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file = {Combining OpenCL and MPI to Support Heterogeneous Computing on a Cluster:/home/noah/Zotero/storage/TXHCQ5S8/Combining OpenCL and MPI to Support Heterogeneous Computing on a Cluster.pdf:application/pdf},
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}
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@article{zeng_cyber_2017,
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@phdthesis{zeng_cyber_2017,
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title = {Cyber {Attack} {Analysis} {Based} on {Markov} {Process} {Model}},
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author = {Zeng, Keming},
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school = "The University of Tulsa",
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year = {2017},
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file = {keming_thesis:/home/noah/Zotero/storage/LQY2YWSR/keming_thesis.pdf:application/pdf},
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address = "Tulsa, OK",
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}
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@inproceedings{baloyi_guidelines_2019,
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@ -104,7 +102,6 @@
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Journal = {BMC systems biology},
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ISSN = {1752-0509},
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Pages = {80},
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Abstract = {<h4>Background</h4>Numerous centrality measures have been introduced to identify "central" nodes in large networks. The availability of a wide range of measures for ranking influential nodes leaves the user to decide which measure may best suit the analysis of a given network. The choice of a suitable measure is furthermore complicated by the impact of the network topology on ranking influential nodes by centrality measures. To approach this problem systematically, we examined the centrality profile of nodes of yeast protein-protein interaction networks (PPINs) in order to detect which centrality measure is succeeding in predicting influential proteins. We studied how different topological network features are reflected in a large set of commonly used centrality measures.<h4>Results</h4>We used yeast PPINs to compare 27 common of centrality measures. The measures characterize and assort influential nodes of the networks. We applied principal component analysis (PCA) and hierarchical clustering and found that the most informative measures depend on the network's topology. Interestingly, some measures had a high level of contribution in comparison to others in all PPINs, namely Latora closeness, Decay, Lin, Freeman closeness, Diffusion, Residual closeness and Average distance centralities.<h4>Conclusions</h4>The choice of a suitable set of centrality measures is crucial for inferring important functional properties of a network. We concluded that undertaking data reduction using unsupervised machine learning methods helps to choose appropriate variables (centrality measures). Hence, we proposed identifying the contribution proportions of the centrality measures with PCA as a prerequisite step of network analysis before inferring functional consequences, e.g., essentiality of a node.},
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URL = {https://europepmc.org/articles/PMC6069823},
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}
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@ -186,7 +183,7 @@ volume = {2},
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number = {1},
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pages = {73-120},
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year = {2005},
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publisher = {Taylor & Francis},
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publisher = "Taylor \& Francis",
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doi = {10.1080/15427951.2005.10129098},
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URL = {https://doi.org/10.1080/15427951.2005.10129098},
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eprint = {https://doi.org/10.1080/15427951.2005.10129098}
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@ -219,8 +216,39 @@ issn = {2692-1626},
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url = {https://doi.org/10.1145/3491257},
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doi = {10.1145/3491257},
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abstract = {As an analytical tool in cyber-security, an attack graph (AG) is capable of discovering multi-stage attack vectors on target computer networks. Cyber-physical systems (CPSs) comprise a special type of network that not only contains computing devices but also integrates components that operate in the continuous domain, such as sensors and actuators. Using AGs on CPSs requires that the system models and exploit patterns capture both token- and real-valued information. In this paper, we describe a hybrid AG model for security analysis of CPSs and computer networks. Specifically, we focus on two issues related to applying the model in practice: efficient hybrid AG generation and techniques for information extraction from them. To address the first issue, we present an accelerated hybrid AG generator that employs parallel programming and high performance computing (HPC). We conduct performance tests on CPU and GPU platforms to characterize the efficiency of our parallel algorithms. To address the second issue, we introduce an analytical regimen based on centrality analysis and apply it to a hybrid AG generated for a target CPS system to discover effective vulnerability remediation solutions.},
