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@book{Sham,
author = "Pak Sham",
title = "Statistics in Human Genetics",
publisher = "Arnold",
year = 1998,
}
@misc{Scot95,
author = "David W. Scott",
note = "Personal communication",
year = 1995,
}
@BOOK{Mathematica,
author = "Stephen Wolfram",
title = "The Mathematica Book",
publisher = "Cambridge University Press",
year = 1996,
@phdthesis{cookrage2018,
title = {{RAGE}: {The} {Rage} {Attack} {Graph} {Engine}},
author = {Cook, Kyle},
year = {2018},
file = {Kyle Cook Thesis:/home/noah/Zotero/storage/2SR28HM2/Kyle Cook Thesis.pdf:application/pdf},
}

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This is the first section of the introduction. For additional
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\TUchapter{THE SECOND CHAPTER}
\TUchapter{UTILITY EXTENSIONS TO THE RAGE ATTACK GRAPH GENERATOR}
\TUsection{First Heading}
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\TUsection{Path Walking}
\par Due to the large-scale nature of Attack Graphs, analysis can prove difficult and time-consuming. With some networks reaching millions of states and edges,
analyzing the entire network can be overwhelming complex. As a means of simplifying analysis, a potential strategy could be to consider only small subsets of
the network at a time, rather than feeding the entire network into an analysis algorithm. To aid in this effort, a Path Walking feature was implemented as a
separate program, and has two primary modes of usage. The goal of this feature is to provide a subset of the network that includes all possible paths from the
root node to a designated node. The first mode is a manual mode, where a user can input the desired state to walk to, and the program will output a separate
graph of all possible paths to the specified state. The second mode is an automatic mode, where the program will output seperate subgraphs to all states in
the network that have qualities of $``compliance$\_$vio = true"$ or $``compliance$\_$vios > 0"$. This often produces multiple subgraphs, that can then be
separately fed into an analysis program.
Lorem ipsum dolor sit amet, consectetur adipiscing elit. Integer luctus feugiat odio et fermentum. Etiam ut vulputate tellus. Aenean sed libero nec nibh gravida consequat eu vel diam. Nullam at accumsan purus. Nullam sit amet nulla et orci dapibus mollis. Etiam placerat, lacus eget venenatis bibendum, metus odio commodo nisi, sed scelerisque nulla odio vel nibh. Mauris vitae elementum turpis.
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\TUsection{Second Heading} Second section of the second chapter.
Figure \ref{fig:PW} demonstates an output of the Path Walking feature when walking to state 14. In this figure, the primary observable feature is that the
network was reduced from 16 states to 6 states, and 32 edges to 12 edges. The reduction from the original network to the subset varies on the overall connectivity
of the original Attack Graph, but the reduction can aid in simplifying the analysis process if only certain states of the network are to be analyzed.
\begin{figure}[htp]
\vspace{.2truein} \centerline{Normally a figure would go here.}
\caption{Title of the Second Figure}
\includegraphics[width=\linewidth]{"./Chapter3_img/PW.png"}
\vspace{.2truein} \centerline{}
\caption{Path Walking to State 14}
\label{fig:PW}
\end{figure}
\begin{table}[htp]
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\caption{Title of the Second Table}
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\TUsection{Compound Operators}
Many of the networks previously generated by RAGE compromise of states with features that can be fully enumerated. In many of the generated networks, there is an
established set of qualities that will be used, with an established set of values. These typically have included $``compliance$\_$vio=true/false"$,
$``root=true/false"$, or other general $``true/false"$ values or $``version=X"$ qualities. To expand on the types and complexities of networks that can be
generated, compound operators have been added to RAGE. When updating a state, rather than setting a quality to a specific value, the previous value can now
be modified by an amount specified through standard compound operators such as $\mathrel{+}=$, $\mathrel{-}=$, $\mathrel{*}=$, or $\mathrel{/}=$.
