Finalizing Report
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\section{Results and Result Analysis} \label{sec:results}
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\subsection{Results}
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In this section, only results for the car network are displayed for brevity. For the HIPAA and PCI DSS networks, results can be seen in Appendices \ref{apx:hipaa} and \ref{apx:pci}, respectively.
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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}. For the HIPAA and PCI DSS networks, results can be seen in Appendices \ref{apx:hipaa} and \ref{apx:pci}, respectively.
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\subsection{Result Analysis}
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When viewing the results of the car networks, unsurprisingly, each centrality method ranks nodes in a different order. These differences in rankings can be used based on additional metrics, such as severity, cost, or disturbance of systems, to identify correction schemes best suited for a given network. However, degree centrality and K-path edge centrality rankings for the top 15 were identical for the car network. This also extends to the HIPAA network, as seen in Appendix \ref{apx:hipaa}, but does not extend to the PCI DSS network. The value for \textit{k} in K-path edge centrality was set to 3. With a relatively small \textit{k} value in comparison to the overall size of the car and HIPAA networks, coupled with the high degree count of the top 15 nodes ranked with degree centrality, it is likely that the high degree count correlates to the K-path edge centrality scoring. This reasoning extends to the PCI DSS network, where the network is substantially smaller and there is a greater connectivity percent.
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Comparing the transitive closure format of compliance graphs, the associated centrality rankings greatly vary from their original compliance graph rankings. As expected however, the root or leaf node has the highest centrality value. Since the root node can reach all nodes, and the leaf node can be reached by all nodes, these two nodes are expectedly ranked high. What is unexpected, however, is that the top 15 rankings are not comprised of the most upstream 15 nodes or the 15 most downstream nodes. While rankings do tend to be higher for more upstream for K-path edge, Katz, and degree centralities, nodes in the 100s, 200s, and 300s all make appearances. Betweenness centrality for the transitive closure representation yielded no valuable insight, since shortest paths to a node from any given node is reachable in 1 step.
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For the dominant tree representation, it was initially hypothesized that nodes ranked highly in the original compliance graph's betweenness centrality or Katz centrality measures would closely relate to the dominant tree results. However, the dominant tree rankings also vary greatly from the original compliance graph's rankings. Even nodes that saw no appearances in the top 15 of the base compliance graph or transitive closure representation made appearances in the dominant tree results. Since the dominant tree format does favor the upstream nodes due to a lesser reordering effect caused by dominance, the PageRank ordering were not predominantly downstream nodes, but mostly nodes in the 300s.
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\section{Conclusions and Future Work}
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\subsection{Conclusions}
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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 closure representations 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 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.
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\clearpage
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\addcontentsline{toc}{section}{Bibliography}
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\bibliography{Bibliography}
|
||||
\bibliographystyle{ieeetr}
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@ -1,25 +1,27 @@