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note = {Just Accepted},
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journal = {Digital Threats},
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month = {oct},
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keywords = {attack graph, breadth-first search, cyber-physical system, high performance computing}
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}
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@article{ZENITANI2023103081,
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title = {Attack graph analysis: An explanatory guide},
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journal = "Computers \& Security",
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volume = {126},
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pages = {103081},
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year = {2023},
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issn = {0167-4048},
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doi = {https://doi.org/10.1016/j.cose.2022.103081},
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url = {https://www.sciencedirect.com/science/article/pii/S0167404822004734},
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author = {Kengo Zenitani},
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keywords = {Attack graph, Exploit dependency graph, Cycle handling, Network security metrics, Network hardening, Bayesian attack graph},
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abstract = {Attack graph analysis is a model-based approach for network-security analysis. It analyzes a directed graph called an attack graph. Usually, each node in it corresponds to a malicious event caused by attackers, and the edges correspond to the causal relations between events. We can obtain an attack graph from the network topology, its configuration, and the distribution of vulnerabilities. An attack graph gives us various information relevant to network security. Also, there are several relevant algorithms to find desirable security controls applicable to the network. Over twenty years of research have made much progress in this field. However, it comprises a breadth of definitions and discussions, and it is difficult for people new to this field to comprehend the key ideas. This article aims to briefly introduce this method to prospective researchers by summarizing their progress by selecting and reviewing foundational studies. We elaborate on the essential concepts, such as exploit dependency, AND/OR graph, monotonicity, and cycle handling.}
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}
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@article{Zeng2019SurveyOA,
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title={Survey of Attack Graph Analysis Methods from the Perspective of Data and Knowledge Processing},
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author={Jianping Zeng and Shuang Wu and Yanyu Chen and Rui Zeng and Chengrong Wu},
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journal={Secur. Commun. Networks},
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year={2019},
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volume={2019},
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pages={2031063:1-2031063:16}
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}
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@phdthesis{ming_diss,
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author = {Li, Ming and Hawrylak, Peter and Hale, John},
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title = "A System for Attack Graph Generation and Analysis",
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school = "The University of Tulsa",
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year = "2021",
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type = "{PhD} dissertation",
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address = "Tulsa, OK",
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}
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\bibitem{Mieghem2018DirectedGA}
|
||||
P.~V. Mieghem, ``Directed graphs and mysterious complex eigenvalues,'' 2018.
|
||||
|
||||
\bibitem{ZENITANI2023103081}
|
||||
K.~Zenitani, ``Attack graph analysis: An explanatory guide,'' {\em Computers \&
|
||||
Security}, vol.~126, p.~103081, 2023.
|
||||
|
||||
\bibitem{Zeng2019SurveyOA}
|
||||
J.~Zeng, S.~Wu, Y.~Chen, R.~Zeng, and C.~Wu, ``Survey of attack graph analysis
|
||||
methods from the perspective of data and knowledge processing,'' {\em Secur.
|
||||
Commun. Networks}, vol.~2019, pp.~2031063:1--2031063:16, 2019.
|
||||
|
||||
\bibitem{ming_diss}
|
||||
M.~Li, P.~Hawrylak, and J.~Hale, {\em A System for Attack Graph Generation and
|
||||
Analysis}.
|
||||
\newblock {PhD} dissertation, The University of Tulsa, Tulsa, OK, 2021.
|
||||
|
||||
\bibitem{10.1145/3491257}
|
||||
M.~Li, P.~Hawrylak, and J.~Hale, ``Strategies for practical hybrid attack graph
|
||||
generation and analysis,'' {\em Digital Threats}, oct 2021.
|
||||
\newblock Just Accepted.
|
||||
|
||||
\bibitem{Guo2017HermitianAM}
|
||||
K.~Guo and B.~Mohar, ``Hermitian adjacency matrix of digraphs and mixed
|
||||
@ -57,6 +70,11 @@ M.~Ashtiani, A.~Salehzadeh-Yazdi, Z.~Razaghi-Moghadam, H.~Hennig,
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||||
L.~Katz, ``{A new status index derived from sociometric analysis},'' {\em
|
||||
Psychometrika}, vol.~18, pp.~39--43, March 1953.
