to p4. For
example, p1 has intermittent structure. Consequently, if each two
random walks are computed in the same space, it is not necessary
to compare the complete set of steps. In such matching, we receive
100% matching rate if the given path has a greater number of steps.
On the other hand, p2 illustrates sets of steps in a unique direction.
Therefore, a sufficient condition for matching is that two given
subpatterns have equivalent length and move in the same direction.
However, p3 and p4 require a set of more complex computations.
6.2 Experimental results
In this section, the results regarding to implementation space and
conditions of experiments are reviewed. Our method is
experimentally validated via a series of attacks belonging to the
DDoS family. We have sampled a set of ten types of attack graphs
generated from the same attack family. In fact, our simulator
generates the network flows corresponding to each DDoS attack.
All parts of our experiments are executed on the same network
structure, and the results are calculated by simulation technique.
The simulation is performed on a dual core computer with 2.53 
GHz speed, 4 GB memory, and 100 Mb/s network controller. In
addition, we have used a local database system for storage of threat
Fig. 7 Two sample attack graphs for applying the pattern-matching
process using the proposed system
(a) AG2, (b) AG3
Fig. 8 Random walk in two dimensions according to generated paths
(a) SARW for AG2, (b) SARW for AG3
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patterns/features, and all programs are written in the JAVA
programming language.
We execute the random walk on the graphs and build proper
outputs according to a set of points. Afterwards, related patterns
are generated and the patterns are tested whether they match. In
each step, we assume one member in the set of attack graphs as
unknown and compare it to the other nine patterns existing in threat
database.
Table 1 indicates sets of specifications elicited from the output
of the patterns after the execution of algorithms discussed in
previous sections. Since we have used MulVAL's logical attack
graphs, the size of graphs has been drastically reduced, and
consequently, random walks are generated in two dimensions.
Therefore, it is meaningful to miss p4 that belongs to three or
higher dimensions.
In this step, we are going to investigate matching results. We
are interested in measuring the matching rates between extracted
patterns. Fig. 9 indicates the results of a set of experiments
performed according to matching algorithms. Based on the results,
we achieved at least one case with 100% matching rate in each
experiment. Each column in the figure shows how much the same
attack graph is matched to the given unknown traffics, indicated by
MR.
Achieving success in experiments depends on both the
proposed algorithms and completeness of the threat database. For
example, in the matching process associated with AG10, the main
challenge is that p3 is not generated. Therefore, it is comparable
only to those that contain no p3 pattern. Since we found two similar
configurations among other graphs, we could match it. According
to differences in the patterns’ distributions and the structures of
graphs, some matching rates are calculated above one. This would
be normalised to one in implementation steps. Also, the impact of
each attack graph in the matching process is shown in Fig. 10. It is
a stacked measurement representing the power of each pattern in
the results.
In the second experiment, we have compared attack graphs
shown in Table 1 (AG1–10) to another family of threats belonging
to a set of brute-force attack graphs (BR1–10). In this experiment,
each attack graph AGn is separately compared to all BRn attack
graphs (0 ≤ n ≤ 10). According to given criteria, an essential
condition for matching two attack graphs is to receive at least 80%
matching rate. As shown in Fig. 11, in all executed experiments,
Table 1Basic specifications and the output patterns of the experiment for each attack graph
Graph id n Δout (G) Source p1p2p3p4
AG1 25 5 3 3 2 4 0
AG2 28 4 5 5 2 3 0
AG3 29 3 4 5 3 0 0
AG4 24 3 3 5 2 3 0
AG5 23 4 2 3 5 3 0
AG6 21 4 3 2 3 4 0
AG7 27 4 3 3 4 3 0
AG8 20 3 2 3 4 0 0
AG9 26 3 4 3 5 3 0
AG10 22 3 3 3 3 0 0
Fig. 9 Set of matching results for different attack graphs using the proposed system
Fig. 10 Stacked matching rate for each attack graph, showing their impact on the matching process
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we did not receive any 100% matching result. However, we obtain
two cases >80% matching result out of hundred tests.
As we have prior knowledge about the existing differences
between these two generations of threats, we can compute the
false-negative (FN) matching rate as 2%. This means that on
average, we may expect receiving two wrong matching results out
of each hundred experiments where we compare two different
generations of threats. According to the first experiment, the result
for FN matching-rate was zero. We can confirm that, in this case,
true-negative and true-positive (TP) rates are more significant than
FN and false-positive rates because our task is to primarily detect
malicious traffics.
In Fig. 12, the stacked impact of matching rates for the second
experiment is indicated. Comparing to the first experiment, the
second has a higher number of matches. In the second experiment,
we have analysed 100 possibilities of potential matching, while in
the first experiment, the number of matching tests was 90.