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\babel@toc {nil}{}\relax
|
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\contentsline {section}{\numberline {1}Introduction}{2}{}%
|
||||
\contentsline {subsection}{\numberline {1.1}Attack Graphs}{2}{}%
|
||||
\contentsline {subsection}{\numberline {1.2}Compliance Graphs}{2}{}%
|
||||
\contentsline {subsection}{\numberline {1.3}Difficulties of Compliance Graph Analysis}{3}{}%
|
||||
\contentsline {section}{\numberline {2}Related Works}{3}{}%
|
||||
\contentsline {section}{\numberline {3}Experimental Networks}{4}{}%
|
||||
\contentsline {section}{\numberline {4}Centralities and their Applications to Compliance Graphs}{5}{}%
|
||||
\contentsline {subsection}{\numberline {4.1}Introduction}{5}{}%
|
||||
\contentsline {subsection}{\numberline {4.2}Degree}{5}{}%
|
||||
\contentsline {subsection}{\numberline {4.3}Betweenness}{5}{}%
|
||||
\contentsline {subsection}{\numberline {4.4}Katz}{6}{}%
|
||||
\contentsline {subsection}{\numberline {4.5}K-Path Edge}{7}{}%
|
||||
\contentsline {subsection}{\numberline {4.6}Adapted Page Rank}{7}{}%
|
||||
\contentsline {section}{\numberline {5}Transitive Closure}{8}{}%
|
||||
\contentsline {subsection}{\numberline {5.1}Introduction and Application}{8}{}%
|
||||
\contentsline {section}{\numberline {6}Dominant Tree}{9}{}%
|
||||
\contentsline {subsection}{\numberline {6.1}Introduction and Application}{9}{}%
|
||||
\contentsline {section}{\numberline {7}Results and Result Analysis}{10}{}%
|
||||
\contentsline {subsection}{\numberline {7.1}HIPAA Network}{10}{}%
|
||||
\contentsline {subsection}{\numberline {7.2}PCI DSS Network}{10}{}%
|
||||
\contentsline {section}{\numberline {8}Conclusions and Future Work}{10}{}%
|
||||
\contentsline {section}{Bibliography}{15}{}%
|
||||
\contentsline {section}{\numberline {A}HIPAA Results}{17}{}%
|
||||
\contentsline {section}{\numberline {B}PCI DSS Results}{21}{}%
|
||||
\contentsline {section}{\numberline {1}Introduction}{2}{section.1}%
|
||||
\contentsline {subsection}{\numberline {1.1}Attack Graphs}{2}{subsection.1.1}%
|
||||
\contentsline {subsection}{\numberline {1.2}Compliance Graphs}{2}{subsection.1.2}%
|
||||
\contentsline {subsection}{\numberline {1.3}Difficulties of Compliance Graph Analysis}{3}{subsection.1.3}%
|
||||
\contentsline {section}{\numberline {2}Related Works}{3}{section.2}%
|
||||
\contentsline {section}{\numberline {3}Experimental Networks}{4}{section.3}%
|
||||
\contentsline {section}{\numberline {4}Centralities and their Applications to Compliance Graphs}{5}{section.4}%
|
||||
\contentsline {subsection}{\numberline {4.1}Introduction}{5}{subsection.4.1}%
|
||||
\contentsline {subsection}{\numberline {4.2}Degree}{5}{subsection.4.2}%
|
||||
\contentsline {subsection}{\numberline {4.3}Betweenness}{5}{subsection.4.3}%
|
||||
\contentsline {subsection}{\numberline {4.4}Katz}{6}{subsection.4.4}%
|
||||
\contentsline {subsection}{\numberline {4.5}K-Path Edge}{7}{subsection.4.5}%
|
||||
\contentsline {subsection}{\numberline {4.6}Adapted Page Rank}{7}{subsection.4.6}%
|
||||
\contentsline {section}{\numberline {5}Transitive Closure}{8}{section.5}%
|
||||
\contentsline {subsection}{\numberline {5.1}Introduction and Application}{8}{subsection.5.1}%
|
||||
\contentsline {section}{\numberline {6}Dominant Tree}{9}{section.6}%
|
||||
\contentsline {subsection}{\numberline {6.1}Introduction and Application}{9}{subsection.6.1}%
|
||||
\contentsline {section}{\numberline {7}Results and Result Analysis}{10}{section.7}%
|
||||
\contentsline {subsection}{\numberline {7.1}Results}{10}{subsection.7.1}%
|
||||
\contentsline {subsection}{\numberline {7.2}Result Analysis}{10}{subsection.7.2}%
|
||||
\contentsline {section}{\numberline {8}Conclusions and Future Work}{15}{section.8}%
|
||||
\contentsline {subsection}{\numberline {8.1}Conclusions}{15}{subsection.8.1}%
|
||||
\contentsline {subsection}{\numberline {8.2}Future Work}{16}{subsection.8.2}%
|
||||
\contentsline {section}{Bibliography}{17}{subsection.8.2}%
|
||||
\contentsline {section}{\numberline {A}HIPAA Results}{19}{appendix.A}%
|
||||
\contentsline {section}{\numberline {B}PCI DSS Results}{23}{appendix.B}%
|
||||
|
||||
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