|
||||
|
||||
\bibitem{ModKatz}
|
||||
M.~Ogura and V.~M. Preciado, ``Katz centrality of markovian temporal networks:
|
||||
Analysis and optimization,'' {\em 2017 American Control Conference (ACC)},
|
||||
pp.~5001--5006, 2017.
|
||||
|
||||
\bibitem{K_Path_Edge}
|
||||
P.~D. Meo, E.~Ferrara, G.~Fiumara, and A.~Ricciardello, ``A novel measure of
|
||||
edge centrality in social networks,'' {\em Knowledge-Based Systems}, vol.~30,
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||||
@ -79,8 +97,8 @@ M.~Li, P.~Hawrylak, and J.~Hale, ``Combining {OpenCL} and {MPI} to support
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||||
Proceeding Series}, 2019.
|
||||
|
||||
\bibitem{zeng_cyber_2017}
|
||||
K.~Zeng, ``Cyber {Attack} {Analysis} {Based} on {Markov} {Process} {Model},''
|
||||
2017.
|
||||
K.~Zeng, {\em Cyber {Attack} {Analysis} {Based} on {Markov} {Process} {Model}}.
|
||||
\newblock PhD thesis, The University of Tulsa, Tulsa, OK, 2017.
|
||||
|
||||
\bibitem{dominance}
|
||||
R.~T. Prosser, ``Applications of boolean matrices to the analysis of flow
|
||||
|
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** Conference Paper **
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\documentclass[conference]{IEEEtran}
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@ -82,10 +69,12 @@ Compliance graphs begin with a root node that contains all the current informati
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Compliance graphs, like attack graphs, are directed acyclic graphs, and analysis of directed graphs is notably more involved compared to their undirected counterparts. The primary contributor to the increased difficulty is due to the asymmetric adjacency matrix present in directed graphs. With undirected graphs, simplifications can be made in the analysis process both computationally and conceptually. Since the ``in" degrees are equal to the ``out" degrees, less work is required both in terms of parsing the adjacency matrix, but also in terms of determining importance of nodes. The author of \cite{newman2010networks} discusses that common analysis techniques such as eigenvector centrality is often unapplicable to directed acyclic graphs. As the author of \cite{Mieghem2018DirectedGA} discusses, the difficulty of directed graphs also extends to the graph Laplacian, where the definition for asymmetric adjacency matrices is not uniquely defined, and is based on either row or column sums computing to zero, but both cannot. The author of \cite{Mieghem2018DirectedGA} continues to discuss that directed graphs lead to complex eigenvalues, and can lead to adjacency matrices that are unable to be diagonalized. These challenges require different approaches for typical clustering or centrality measures.
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\section{Related Works}
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The author of \cite{10.1145/3491257} presents three centrality measures that were applied to various attack graphs. The centrality measures implemented were Katz, K-path Edge, and Adapted PageRank. Each of these centrality measures are applicable to the directed format of attack graphs, and conclusions were drawn regarding patching schemes for preventing exploits. As an approach for avoiding complex eigenvalues, the authors of \cite{Guo2017HermitianAM} present work examining directed, undirected, and mixed graphs using its Hermitian adjacency matrix. Other works, such as that discussed by the author of \cite{Mieghem2018DirectedGA}, include mathematical manipulation of directed graph spectra (originally presented by the author of \cite{Brualdi2010SpectraOD}) with Schur's Theorem to bound eigenvalues and allow for explicit computation, which can then be used for additional analysis metrics.
|
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Though compliance graphs have not yet had formal analysis methodologies defined, they are analyzed similarly to attack graphs, which have various analysis approaches. The authors of \cite{ZENITANI2023103081} and the authors of \cite{Zeng2019SurveyOA} both present surveys on attack graph analysis that have been categorized by approach. These categories include analysis based on graph or network theory, Bayesian Networks, Markov Models, cost optimization, and uncertainty analysis. Each of these approaches have seen varying ranges of success across multiple subcategories.
