Adding images to manuscript; adding new analysis blurb; adding normalization commentary to psql section
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\newlabel{fig:non-sync_ex}{{1}{2}{A network without Synchronous Firing generating infeasible states}{figure.1}{}}
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\citation{cook_rage_2018}
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\citation{louthan_hybrid_2011}
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\citation{nichols_2018}
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\citation{cook_rage_2018}
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\citation{nichols_2018}
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\citation{cook_rage_2018}
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\citation{cook_rage_2018}
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\bibdata{Bibliography}
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\bibcite{phillips_graph-based_1998}{1}
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\bibcite{schneier_modeling_1999}{2}
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\bibcite{cook_rage_2018}{12}
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\bibcite{nichols_2018}{13}
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\bibstyle{ieeetr}
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[]\OT1/ptm/m/n/10 Many of the graphs previously generated by RAGE
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@ -139,7 +139,7 @@ This new token also required changes to the processing of the ``exploit" keyword
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\subsection{PostgreSQL}
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As seen in Figure \ref{fig:bison-flex}, Bison and Flex feed into the Model Database. With the addition of a new group identifier and the group keyword, minor alterations were needed to ensure compatibility with the PostgreSQL database.
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One adjustment was to alter the exploit table in the SQL schema to include new columns of type ``TEXT". The second adjustment was to update the SQL builder functions. This included updating the related functions such as exploit creations, exploit parsing, database fetching, and SQL string builders to add additional room for the group identifier.
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One adjustment was to alter the exploit table in the SQL schema to include new columns of type ``TEXT". The second adjustment was to update the SQL builder functions. This included updating the related functions such as exploit creations, exploit parsing, database fetching, and SQL string builders to add additional room for the group identifier. Additional care was taken to ensure that the normalization form of the database was not altered. Before adding the group identifier to its appropriate table, additional checking was performed to ensure there would be no partial functional dependencies or transitive dependencies.
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\subsection{Compound Operators}
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Many of the graphs previously generated by RAGE comprise of states with features that can be fully enumerated. In many of these generated graphs, there was an established set of qualities that was 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.
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\end{table}
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\subsubsection{Results for a Grouped Environment}
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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.
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The environment and resulting graphs presented in Section \ref{sec:theo_res} 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.
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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 `comprehensive services", where a car would undergo multiple services simultaneously. These results are seen in Table \ref{table:Sync-Comp-Table} for the synchronous firing enabled generation, and Table \ref{table:Non-Sync-Comp-Table} for the non-synchronous firing generation.
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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 `comprehensive services", where a car would undergo multiple services simultaneously. With three services used, there are a total of three permutations: all three services are done individually, two services are performed simultaneously while the other is performed later, and all three services are performed simultaneously.
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For this set of examples, all compliance checks have the same time requirements. This work does not introduce any heuristics or methodologies for intentionally performing services early or late. If Service A was required no later than every 6 months, but Service B was required no later than every 8 months, then joining Service A and Service B together would either mean: 1. Service B was completed 2 months earlier than it needed to be, or 2. Service A was completed 2 months later than it needed to be. This was considered out of scope for this approach, but this is noted in the Future Works Section (Section \ref{sec:fw}).
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These results are seen in Table \ref{table:Sync-Comp-Table} for the synchronous firing enabled generation, and Table \ref{table:Non-Sync-Comp-Table} for the non-synchronous firing generation. The corresponding figures for the runtime can be seen in Figure \ref{fig:Comp-Sync-RT}, and the corresponding figures for state space can be seen in Figure \ref{fig:Comp-Sync-State}. It is noticeable that there is a state space reduction achieved through synchronous firing in this set of examples, along with a runtime improvement. When all three services were conjoined, synchronous firing provided a 5.09x speedup over non-synchronous firing. Using comprehensive services on their own also provided a reduction in state space and an improvement in runtime. When synchronous firing was enabled and comprehensive services were used, the total number of states could be reduced from 25,317 to 3,774, providing a a 6.7x reduction in state space solely from combining services.
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Leveraging comprehensive services with synchronous firing enables users to significantly reduce the size of the resulting attack or compliance graphs. Comprehensive services also enable users to introduce heuristics to analyze and identify optimal service plans for compliance, or attack mitigation strategies for attack graphs. Coupled with synchronous firing, analysis of these optimal plans can be performed quicker due to the inexistence of superfluous, unattainable states.
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\begin{table}[htp]
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\centering
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\label{table:Sync-Comp-Table}
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\end{table}
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\begin{figure}
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\centering
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\includegraphics[width=\linewidth]{"./images/Comp-Sync-Runtime-Bar.png"}
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\includegraphics[width=\linewidth]{"./images/Comp-Sync-Runtime.png"}
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\caption[Synchronous Firing on Runtime]{Bar Graph and Line Graph Representations of Synchronous Firing with Comprehensive Services on Runtime}
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\label{fig:Comp-Sync-RT}
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\end{figure}
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\begin{figure}
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\centering
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\includegraphics[width=\linewidth]{"./images/Comp-Sync-StateSpace-Bar.png"}
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\includegraphics[width=\linewidth]{"./images/Comp-Sync-StateSpace.png"}
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\caption{Bar Graph and Line Graph Representations of Synchronous Firing with Comprehensive Services on State Space}
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\label{fig:Comp-Sync-State}
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\end{figure}
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\begin{figure}[htp]
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\centering
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\includegraphics[width=\linewidth]{"./images/Comp-Sync_Speedup.png"}
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\vspace{.2truein} \centerline{}
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\caption{Speedup (Amdahl's) Obtained When Using Synchronous Firing with Comprehensive Services}
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\label{fig:Comp-Sync-Spd}
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\end{figure}
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\section{Future Works}
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\section{Future Works} \label{sec:fw}
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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.
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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.
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