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Work}{6}{section.8}\protected@file@percent } -\@writefile{toc}{\contentsline {subsection}{\numberline {\mbox {VIII-A}}Conclusions}{6}{subsection.8.1}\protected@file@percent } \bibdata{Bibliography} -\bibcite{phillips_graph-based_1998}{1} -\bibcite{schneier_modeling_1999}{2} -\bibcite{j_hale_compliance_nodate}{3} -\bibcite{baloyi_guidelines_2019}{4} -\bibcite{allman_complying_2006}{5} -\bibcite{newman2010networks}{6} -\bibcite{Mieghem2018DirectedGA}{7} -\bibcite{10.1145/3491257}{8} -\bibcite{Guo2017HermitianAM}{9} -\bibcite{Brualdi2010SpectraOD}{10} -\bibcite{noauthor_health_1996}{11} -\bibcite{PCI}{12} -\bibcite{PMID:30064421}{13} -\bibcite{Katz}{14} -\bibcite{K_Path_Edge}{15} -\bibcite{PageRank}{16} -\bibcite{Adapted_PageRank}{17} -\bibcite{li_combining_2019}{18} -\bibcite{zeng_cyber_2017}{19} -\bibcite{dominance}{20} +\bibcite{j_hale_compliance_nodate}{1} +\bibcite{baloyi_guidelines_2019}{2} +\bibcite{allman_complying_2006}{3} +\bibcite{newman2010networks}{4} +\bibcite{Mieghem2018DirectedGA}{5} +\bibcite{10.1145/3491257}{6} +\bibcite{Guo2017HermitianAM}{7} +\bibcite{Brualdi2010SpectraOD}{8} +\bibcite{noauthor_health_1996}{9} +\bibcite{PCI}{10} +\bibcite{PMID:30064421}{11} +\bibcite{Katz}{12} +\bibcite{K_Path_Edge}{13} +\bibcite{PageRank}{14} +\bibcite{Adapted_PageRank}{15} +\bibcite{li_combining_2019}{16} +\bibcite{zeng_cyber_2017}{17} +\bibcite{dominance}{18} \bibstyle{ieeetr} +\@writefile{toc}{\contentsline {section}{\numberline {VIII}Conclusions and Future Work}{7}{section.8}\protected@file@percent } +\@writefile{toc}{\contentsline {subsection}{\numberline {\mbox {VIII-A}}Conclusions}{7}{subsection.8.1}\protected@file@percent } \@writefile{toc}{\contentsline {subsection}{\numberline {\mbox {VIII-B}}Future Work}{7}{subsection.8.2}\protected@file@percent } \@writefile{toc}{\contentsline {section}{Bibliography}{7}{subsection.8.2}\protected@file@percent } \@writefile{toc}{\contentsline {section}{References}{7}{section*.4}\protected@file@percent } diff --git a/Schrick-Noah_CS-7863_Final-Report.bbl b/Schrick-Noah_CS-7863_Final-Report.bbl index 081a1c4..8852ebd 100644 --- a/Schrick-Noah_CS-7863_Final-Report.bbl +++ b/Schrick-Noah_CS-7863_Final-Report.bbl @@ -1,15 +1,5 @@ \begin{thebibliography}{10} -\bibitem{phillips_graph-based_1998} -C.~Phillips and L.~P. Swiler, ``A graph-based system for network-vulnerability - analysis,'' {\em Proceedings New Security Paradigms Workshop}, vol.~Part - F1292, pp.~71--79, 1998. -\newblock doi: 10.1145/310889.310919. - -\bibitem{schneier_modeling_1999} -B.~Schneier, ``Modeling {Security} {Threats},'' {\em Dr. Dobb's Journal}, 1999. -\newblock vol. 24, no.12. - \bibitem{j_hale_compliance_nodate} {J. Hale}, P.~Hawrylak, and M.~Papa, ``Compliance {Method} for a {Cyber}-{Physical} {System}.'' diff --git a/Schrick-Noah_CS-7863_Final-Report.blg b/Schrick-Noah_CS-7863_Final-Report.blg index 5fa8b3f..c0dcbfc 100644 --- a/Schrick-Noah_CS-7863_Final-Report.blg +++ b/Schrick-Noah_CS-7863_Final-Report.blg @@ -6,45 +6,45 @@ A level-1 auxiliary file: Appendices.aux Database file #1: Bibliography.bib Warning--empty booktitle in Mieghem2018DirectedGA Warning--empty journal in zeng_cyber_2017 -You've used 20 entries, +You've used 18 entries, 1876 wiz_defined-function locations, - 601 strings with 7015 characters, -and the built_in function-call counts, 4391 in all, are: -= -- 431 -> -- 153 + 588 strings with 6705 characters, +and the built_in function-call counts, 3949 in all, are: += -- 382 +> -- 141 < -- 0 -+ -- 61 -- -- 41 -* -- 281 -:= -- 628 -add.period$ -- 26 -call.type$ -- 20 -change.case$ -- 19 ++ -- 56 +- -- 38 +* -- 255 +:= -- 563 +add.period$ -- 22 +call.type$ -- 18 +change.case$ -- 17 chr.to.int$ -- 0 -cite$ -- 22 -duplicate$ -- 242 -empty$ -- 449 -format.name$ -- 41 -if$ -- 1088 +cite$ -- 20 +duplicate$ -- 218 +empty$ -- 405 +format.name$ -- 38 +if$ -- 979 int.to.chr$ -- 0 -int.to.str$ -- 20 -missing$ -- 18 -newline$ -- 71 -num.names$ -- 19 -pop$ -- 78 +int.to.str$ -- 18 +missing$ -- 16 +newline$ -- 63 +num.names$ -- 17 +pop$ -- 74 preamble$ -- 1 purify$ -- 0 quote$ -- 0 -skip$ -- 147 +skip$ -- 134 stack$ -- 0 -substring$ -- 198 -swap$ -- 85 +substring$ -- 174 +swap$ -- 77 text.length$ -- 0 text.prefix$ -- 0 top$ -- 0 type$ -- 0 warning$ -- 2 -while$ -- 35 -width$ -- 22 -write$ -- 193 +while$ -- 30 +width$ -- 20 +write$ -- 171 (There were 2 warnings) diff --git a/Schrick-Noah_CS-7863_Final-Report.log b/Schrick-Noah_CS-7863_Final-Report.log index deed08f..34a645c 100644 --- a/Schrick-Noah_CS-7863_Final-Report.log +++ b/Schrick-Noah_CS-7863_Final-Report.log @@ -1,8 +1,8 @@ -This is pdfTeX, Version 3.141592653-2.6-1.40.24 (TeX Live 2022/Arch Linux) (preloaded format=pdflatex 2022.11.8) 13 JAN 2023 13:56 +This is pdfTeX, Version 3.141592653-2.6-1.40.24 (TeX Live 2022/Arch Linux) (preloaded format=pdflatex 2022.11.8) 16 JAN 2023 14:55 entering extended mode restricted \write18 enabled. %&-line parsing enabled. -**Schrick-Noah_CS-7863_Final-Report +**Schrick-Noah_CS-7863_Final-Report.tex (./Schrick-Noah_CS-7863_Final-Report.tex LaTeX2e <2021-11-15> patch level 1 L3 programming layer <2022-04-10> @@ -592,148 +592,135 @@ LaTeX Font Info: Trying to load font information for U+dsrom on input line 1 (/usr/share/texmf-dist/tex/latex/doublestroke/Udsrom.fd File: Udsrom.fd 1995/08/01 v0.1 Double stroke roman font definitions ) [3] -LaTeX Font Info: External font `cmex10' loaded for size -(Font) <8> on input line 166. -LaTeX Font Info: External font `cmex10' loaded for size -(Font) <6> on input line 166. +<./images/TC.png, id=183, 378.41376pt x 522.95375pt> +File: ./images/TC.png Graphic file (type png) + +Package pdftex.def Info: ./images/TC.png used on input line 170. +(pdftex.def) Requested size: 227.05pt x 313.77466pt. +<./images/dom_net.png, id=186, 319.1925pt x 432.61626pt> +File: ./images/dom_net.png Graphic file (type png) + +Package pdftex.def Info: ./images/dom_net.png used on input line 186. +(pdftex.def) Requested size: 191.51697pt x 259.57176pt. +<./images/dom_tree.png, id=187, 352.31625pt x 312.16624pt> +File: ./images/dom_tree.png Graphic file (type png) + +Package pdftex.def Info: ./images/dom_tree.png used on input line 193. +(pdftex.def) Requested size: 211.39137pt x 187.3012pt. -Overfull \hbox (28.88863pt too wide) in paragraph at lines 166--166 -[][][][]\OT1/ptm/m/n/8 Image origin can be located at: https://commons.wikimedi -a.org/wiki/File:Transitive- - 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LaTeX Warning: No positions in optional float specifier. - Default added (so using `tbp') on input line 335. + Default added (so using `tbp') on input line 338. -Underfull \hbox (badness 10000) in paragraph at lines 369--370 +Underfull \hbox (badness 10000) in paragraph at lines 372--373 []\OT1/ptm/m/n/10 When viewing the results of the car networks, [] -Underfull \hbox (badness 1997) in paragraph at lines 369--370 +Underfull \hbox (badness 1997) in paragraph at lines 372--373 \OT1/ptm/m/n/10 based on additional metrics, such as severity, cost, or [] - -Underfull \hbox (badness 3428) in paragraph at lines 371--372 +[5 <./images/dom_net.png> <./images/dom_tree.png>] +Underfull \hbox (badness 3428) in paragraph at lines 374--375 \OT1/ptm/m/n/10 their original compliance graph rankings. 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PDF statistics: - 332 PDF objects out of 1000 (max. 8388607) - 288 compressed objects within 3 object streams - 85 named destinations out of 1000 (max. 500000) - 224 words of extra memory for PDF output out of 10000 (max. 10000000) + 322 PDF objects out of 1000 (max. 8388607) + 276 compressed objects within 3 object streams + 79 named destinations out of 1000 (max. 500000) + 216 words of extra memory for PDF output out of 10000 (max. 10000000) diff --git a/Schrick-Noah_CS-7863_Final-Report.pdf b/Schrick-Noah_CS-7863_Final-Report.pdf index ee3e043..338ca9f 100644 Binary files a/Schrick-Noah_CS-7863_Final-Report.pdf and b/Schrick-Noah_CS-7863_Final-Report.pdf differ diff --git a/Schrick-Noah_CS-7863_Final-Report.tex b/Schrick-Noah_CS-7863_Final-Report.tex index b71fd12..2052701 100644 --- a/Schrick-Noah_CS-7863_Final-Report.tex +++ b/Schrick-Noah_CS-7863_Final-Report.tex @@ -163,11 +163,12 @@ For compliance graphs, the Adapted Page Rank algorithm is useful for a few reaso \section{Transitive Closure} \subsection{Introduction and Application} -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} \footnote{Image origin can be located at: https://commons.wikimedia.org/wiki/File:Transitive-closure.svg, and this image has been licensed under the terms of the GNU Free Documentation License.