|
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|
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Regarding network science approaches, the author of \cite{ming_diss} presents three centrality measures that were applied to various attack graphs. The centrality measures implemented were Katz, K-path Edge, and Adapted PageRank, with the authors of \cite{10.1145/3491257} expanding on the Adapted PageRank approach. Each of these centrality measures are applicable to the directed format of attack graphs, and conclusions were drawn regarding patching schemes for preventing exploits. As an approach for avoiding complex eigenvalues, the authors of \cite{Guo2017HermitianAM} present work examining directed, undirected, and mixed graphs using its Hermitian adjacency matrix. Other works, such as that discussed by the author of \cite{Mieghem2018DirectedGA}, include mathematical manipulation of directed graph spectra (originally presented by the author of \cite{Brualdi2010SpectraOD}) with Schur's Theorem to bound eigenvalues and allow for explicit computation, which can then be used for additional analysis metrics.
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\section{Experimental Networks} \label{sec:networks}
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The work conducted in this approach utilized three compliance graphs, with their properties displayed in Table \ref{table:networks}. Connectivity in this table refers to the mean degree, divided by the number of nodes in the network, multiplied by 100 to return a percentage. Network 1 is a vehicle maintenance network. This network has one car asset that is deemed ``brand new", and has zero mileage. This network is examined at its current state, and progresses through time with time steps of 1 month, up to 12 months total. At each time step the car gains mileage and increases its age property, and is reexamined to evaluate its standing in regards to its vehicular regulatory maintenance schedule. Network 2 is an artificial company network that is attempting to maintain HIPAA compliance \cite{noauthor_health_1996}. This network examines its standing in relation to security properties that are required per HIPAA guidelines, as well as employee cooperation to training and administrative policies. This network is also progressed through time to illustrate the company's standing in relation to yearly audits and trainings that must be followed. Employees are also added and removed through the network at set points during the time progression process. Network 3 is another artificial company network. This company is attempting to maintain PCI DSS compliance \cite{PCI}. This network generation was static and did not progress through time. This network examined the company and its current state, and examined a list of changes that could occur. These changes were primarily tied to security properties such as physical break-ins on the property, disabling firewalls, leaving default system settings, and encryption expiration.
|
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The work conducted in this approach utilized three compliance graphs, with their properties displayed in Table \ref{table:networks}. Connectivity in this table refers to the mean degree, divided by the number of nodes in the network, multiplied by 100 to return a percentage. Network 1 is a vehicle maintenance network. This network has one car asset that is deemed ``brand new", and has zero mileage. This network is examined at its current state, and progresses through time with time steps of 1 month, up to 12 months total. At each time step the car gains mileage and increases its age property, and is reexamined to evaluate its standing in regards to its vehicular regulatory maintenance schedule. Network 2 is an artificial company network that is attempting to maintain HIPAA compliance \cite{noauthor_health_1996}. This network examines its standing in relation to security properties that are required per HIPAA guidelines, as well as employee cooperation to training and administrative policies. This network is also progressed through time to illustrate the company's standing in relation to yearly audits and trainings that must be followed. Employees are also added and removed through the network at set points during the time progression process. Network 3 is another artificial company network. This organization is attempting to maintain PCI DSS compliance \cite{PCI}. This network generation was static and did not progress through time. This network examined the company and its current state, and examined a list of changes that could occur. These changes were primarily tied to security properties such as physical break-ins on the property, disabling firewalls, leaving default system settings, and encryption expiration.
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\begin{table}[]
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\centering
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@ -103,10 +92,10 @@ The work conducted in this approach utilized three compliance graphs, with their
|
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\section{Centralities and their Contextualizations to Compliance Graphs} \label{sec:centralities}
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\subsection{Introduction}
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The author of \cite{PMID:30064421} provides a survey of centrality measures, and discusses how various centrality measures have been implemented and brought forth in order to determine node importance in networks. By determining the importance of nodes, various conclusions can be drawn regarding the network. In the case of compliance graphs, conclusions can be drawn regarding the prioritization of patching or correction schemes. If one node is known to lead to the creation of many other nodes, it may be said that a patch is imperative to prevent further opportunities for compliance violation. This work discusses five centrality measures, and discusses their application to compliance graphs.