Therefore, the overall stacked matching rate of the second
experiment is higher than the first one.
6.3 Discussion
The mentioned results have been achieved on a specific sample of
real attacks. Repeating such experiments in large scale requires
access to larger data sets. We also need to come up with new tool
chains for automating attack-graph generation. The strength of this
approach is provided by the power of the pattern theorem. For each
attack graph on which we are able to execute a random walk, it is
possible to apply the proposed approach. For new types of attack
graphs that may contain additional features, the proposed
algorithms can be customised.
In Table 2, we compare our proposed method to the other
research studies in this field. The comparison is based on average
true detection rate, the ability to detect unknown threats, the
complexity of implementation, sensitivity to a special attack
family, and online/offline approach. In comparison to the previous
works, our method reaches high precision in detecting
unprecedented threats. However, it has costs of higher complexity
of the algorithm and a limitation to network-level threats. Here, in
terms of complexity, n refers to the number of nodes in the given
attack graph.
We should emphasise that the complexity of our method is the
total complexity reflected by Algorithms 1–3. We did not discuss
the FN rate of the proposed system. This is due to the completeness
assumption about the threat database. We assume that the threat
database covers all the threats related to the network environment.
If the database would be complete, the number of patterns related
to the same family of threats is considerable. Therefore, when the
FN rate increases, it does not affect the overall decision because we
need to match one pattern at a time. This means that we do not care
if the FN rate increases; it suffices to achieve at least one accurate
pattern matching. To show the strength of our method, we can
Fig. 11 Set of matching results for different families of attack graph using the proposed system
Fig. 12 Stacked matching rate for each attack graph in the second experiment
Table 2Comparing approaches in detecting threats
Techniques Average True detection
rate, %
Detecting unknown
threats
Complexity Sensitivity to attack families Online/offline
hidden Markov model [3] 80 no enneutral online
EPM [1] 90 yes O(n) exploit offline
co-clustering [25] 93 no enneutral online
RAPS [14] 95 yes O(n4)neutral online/offline
proposed system 100 yes O(n4)network attacks online
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compute the sensitivity of the system based on the TP and FN
rates. It is computed according to (13), where TP and FN are
computed as 100 and 2%, respectively. To this end, the sensitivity
of the proposed method would be >0.98%. Note that the average
true detection rate that is mentioned in Table 2 actually is the TP
rate among the results. The high level of sensitivity shows the
validity and strength of our proposed method. In addition, looking
at true detection rate indicates the precision and correctness of the
method
Sensitivity = TP
TP + FN .
(13)
7Conclusion and future work
In this research, we focused on detecting new generations of threats
using a pattern-matching approach. The basis for this matching is
the utilisation of attack graphs. An attack graph indicates the set of
possible paths accessible to the adversary. According to the
proposed algorithms, we introduced a new approach for generating
random walks on the attack graphs. Based on the pattern theorem,
we elicited similar patterns through the graphs. In this research, ten
types of attack graphs belonging to the same family of threats were
generated. In each of ten separated experiments, we observed at
least one case with 100% matching rate. The approach is
generalised for other types of threats, and we can consider it as a
basic approach to address the detecting of new generations of
threats.
The proposed approach is not appropriate for very large graphs
and only tested for logical attack graphs. One of the future
directions for this research is to extend it to large-scale attack
graphs. For instance, DBIR is a good case to experiment with [28].
In addition, working on the other metrics related to the analysis and
design process is crucial. This part of research requires creative
solutions in order to improve the matching results.
8References
[1] Goodwin, S.: ‘The harsh reality of cyber protection’, in ‘ISACA online
webinar, Palo Alto networks’ (Enterprise Network Security Company, USA,
2015)
[2] National Vulnerability Database: ‘CVSS severity distribution over time’.
Annual report of NIST, September 2016
[3] Wright, C. V., Monrose, F., Masson, G. M.: ‘On inferring application protocol
behaviors in encrypted network traffic’, J. Mach. Learn. Res., 2006, 7, pp.
2745–2769
[4] Nia, M. A., Atani, R. E., Ruiz-Martinez, A.: ‘Privacy enhancement in
anonymous network channels using multimodality injection’, in ‘Security and
communication networks’, vol. 8 (Wiley Online Library, USA, 2015), Issue
16, pp. 2917–2932
[5] Ingols, K., Lippmann, R., Piwowarski, K.: ‘Practical attack graph generation
for network defense’. 22nd Annual Computer Security Applications Conf.
(ACSAC'06), Miami Beach, FL, 2006, pp. 121–130
[6] Liu, C., Singhal, A., Wijesekera, D.: ‘Using attack graphs in forensic
examinations’. Int. Conf. on Availability, Reliability and Security (ARES),
Prague, 2012, pp. 596–603
[7] Jeh, G., Widom, J.: ‘Simrank: a measure of structural-context similarity’.
