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Fixing tables

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Noah L. Schrick 2022-10-04 18:47:48 -05:00
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5 changed files with 127 additions and 67 deletions
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Schrick-Noah_AG-CG-SyncFire.aux
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\bibdata{Bibliography} \bibdata{Bibliography}
\bibcite{phillips_graph-based_1998}{1} \bibcite{phillips_graph-based_1998}{1}
\bibcite{schneier_modeling_1999}{2} \bibcite{schneier_modeling_1999}{2}
@ -75,16 +84,6 @@
\bibcite{j_hale_compliance_nodate}{4} \bibcite{j_hale_compliance_nodate}{4}
\bibcite{baloyi_guidelines_2019}{5} \bibcite{baloyi_guidelines_2019}{5}
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\bibcite{cook_rage_2018}{12} \bibcite{cook_rage_2018}{12}
\bibcite{nichols_2018}{13} \bibcite{nichols_2018}{13}
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Schrick-Noah_AG-CG-SyncFire.tex
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@ -240,9 +240,9 @@ The compliance checks are as follows:
\subsubsection{Results for the Theoretical Environment} \label{sec:theo_res} \subsubsection{Results for the Theoretical Environment} \label{sec:theo_res}
Using the testing setup described in Section \ref{sec:test-platform} on the platform described at the beginning of Section \ref{sec:test-platform}, results were collected in regards to the effect of synchronous firing on both state space and runtime. There was also a collection of the graphs' edge to state ratio (E/S Ratio). These results can be seen in Figures \ref{fig:Sync-RT} and \ref{fig:Sync-State}. The respective tables are seen in Tables \ref{table:NS-Table} and \ref{table:S-Table}. Both figures show a decrease in the number of states and a decrease in the runtime when synchronous firing is utilized. Since synchronous firing prevents the generation of unattainable states, there is no meaningful information loss that occurs in the graphs generated with the synchronous firing feature. Since the resulting number of states was also reduced, there will be increased justification for the synchronous firing approach due to a reduced runtime for the analysis process. Figure \ref{fig:Sync-Spd} displays the speedup (according to Amdahl's Law) obtained when using synchronous firing instead of non-synchronous firing for identical setups. Using the testing setup described in Section \ref{sec:test-platform} on the platform described at the beginning of Section \ref{sec:test-platform}, results were collected in regards to the effect of synchronous firing on both state space and runtime. There was also a collection of the graphs' edge to state ratio (E/S Ratio). These results can be seen in Figures \ref{fig:Sync-RT} and \ref{fig:Sync-State}. The respective tables are seen in Tables \ref{table:NS-Table} and \ref{table:S-Table}. Both figures show a decrease in the number of states and a decrease in the runtime when synchronous firing is utilized. Since synchronous firing prevents the generation of unattainable states, there is no meaningful information loss that occurs in the graphs generated with the synchronous firing feature. Since the resulting number of states was also reduced, there will be increased justification for the synchronous firing approach due to a reduced runtime for the analysis process. Figure \ref{fig:Sync-Spd} displays the speedup (according to Amdahl's Law) obtained when using synchronous firing instead of non-synchronous firing for identical setups.
When examining the E/S ratio for the non-synchronous graphs, it is both expected and observed that the ratio slightly increases as the number of services increases. When more applicable exploits are used during the generation process, the number of permutations increases, which corresponds with the growing number of states and edges. However, the increase in the number of services also increases the relation between states and the new permutations. When examining the E/S Ratio for the non-synchronous graphs, it is both expected and observed that the ratio slightly increases as the number of services increases. When more applicable exploits are used during the generation process, the number of permutations increases, which corresponds with the growing number of states and edges. However, the increase in the number of services also increases the relation between states and the new permutations.
When comparing the E/S ratio for the non-synchronous graphs to the E/S ratio for the synchronous graphs, it is observed that the ratio does not remain constant. For example, for the 5 service case, the non-synchronous graph has an E/S ratio of 6.398, and the synchronous graph has an E/S ratio of 7.209. While the number of states and the number of edges is reduced when using synchronous firing, the ratio of edges to states is not necessarily constant or reduced. When comparing the E/S Ratio for the non-synchronous graphs to the E/S Ratio for the synchronous graphs, it is observed that the ratio does not remain constant. For example, for the 5 service case, the non-synchronous graph has an E/S Ratio of 6.398, and the synchronous graph has an E/S Ratio of 7.209. While the number of states and the number of edges is reduced when using synchronous firing, the ratio of edges to states is not necessarily constant or reduced.