The work conducted by the author of \cite{cookrage2018} when designing the software architecture included specifications for a quality encoding scheme. As the
author discusses, qualities have four fields, which include the asset ID, attributes, operator, and value. The operator field is 4 bits, which allows for a total
of 16 operators. Since the only operator in use at the time was the $``\mathrel{=}"$ operator, the addition of four compound operators does not surpass the 16 operator limit,
and no encoding scheme changes were necessary. This also allows for additional compound operators to be incorporated in the future.
A few changes were necessary to allow for the addition of compound operators. Before the generation of an Attack Graph begins, all values are stored in a hash
table. For previous networks generated by RAGE, this was not a difficulty, since all values could be fully enumerated and all possible values were known. When
using compound operators however, not all values can be fully known. The concept of approximating which exploits will be applicable and what absolute minimum
or maximum values will be prior to generation is a difficult task, so not all values can be enumerated and stored into the hash table. As a result, on-the-fly
updates to the hash table needed to be added to the generator. The original key-value scheme for hash tables relied on utilizing the size of the hash table for
values. Since the order in which updates happen may not always remain consistent (and is especially true in distributed computing environments), it is possible
for states to receive different hash values with the original hashing scheme. To prevent this, the hashing scheme was adjusted so that the new value of the
compound operator is inserted into the hash table values if it was not found, rather than the size of the hash table. Previously, there was no safety check
for the hash table, so if the value was not found, the program would end execution. The assumption that this value can be inserted into the hash table is safe
to make, since compound operators are conducted on numeric values, and matches the numeric type of the hash table.
\TUsection{Color Coding}
As a visual aid for analysis purposes, color coding was another feature implemented as a postprocessing tool for RAGE. When viewing the output graph of RAGE, all states are
originally identical in appearance, apart from number of edges, edge IDs, and state IDs. To allow for visual differentiation, color coding can be enabled in the run script.
Color coding currently functions by working through the graph output text file, but it can be extended to read directly from Postgres instead. The feature scans through the
output file, and locates states that have $``compliance$\_$vios = X"$ (where \textit{X} is a number greater than 0), or $``compliance$\_$vio = true"$. For states that meet these
properties, the color coding feature will add a color to the graphviz DOT file through the $[color=COL]$ attribute for the given node, where \textit{COL} is assigned based on severity.
For this version of color coding, severity is determined by the total number of compliance violations, but future versions can alter the severity measure through alternative means.
Figure \ref{fig:CC} displays an example graph that leverages color coding to easily identify problem states.
\begin{figure}[htp]
\includegraphics[width=\linewidth]{"./Chapter3_img/CC.png"}
\vspace{.2truein} \centerline{}
\caption{Color Coding a Small Network Based on Violations}
\label{fig:CC}
\end{figure}
\TUsection{Intermediate Database Storage} Fourth section of the third chapter.
\TUsection{Relational Operators} Fifth section of the third chapter.

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\numofchapters=6 % number of chapters in the document
\lastchapter{Conclusions} % the title of the last numbered chapter
\numofchapters=7 % number of chapters in the document
\lastchapter{Conclusions and Future Works} % the title of the last numbered chapter
\numofabstractwords{29} % number of words in the abstract
%
@ -200,8 +201,13 @@ over the place.
% Main Body of Document
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\include{Chapter1.sample}
\include{Chapter2.sample}
\include{Chapter1}
\include{Chapter2}
\include{Chapter3}
\include{Chapter4}
\include{Chapter5}
\include{Chapter6}
\include{Chapter7}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% BIBLIOGRAPHY
@ -210,7 +216,7 @@ over the place.
