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Noah L. Schrick 2023-04-04 14:30:40 -05:00
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28
Bibliography.bib
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@ -18,7 +18,7 @@
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},
}
@phdthesis{zeng_cyber_2017,
@mastersthesis{zeng_cyber_2017,
title = {Cyber {Attack} {Analysis} {Based} on {Markov} {Process} {Model}},
author = {Zeng, Keming},
school = "The University of Tulsa",
@ -252,3 +252,29 @@
type = "{PhD} dissertation",
address = "Tulsa, OK",
}
@article{MO2019121538,
title = {Identifying node importance based on evidence theory in complex networks},
journal = {Physica A: Statistical Mechanics and its Applications},
volume = {529},
pages = {121538},
year = {2019},
issn = {0378-4371},
doi = {https://doi.org/10.1016/j.physa.2019.121538},
url = {https://www.sciencedirect.com/science/article/pii/S0378437119309021},
author = {Hongming Mo and Yong Deng},
keywords = {Complex networks, Important nodes, Evidence theory, Multi-evidence centrality, Comprehensive measure},
}
@article{LI2018512,
title = {Identification of influential spreaders based on classified neighbors in real-world complex networks},
journal = {Applied Mathematics and Computation},
volume = {320},
pages = {512-523},
year = {2018},
issn = {0096-3003},
doi = {https://doi.org/10.1016/j.amc.2017.10.001},
url = {https://www.sciencedirect.com/science/article/pii/S0096300317306884},
author = {Chao Li and Li Wang and Shiwen Sun and Chengyi Xia},
keywords = {Influential spreaders, Identification algorithms, Classified neighbors, Complex networks},
}

28
Schrick-Noah_CG-Network_Theory.aux
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@ -28,22 +28,21 @@
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@ -91,13 +91,15 @@
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14
Schrick-Noah_CG-Network_Theory.bbl
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@ -97,8 +97,8 @@ M.~Li, P.~Hawrylak, and J.~Hale, ``Combining {OpenCL} and {MPI} to support
Proceeding Series}, 2019.
\bibitem{zeng_cyber_2017}
K.~Zeng, {\em Cyber {Attack} {Analysis} {Based} on {Markov} {Process} {Model}}.
\newblock PhD thesis, The University of Tulsa, Tulsa, OK, 2017.
K.~Zeng, ``Cyber {Attack} {Analysis} {Based} on {Markov} {Process} {Model},''
Master's thesis, The University of Tulsa, Tulsa, OK, 2017.
\bibitem{dominance}
R.~T. Prosser, ``Applications of boolean matrices to the analysis of flow
@ -106,4 +106,14 @@ R.~T. Prosser, ``Applications of boolean matrices to the analysis of flow
IRE-AIEE-ACM Computer Conference}, IRE-AIEE-ACM '59 (Eastern), (New York, NY,
USA), p.~133–138, Association for Computing Machinery, 1959.
\bibitem{LI2018512}
C.~Li, L.~Wang, S.~Sun, and C.~Xia, ``Identification of influential spreaders
based on classified neighbors in real-world complex networks,'' {\em Applied
Mathematics and Computation}, vol.~320, pp.~512--523, 2018.
\bibitem{MO2019121538}
H.~Mo and Y.~Deng, ``Identifying node importance based on evidence theory in
complex networks,'' {\em Physica A: Statistical Mechanics and its
Applications}, vol.~529, p.~121538, 2019.
\end{thebibliography}