|
||||
The author of \cite{PMID:30064421} provides a survey of centrality measures, and discusses how various centrality measures have been implemented in order to determine node importance in networks. By determining the importance of nodes, various conclusions can be drawn regarding the network. In the case of compliance graphs, conclusions can be drawn regarding the prioritization of patching or correction schemes. If one node directs to many other nodes, a mitigation enforcement may be considered imperative to prevent further opportunities for compliance violation. This work discusses five centrality measures across various structural changes, and contextualizes their applications to compliance graphs.
|
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\subsection{Degree}
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Degree centrality is a trivial, localized measure of node importance based on the number of edges that a node has. In an undirected graph, the degree centrality is predicated solely on the number of edges. However, in the case of a directed graph, a distinction is drawn with a degree centrality oriented on the number of edges coming into a node, and another measure focused on the number of edges leaving a node. Both of these cases provide useful information for compliance graphs. When a node has a large number of other nodes it directs to, this node may be prioritized since it creates further opportunity for violation. When a node has a large number of edges pointing to it, this node may be prioritized since the probability that systems may enter this state is higher due to the increased number of possibilities that a system change could lead to this state.
|
||||
Degree centrality is a trivial, localized measure of node importance based on the number of edges that a node has. In an undirected graph, the degree centrality is predicated solely on the number of edges. However, in the case of a directed graph, a distinction is drawn with a degree centrality oriented on the number of edges entering a node, and another measure focused on the number of edges leaving a node. Both of these cases provide useful information for compliance graphs. When a node has a large number of other nodes it directs to, this node may be prioritized since it creates further opportunity for violation. When a node has a large number of edges pointing to it, this node may be prioritized since the probability that systems may enter this state is higher due to the increased number of possibilities that a system change could lead to this state.
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\subsection{Betweenness}\label{sec:between}
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Betweenness centrality ranks node importance based on its ability to transfer information in a network. For all pairs of nodes in a network, a shortest path is determined. A node that is in this shortest path is considered to have importance. The total betweenness centrality is based on the number of shortest paths that pass through a given node. For compliance graphs, the shortest paths are useful to identify the quickest way (least number of steps) that systems may fall out of compliance. By prioritizing the nodes that fall in the highest number of shortest paths, correction schemes can be employed to prolong or prevent systems from falling out of compliance.
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@ -126,7 +115,7 @@ Katz centrality was first introduced by the author of \cite{Katz}, and measures
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\label{eq:Katz}
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\end{equation}
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Later works have expanded on the original Katz to include a $\beta$ vector that allows for additional scaling in the instance that prior knowledge of the network exists. The modified equation can be seen in Equation \ref{eq:mod_katz}.
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Later works have expanded on the original Katz to include a $\beta$ vector that allows for additional scaling in the instance that prior knowledge of the network exists. The modified equation implemented by the authors of \cite{ModKatz} can be seen in Equation \ref{eq:mod_katz}.
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\begin{equation}
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\vec{x} = \left(I - \alpha A \right)^{-1}\vec{\beta}
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@ -163,7 +152,6 @@ The adapted PageRank algorithm includes additional data that may be present in a
|
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For compliance graphs, the Adapted Page Rank algorithm is useful for a few reasons. First, it is able to include user-defined data regarding the network. This could include scaling certain nodes to have greater weight, such as those known to be a compromised state. Second, since nodes are penalized for pointing to other nodes, this algorithm is useful for determining nodes that are likely to be visited. If a state has a greater in-degree, it may require greater prioritization since the system has a higher likelihood of falling into this state.
|
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\section{Transitive Closure}
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\subsection{Introduction and Application}
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Transitive closure represents a transitive relation on a given binary set, and can be used to determine reachability of a given network. Figure \ref{fig:TC} displays an example output when performing transitive closure. In context of compliance graphs, it is useful to consider that an adversary (whether an internal or external malicious actor, poor policy execution by an organization, accidental misuse, or any other adversarial occurrence) could have no time constraints. That is, for any given state of the system or set of systems, an adversarial act could have ``infinite" time to perform a series of actions. If no prior knowledge is known about the network, it can be assumed that all changes performed on the systems are equally likely. In practice, specifying a probability that a change can occur has been performed through a Markov Decision Process, such as that seen by the authors of \cite{li_combining_2019} and \cite{zeng_cyber_2017}. When under these assumptions, it is useful to then consider which nodes are important, assuming they have 1-step reachability to any downstream node they may have a transitive connection to. This work identified a transitive closure for all networks described in
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Section \ref{sec:networks}, and this transitive closure was then analyzed through the five centrality methods discussed in Section \ref{sec:centralities}. Results and a discussion of the results can be seen in Section \ref{sec:results}.