\addtocontents{toc}{\protect{\hfill \ }}
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\bibliographyp
\bibliography{MyBibliography.sample}
\bibliography{Bibliography}
\bibliographystyle{plain}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@ -218,5 +224,5 @@ over the place.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\appendixpages % prepare for the generation of the appendices
\include{Appendices.sample}
\include{Appendices}
\end{document}

43
Schrick-Noah_MS-Thesis.toc
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@ -5,8 +5,45 @@
{\hfill \ }
\contentsline {section}{\hspace {-\parindent }ACKNOWLEDGEMENTS}{v}{}%
{\hfill \ }
\contentsline {section}{\hspace {-\parindent }TABLE OF CONTENTS}{vi}{}%
\contentsline {section}{\hspace {-\parindent }TABLE OF CONTENTS}{vii}{}%
{\hfill \ }
\contentsline {section}{\hspace {-\parindent }LIST OF TABLES}{vii}{}%
\contentsline {section}{\hspace {-\parindent }LIST OF TABLES}{viii}{}%
{\hfill \ }
\contentsline {section}{\hspace {-\parindent }LIST OF FIGURES}{viii}{}%
\contentsline {section}{\hspace {-\parindent }LIST OF FIGURES}{ix}{}%
\contentsline {chapter}{\numberline {CHAPTER 1: }{\bf \uppercase {INTRODUCTION}}}{1}{}%
\contentsline {section}{\numberline {1.1}\bf First Heading: The Introduction}{1}{}%
\contentsline {section}{\numberline {1.2}\bf Second Heading}{1}{}%
\contentsline {subsection}{\numberline {1.2.1}\it First Subheading}{1}{}%
\contentsline {subsection}{\numberline {1.2.2}\it Second Subheading}{1}{}%
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\contentsline {chapter}{\numberline {CHAPTER 2: }{\bf \uppercase {RELATED WORKS}}}{3}{}%
\contentsline {section}{\numberline {2.1}\bf First Heading}{3}{}%
\contentsline {section}{\numberline {2.2}\bf Second Heading}{4}{}%
\contentsline {chapter}{\numberline {CHAPTER 3: }{\bf \uppercase {UTILITY EXTENSIONS TO THE RAGE ATTACK GRAPH GENERATOR}}}{5}{}%
\contentsline {section}{\numberline {3.1}\bf Path Walking}{5}{}%
\contentsline {section}{\numberline {3.2}\bf Compound Operators}{6}{}%
\contentsline {section}{\numberline {3.3}\bf Color Coding}{7}{}%
\contentsline {section}{\numberline {3.4}\bf Intermediate Database Storage}{9}{}%
\contentsline {section}{\numberline {3.5}\bf Relational Operators}{9}{}%
\contentsline {chapter}{\numberline {CHAPTER 4: }{\bf \uppercase {SYNCHRONOUS FIRING}}}{10}{}%
\contentsline {section}{\numberline {4.1}\bf First Heading}{10}{}%
\contentsline {section}{\numberline {4.2}\bf Second Heading}{11}{}%
\contentsline {chapter}{\numberline {CHAPTER 5: }{\bf \uppercase {IMPLEMENTATION OF MESSAGE PASSING INTERFACE}}}{12}{}%
\contentsline {section}{\numberline {5.1}\bf Tasking Approach}{12}{}%
\contentsline {section}{\numberline {5.2}\bf Subgraphing Approach}{13}{}%
\contentsline {chapter}{\numberline {CHAPTER 6: }{\bf \uppercase {PERFORMANCE ANALYSIS}}}{14}{}%
\contentsline {section}{\numberline {6.1}\bf First Heading}{14}{}%
\contentsline {section}{\numberline {6.2}\bf Second Heading}{15}{}%
\contentsline {chapter}{\numberline {CHAPTER 7: }{\bf \uppercase {CONCLUSIONS AND FUTURE WORKS}}}{16}{}%
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{\hfill \ }
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{\hfill \ }
\contentsline {section}{\hspace {-\parindent }APPENDIX A:\ \ {\bf \uppercase {THE FIRST APPENDIX}} }{19}{}%
\contentsline {section}{\hspace {-\parindent }APPENDIX B:\ \ {\bf \uppercase {THE SECOND APPENDIX}} }{20}{}%
\contentsline {section}{\numberline {B.1}\bf A Heading in an Appendix}{20}{}%
\contentsline {subsection}{\numberline {B.1.1}\it A Subheading in an Appendix}{20}{}%
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21
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