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@ -44,6 +44,16 @@
Tulsa, USA \\
peter-hawrylak@utulsa.edu
}
\and
\IEEEauthorblockN{Brett A. McKinney}
\IEEEauthorblockA{
\textit{Tandy School of Computer Science} \\
\textit{The University of Tulsa}\\
Tulsa, USA \\
brett-mckinney@utulsa.edu
}
}
\maketitle
@ -61,9 +71,9 @@ Attack Graph; Compliance Graph; Cybersecurity; Compliance and Regulation; Networ
\subsection{Compliance Graphs}
Compliance graphs are an alternate form of attack graphs, utilized specifically for examining compliance and regulation statuses of systems. Like attack graphs, compliance graphs can be used to determine all ways that systems may fall out of compliance or violate regulations, or highlight the ways in which violations are already present. These graphs are notably useful for cyber-physical systems due to the increased need for compliance. As the authors of \cite{j_hale_compliance_nodate}, \cite{baloyi_guidelines_2019}, and \cite{allman_complying_2006} discuss, cyber-physical systems have seen greater usage, especially in areas such as critical infrastructure and Internet of Things.
The semantics of compliance graphs are similar to that of attack graphs, but with a few differences regarding the information at each state. While security and compliance statuses are related, the information that is analyzed in compliance graphs is focused less on certain security properties, but is expanded to also examine administrative policies and properties of systems. Since compliance and regulation is broad and can vary by industry and application, the information to analyze can range from safety regulations, maintenance compliance, or any other regulatory compliance, including internal company standards. However, the graph structure of compliance graphs is identical to that of attack graphs, where edges represent a modification to the systems, and nodes represent all current information in the system.
The semantics of compliance graphs are similar to that of attack graphs, but with a few differences regarding the information at each state. While security and compliance statuses are related, the information that is analyzed in compliance graphs is focused less on certain security properties, but is expanded to also examine administrative policies and properties of systems. Since compliance and regulation is broad and can vary by industry and application, the information to analyze can range from safety regulations, maintenance compliance, or any other regulatory compliance, including internal company standards. However, the graph structure of compliance graphs is identical to that of attack graphs, where edges represent a modification to the system, and nodes represent all current information in the system.
Compliance graphs begin with a root node that contains all the current information of the system or set of systems. From this initial root state, all assets in the system are examined to see if any single modification can be made, where a modification can include a change in system policy or security settings. If a modification can be made, an edge is drawn from the previous state to a new state that includes all of the previous state's information, but now reflects the change in the system. This edge is labeled to reflect which change was made to the system. This process is exhaustively repeated, where all system properties are examined, all modification options are fully enumerated, all permutations are examined, and all changes to a system are encoded into their own independent states, where these states are then individually analyzed through the process.
Compliance graphs begin with a root node that contains all the current information of the system or set of systems. From this initial root state, all assets in the system are examined to see if any single modification can be made, where a modification can include a change in system policy, security settings, or standing in relation to a compliance or regulatory mandate. If a modification can be made, an edge is drawn from the previous state to a new state that includes all of the previous state's information, but now reflects the change in the system. This edge is labeled to reflect which change was made to the system. This process is exhaustively repeated, where all system properties are examined, all modification options are fully enumerated, all permutations are examined, and all changes to a system are encoded into their own independent states, where these states are then individually analyzed through the process.
\subsection{Difficulties of Attack and Compliance Graph Analysis}
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.
@ -91,7 +101,6 @@ The work conducted in this approach utilized three compliance graphs, with their
\end{table}
\section{Centralities and their Contextualizations to Compliance Graphs} \label{sec:centralities}
\subsection{Introduction}
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.
\subsection{Degree}
@ -187,7 +196,6 @@ Following the properties of dominance, a dominator tree can be derived. In a dom
Dominant trees do alter the structure of compliance graphs, and lead to leaf nodes and branches that do not exist in the original network. As a result, some nodes that have directed edges to other nodes may be moved to a position where the edge no longer points to the original nodes. However, in dominant trees, all node parents dominate their children. In this format, the information flow is guided predominantly by the upstream nodes, and all parents in the dominant tree exist as upstream nodes in the original compliance graph. While some downstream nodes may be altered, the importance of nodes can be reexamined in the dominant tree to see how importance differs when information flow is refined. To this end, dominant trees were identified for all networks described in Section \ref{sec:networks}, and these dominant trees were 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}.
\section{Results and Result Analysis} \label{sec:results}
\subsection{Results}
In this section, only results for the car network are displayed for brevity. These results can be seen in Tables \ref{table:car-deg} through \ref{table:car-betweenness}. The results for the HIPAA and PCI DSS networks can be found in the Supplementary Material included with this work.
\begin{table}[]
@ -367,7 +375,9 @@ For the dominant tree representation, it was initially hypothesized that nodes r
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.
\subsection{Future Work}
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.
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. Extensions to the ranking and correction schemes could be made by creating a single source of importance ranking by collapsing or combining the vector of centrality method rankings. Since each centrality method highlights unique properties of the network, it may be useful to take each into consideration and determine a final, overall importance ranking. This approach has been seen in works such as those presented by the authors of \cite{LI2018512} and \cite{MO2019121538}.
Further research could examine how node importance varies based on user-defined metrics by using a user-defined data matrix in centrality methods like PageRank. 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.
\addcontentsline{toc}{section}{Bibliography}
\bibliography{Bibliography}

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