ACM SIGKDD Int. Conf. on Knowledge Discovery and Data Mining (KDD
‘02), New York, USA, 2002, pp. 538–543
[8] Danai Koutra, A. R., Parikh, A., Xiang, J.: ‘Algorithms for graph similarity
and subgraph matching’. Ecological Inference Conf., Harvard University,
2011
[9] Allen, B., Nowak, M.: ‘Games on graphs’, EMS Surv. Math. Sci., 2014, 1, (2),
pp. 113–151
[10] Ou, X., Boyer, W. F., McQueen, M. A.: ‘A scalable approach to attack graph
generation’. The 13th ACM Conf. on Computer and Communications
Security, 2006, pp. 336–345
[11] Fouss, F., Pirotte, A., Renders, J. M., et al.: ‘Random-walk computation of
similarities between nodes of a graph with application to collaborative
recommendation’, IEEE Trans. Knowl. Data Eng., 2007, 19, (3), pp. 355–369
[12] Chu, M., Ingols, K., Lippmann, R., et al.: ‘Visualizing attack graphs,
reachability, and trust relationships with NAVIGATOR’. The Seventh Int.
Symp. on Visualization for Cyber Security (VizSec ‘10), New York, USA,
2010, pp. 22–33
[13] Liu, C.: ‘A probabilistic logic programming based model for network
forensics’. PhD thesis, Graduate Faculty of George Mason University, 2015
[14] Nia, M. A., Ebrahimi Atani, R., Fabian, B., et al.: ‘On detecting unidentified
network traffic using pattern-based random walk’, in Security &
communication network’, vol. 9 (John Wiley & Sons, USA, 2016), Issue 16,
pp. 3509–3526
[15] Lovász, L.: ‘Random walks on graphs: a survey’, J. Math. Stud., 1993, 2, pp.
1–46
[16] Kozdron, M.: ‘An introduction to random walks from Polya to self-
avoidance’. Technical report, Duke University, December 1998
[17] Slade, G., Blath, J., Imkeller, P., et al.: ‘The self-avoiding walk: a brief
survey’. Surveys in Stochastic Processes, The Thirty-third SPA Conf., Berlin,
2009, pp. 181–199
[18] Bauerschmidt, R., Duminil-Copin, H., Goodman, J., et al.: ‘Lectures on self-
avoiding walks’, Clay Math. Proc., 2012, 15, pp. 395–467
[19] Madras, N., Slade, G.: ‘The self-avoiding walk’ (Birkhäuser Basel-Springer,
Switzerland, 2013, 1st edn.), pp. 229–255
[20] Noh, J. D., Rieger, H.: ‘Random walks on complex networks’, Phys. Rev.
Lett., 2004, 92, pp. 1–4
[21] Akyildiz, I. F., Lin, Y. B., Lai, W. R., et al.: ‘A new random walk model for
PCS networks’, IEEE J. Sel. Areas Commun., 2000, 18, (7), pp. 1254–1260
[22] Bunke, H., Shearer, K.: ‘A graph distance metric based on the maximal
common subgraph’, Pattern Recognit. Lett., 1998, 19, (3–4), pp. 255–259
[23] Fouss, F., Pirotte, A., Renders, J. M., et al.: ‘Random-walk computation of
similarities between nodes of a graph, with application to collaborative
recommendation’, IEEE Trans. Knowl. Data Eng., 2006, 19, (3), pp. 355–369
[24] Minkov, E., Cohen, W. W.: ‘Learning graph walk based similarity measures
for parsed text’. The Conf. on Empirical Methods in Natural Language
Processing (EMNLP ‘08), Stroudsburg, PA, USA, 2008, pp. 907–916
[25] Ahmed, M., Mahmood, A. N.: ‘Network traffic pattern analysis using
improved information theoretic co-clustering based collective anomaly
detection’. Int. Conf. on Security and Privacy in Communication Networks,
2015, pp. 204–219
[26] Nia, M. A., Ruiz-Martinez, A.: ‘Systematic literature review on the state of
the art and future research work in anonymous communications systems’, in
Computers & electrical engineering (Elsevier, Netherlands, 2017), pp. 497–
520
[27] Sommer, R., Vern, P.: ‘Outside the closed world: on using machine learning
for network intrusion detection’. IEEE Symp. on Security and Privacy (SP
‘10), Washington, DC, USA, 2010, pp. 305–316
[28] ‘Mitigations aren't effective after the first six (a DBIR attack graph analysis)’.
Available at https://securityblog.verizonenterprise.com/?p=7077, accessed
August 2017
IET Inf. Secur., 2019, Vol. 13 Iss. 4, pp. 293-303
© The Institution of Engineering and Technology 2019
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