} 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 +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 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}. \begin{figure}[htp] - \includegraphics[width=\linewidth]{"./images/Transitive-closure.png"} + \includegraphics[scale=0.6]{"./images/TC.png"} + \centering \vspace{.2truein} \centerline{} \caption{Example of Transitive Closure} \label{fig:TC} @@ -181,17 +182,19 @@ Dominance, as initially introduced by the author of \cite{dominance} in terms of 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. -\begin{figure}[htp] \label{fig:preDtree} - \includegraphics[width=\linewidth]{"./images/pre-Dtree.png"} +\begin{figure}[htp] + \includegraphics[scale=0.6]{"./images/dom_net.png"} + \centering \vspace{.2truein} \centerline{} - \caption[]{Example Network for Illustrating Dominance \footnote{Image origin can be located at: https://commons.wikimedia.org/wiki/File:Dominator$\_$control$\_$flow$\_$graph.svg, and this image has been released into the public domain for use for any purpose, unless such conditions are required by law.}} + \caption{Example Network for Illustrating Dominance}\label{fig:domNet} \end{figure} \begin{figure}[htp] - \includegraphics[width=\linewidth]{"./images/post-Dtree.png"} + \includegraphics[scale=0.6]{"./images/dom_tree.png"} + \centering \vspace{.2truein} \centerline{} - \caption[]{Dominant Tree Derived from the Network Displayed in Figure 2 \footnote{Image origin can be located at: https://commons.wikimedia.org/wiki/File:Dominator$\_$tree.svg, and this image has been released into the public domain for use for any purpose, unless such conditions are required by law.}} - \label{fig:post-Dtree} + \caption{Dominant Tree Derived from the Network Displayed in Figure \ref{fig:domNet}}\label{fig:domTree} + \end{figure} 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}. diff --git a/Schrick-Noah_Supplemental.tex b/Schrick-Noah_Supplemental.tex new file mode 100644 index 0000000..e69de29 diff --git a/images/TC.drawio b/images/TC.drawio new file mode 100644 index 0000000..0b488f2 --- /dev/null +++ b/images/TC.drawio @@ -0,0 +1 @@ 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 \ No newline at end of file diff --git a/images/TC.png b/images/TC.png new file mode 100644 index 0000000..cb93012 Binary files /dev/null and b/images/TC.png differ diff --git a/images/Transitive-closure.png b/images/Transitive-closure.png deleted file mode 100644 index 2bf1420..0000000 Binary files a/images/Transitive-closure.png and /dev/null differ diff --git a/images/dom_net.drawio b/images/dom_net.drawio new file mode 100644 index 0000000..bf1a6ff --- /dev/null +++ b/images/dom_net.drawio @@ -0,0 +1 @@ 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 \ No newline at end of file diff --git a/images/dom_net.png b/images/dom_net.png new file mode 100644 index 0000000..f73b650 Binary files /dev/null and b/images/dom_net.png differ diff --git a/images/dom_tree.drawio b/images/dom_tree.drawio new file mode 100644 index 0000000..b025fbc --- /dev/null +++ b/images/dom_tree.drawio @@ -0,0 +1 @@ + \ No newline at end of file diff --git a/images/dom_tree.png b/images/dom_tree.png new file mode 100644 index 0000000..c87fdf4 Binary files /dev/null and b/images/dom_tree.png differ diff --git a/images/post-Dtree.png b/images/post-Dtree.png deleted file mode 100644 index 9f19207..0000000 Binary files a/images/post-Dtree.png and /dev/null differ diff --git a/images/pre-Dtree.png b/images/pre-Dtree.png deleted file mode 100644 index 6c7f2c5..0000000 Binary files a/images/pre-Dtree.png and /dev/null differ