\begin{figure} \begin{figure}
\centering \centering
@ -270,10 +270,13 @@ When comparing the E/S ratio for the non-synchronous graphs to the E/S ratio for
\begin{table}[htp] \begin{table}[htp]
\centering \centering
\begin{tabular}{|c|c|c|} \begin{tabular}{|c|c|c|c|}
\hline \hline
\multicolumn{3}{|c|}{Non-Synchronous Firing} \\ \hline \multicolumn{4}{|c|}{Non-Synchronous Firing} \\ \hline
\textbf{Number of Services} & \textbf{Number of States} & \textbf{Runtime (ms)} & \textbf{E/S Ratio} \\ \hline \textbf{Number of Services}
& \textbf{Number of States}
& \textbf{Runtime (ms)}
& \textbf{E/S Ratio} \\ \hline
1 & 37001 & 87366.65 & 5.484 \\ \hline 1 & 37001 & 87366.65 & 5.484 \\ \hline
2 & 46361 & 115929.97 & 5.595 \\ \hline 2 & 46361 & 115929.97 & 5.595 \\ \hline
3 & 72489 & 184634.34 & 5.590 \\ \hline 3 & 72489 & 184634.34 & 5.590 \\ \hline
@ -287,9 +290,9 @@ When comparing the E/S ratio for the non-synchronous graphs to the E/S ratio for
\begin{table}[htp] \begin{table}[htp]
\centering \centering
\begin{tabular}{|c|c|c|c|} \begin{tabular}{|c|c|c|c|c|}
\hline \hline
\multicolumn{4}{|c|}{Synchronous Firing} \\ \hline \multicolumn{5}{|c|}{Synchronous Firing} \\ \hline
\textbf{\begin{tabular}[c]{@{}c@{}}Number of \\ Services\end{tabular}} \textbf{\begin{tabular}[c]{@{}c@{}}Number of \\ Services\end{tabular}}
& \textbf{\begin{tabular}[c]{@{}c@{}}Number of \\ States\end{tabular}} & \textbf{\begin{tabular}[c]{@{}c@{}}Number of \\ States\end{tabular}}
& \textbf{\begin{tabular}[c]{@{}c@{}}Runtime\\ (ms)\end{tabular}} & \textbf{\begin{tabular}[c]{@{}c@{}}Runtime\\ (ms)\end{tabular}}
@ -310,29 +313,51 @@ When comparing the E/S ratio for the non-synchronous graphs to the E/S ratio for
\subsubsection{Results for a Grouped Environment} \subsubsection{Results for a Grouped Environment}
The environment and resulting graphs presented in Section \ref{sec:theo_results} depict the possible states of the two cars in compliance graph formats. While these graphs demonstrated accurate, exhaustive depictions of the cars and their compliance standings, they may not be realistic representations of the most likely outcomes. If a car was due for two compliance checks at the same time, it is unlikely that the car would be taken for one maintenance, returned to its original destination, then driven immediately back for maintenance, and finally to its original destination once more. The more realistic scenario is that the car is taken for maintenance, both services are performed at the same visit, and then the car is returned to its original destination. The environment and resulting graphs presented in Section \ref{sec:theo_results} depict the possible states of the two cars in compliance graph formats. While these graphs demonstrated accurate, exhaustive depictions of the cars and their compliance standings, they may not be realistic representations of the most likely outcomes. If a car was due for two compliance checks at the same time, it is unlikely that the car would be taken for one maintenance, returned to its original destination, then driven immediately back for maintenance, and finally to its original destination once more. The more realistic scenario is that the car is taken for maintenance, both services are performed at the same visit, and then the car is returned to its original destination.
Another set of graphs were generated using only the 3 service case. These services were for a driveshaft boot check, an AC filter change, and an oil change. This set of graphs used `super services", where a car would undergo multiple services simultaneously. These results are seen in Table Another set of graphs were generated using only the 3 service case. These services were for a driveshaft boot check, an AC filter change, and an oil change. This set of graphs used `super services", where a car would undergo multiple services simultaneously. These results are seen in Table \ref{table:Sync-Super-Table} for the synchronous firing enabled generation, and Table \ref{table:Non-Sync-Super-Table} for the non-synchronous firing generation.