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@ -177,8 +165,6 @@ Section \ref{sec:networks}, and this transitive closure was then analyzed throug
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\section{Dominant Tree}
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\subsection{Introduction and Application}
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Dominance, as initially introduced by the author of \cite{dominance} in terms of flow, is defined as a node that is in every path to another node. If a node \textit{i} is a destination node, and every path to \textit{i} from a source node includes node \textit{j}, then node \textit{j} is said to dominate node \textit{i}. Figure 2 displays an example starting network. With node 1 as the source node, it is evident that node 2 immediately dominates nodes 3, 4, 5, and 6, since all messages from node 1 must pass through node 2. By definition, each node must also dominate itself, so node 2 also dominates node 2.
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Following the properties of dominance, a dominator tree can be derived. In a dominator tree, each node has children that it immediately dominates. Immediate dominance is referred to nodes that strictly dominate a given node, but do not strictly dominate any other node that may strictly dominate a node. Figure 3 displays the dominant tree of the network seen in Figure 2.
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@ -381,7 +367,7 @@ For the dominant tree representation, it was initially hypothesized that nodes r
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Each centrality measure implemented in this work provides various information that is useful for identifying correction schemes based on a network science approach. The results from the centrality methods differ, and each network can determine which rankings should be preferred based on prior knowledge of the network and the overhead of implementing correction measures. In addition, transitive closures and dominant trees were derived from the original compliance graphs, and unique rankings were identified. Transitive closure rankings are useful for determining which nodes are most important when an adversarial action can be considered to have infinite time and resources to perform changes to the original system. Dominant tree rankings are useful for determining which nodes are most important from an information flow perspective, where adversarial actions must pass though a series of nodes to reach any other node in the network. By applying correction schemes to the bottlenecks of the network, it may be possible to eliminate branches of the dominant tree entirely, leading to a removal of nodes in the original compliance graph.
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\subsection{Future Work}
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Based on the results of this work, there is ample room to continue investigation of centrality methods for compliance graphs. With three compliance graphs generated for three different networks along with various node importance rankings, it would be useful to artificially implement correction schemes based on the rankings to see their effects on the compliance graph. Likewise, using a user-defined data matrix in centrality methods like PageRank, further research could examine how node importance varies based on user-defined metrics. Edge weights could also be assigned to the original compliance graphs to represent the probability that a given change in the network could occur. Edge weights would be reflected in the adjacency matrices of the graphs, and centrality methods could be reexamined to determine node importance when state transition probabilities are given. Transitive closures and dominant trees derived from the compliance graphs present a new approach for examining compliance graphs. Further research can be conducted to determine the effects of correction schemes when employed on nodes ranked highly in their respective centrality measures in these formats.
|
||||
Based on the results of this work, there is considerable opportunity to continue investigation of centrality methods for compliance graphs. With three compliance graphs generated for three different applications, along with various node importance rankings, it would be useful to artificially implement correction schemes based on the rankings to see their effects on the compliance graph. Likewise, using a user-defined data matrix in centrality methods like PageRank, further research could examine how node importance varies based on user-defined metrics. Edge weights could also be assigned to the original compliance graphs to represent the probability that a given change in the network could occur. Edge weights would be reflected in the adjacency matrices of the graphs, and centrality methods could be reexamined to determine node importance when state transition probabilities are given. Transitive closures and dominant trees derived from the compliance graphs present a new approach for examining compliance graphs. Further research can be conducted to determine the effects of correction schemes when employed on nodes ranked highly in their respective centrality measures in these formats.
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\addcontentsline{toc}{section}{Bibliography}
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\bibliography{Bibliography}
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