\begin{table}[htp] \begin{table}[htp]
\centering \centering
\begin{tabular}{|c|c|c|} \begin{tabular}{|c|c|c|c|}
\hline \hline
\multicolumn{3}{|c|}{Super Services with Synchronous Firing} \\ \hline \multicolumn{4}{|c|}{Super Services with Synchronous Firing} \\ \hline
\textbf{Permutation} \textbf{Permutation}
& \textbf{Number of States} & \textbf{Number of States}
& \textbf{Runtime (ms)} & \textbf{Runtime (ms)}
& \textbf{E/S Ratio} \\ \hline & \textbf{E/S Ratio}
& & & \\ \hline \\ \hline
Non-Synchronous & & & \\ \hline All Disjoint & & & \\ \hline
\begin{tabular}[c]{@{}c@{}}Any Two Services, \\ One Disjoint\end{tabular}
& & & \\ \hline
All Three Services & & & \\ \hline
\end{tabular} \end{tabular}
\caption{Tabled Results for the Non-Synchronous Firing Testing} \caption{Tabled Results for the Super Services with Synchronous Firing}
\label{table:NS-Table} \label{table:Sync-Super-Table}
\end{table}
\begin{table}[htp]
\centering
\begin{tabular}{|c|c|c|c|}
\hline
\multicolumn{4}{|c|}{Super Services with Non-Synchronous Firing} \\ \hline
\textbf{Permutation}
& \textbf{Number of States}
& \textbf{Runtime (ms)}
& \textbf{E/S Ratio}
\\ \hline
All Disjoint & & & \\ \hline
\begin{tabular}[c]{@{}c@{}}Any Two Services, \\ One Disjoint\end{tabular}
& & & \\ \hline
All Three Services & & & \\ \hline
\end{tabular}
\caption{Tabled Results for the Super Services without Synchronous Firing}
\label{table:Non-Sync-Super-Table}
\end{table} \end{table}
\section{Future Works} \section{Future Works}
As seen and discussed in Section \ref{sec:inseparable}, when unattainable states are generated, there is a compounding effect. Each unattainable state is explored, and is likely to generate additional unattainable states. Future works include examining the effect of synchronous firing when more assets are utilized. It is hypothesized that the synchronous firing approach will lead to an increased runtime reduction and state space reduction due to the increased number of unattainable state permutations. This work had a limited number of assets, but generated upwards of 400,000 states due to repeated applications of the exploit set due to the services corresponding with the compliance graph. Future work could alter the test scenario to have a greater number of assets, and a standard set of exploits more akin to an attack graph. Other future works could include measuring the performance of synchronous firing when multiple groups of inseparable features are used. This work used a single group, but multiple groups be added to examine the performance of the feature. As seen and discussed in Section \ref{sec:inseparable}, when unattainable states are generated, there is a compounding effect. Each unattainable state is explored, and is likely to generate additional unattainable states. Future works include examining the effect of synchronous firing when more assets are utilized. It is hypothesized that the synchronous firing approach will lead to an increased runtime reduction and state space reduction due to the increased number of unattainable state permutations. This work had a limited number of assets, but generated upwards of 400,000 states due to repeated applications of the exploit set due to the services corresponding with the compliance graph. Future work could alter the test scenario to have a greater number of assets, and a standard set of exploits more akin to an attack graph. Other future works could include measuring the performance of synchronous firing when multiple groups of inseparable features are used. This work used a single group, but multiple groups be added to examine the performance of the feature.
Network science (degree) before and after Another avenue for future works would be to take a network science approach. There may be features of interest from examining the topology of the resulting graphs with and without synchronous firing. Various centrality metrics could be examined, as well as examining transformations such as dominant trees or transitive closures derived from the original graphs. Each approach could compare each graph when using or not using synchronous firing to determine if there are possible points of interest. Taking a network science approach could also examine and analyze the E/S Ratio differences between the graphs when using or not using synchronous firing, and attempt to provide further insight on what those differences mean in terms of usability of the graphs.
\section{Conclusion} \section{Conclusion}
This work implemented a state space explosion mitigation technique called synchronous firing. This feature is able to fire exploits simultaneously among a group of assets through a single state transition. By firing exploits across multiple assets, it is able to prevent the separation of features that should normally be inseparable (such as time), and successfully reduces the number of total states in the resulting attack or compliance graph. This feature does not alter the procedure of the generation process in a way that undermines the integrity of the resulting attack or compliance graph, and only groups assets through defined inseparable features. This feature is also toggleable, and the generation process seen in Figure \ref{fig:sync-fire} does not change if the feature is disabled. This feature successfully reduced the total number of states, reduced the runtime of the generation process, and can lead to a reduced analysis process due to a smaller resulting graph. This work implemented a state space explosion mitigation technique called synchronous firing. This feature is able to fire exploits simultaneously among a group of assets through a single state transition. By firing exploits across multiple assets, it is able to prevent the separation of features that should normally be inseparable (such as time), and successfully reduces the number of total states in the resulting attack or compliance graph. This feature does not alter the procedure of the generation process in a way that undermines the integrity of the resulting attack or compliance graph, and only groups assets through defined inseparable features. This feature is also toggleable, and the generation process seen in Figure \ref{fig:sync-fire} does not change if the feature is disabled. This feature successfully reduced the total number of states, reduced the runtime of the generation process, and can lead to a reduced analysis process due to a smaller resulting graph.