\TUchapter{UTILITY EXTENSIONS TO THE RAGE ATTACK GRAPH GENERATOR}

\TUsection{Path Walking} \label{sec:PW}
\par Due to the large-scale nature of attack graphs, analysis can become difficult and time-consuming. With some graphs reaching millions of states and edges, 
analyzing the entire graph can be overwhelmingly complex. As a means of simplifying analysis, a potential strategy could be to consider only small subsets of
the graph at a time, rather than feeding the entire graph 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 output a subset of the graph that includes all possible paths from the
root state to a designated state. 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 separate subgraphs to all states in
the network that have qualities of $``compliance$\_$vio = true"$,$``compliance$\_$vios > 0"$, or any other quality that can be specified by the user. The automatic mode can produce multiple subgraphs simultaneously if multiple states contain the quality being examined, and these subgraphs can then be 
separately input into an analysis program. 

Figure \ref{fig:PW} demonstrates an output of the Path Walking feature when walking to state 14. In this figure, the primary observable feature is that the
graph was reduced from 16 states to 6 states, and from 32 edges to 12 edges. The amount of reduction from the original graph to the subset varies on the overall connectivity 
of the original attack graph.
\begin{figure}[htp]
    \includegraphics[width=\linewidth]{"./Chapter3_img/PW.png"}
    \vspace{.2truein} \centerline{}
        \caption{Path Walking to State 14}
        \label{fig:PW}
\end{figure}

\TUsection{Compound Operators} \label{sec:compops}
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. To expand on the types and complexities of graphs 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{cook_rage_2018} when designing the software architecture of RAGE 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 concern 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 task of approximating which exploits will be applicable and what absolute minimum
or maximum value bounds will be prior to generation is difficult, and not all values can be enumerated and stored into the hash table. As a result, real-time
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 assertion that the new 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.

Other changes involved updating classes (namely the Quality, EncodedQuality, ParameterizedQuality, NetworkState, and Keyvalue classes) to include a new member for the operator in question. Auxiliary functions related to this new member, such as prints and getters, were also added. In addition, preconditions were altered to include operator overloads to check the asset identifier, quality name, and quality values for the update process.

\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
visibly 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 the PostgreSQL database 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 a node has, 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}\label{sec:db-stor}
\TUsubsection{Memory Constraint Difficulties}
Previous works with RAGE have been designed around maximizing performance to limit the longer runtime caused by the state space explosion, such as the works seen by the authors of \cite{cook_rage_2018},
\cite{li_concurrency_2019}, and \cite{li_combining_2019}. To this end, the output graph is contained in memory during the generation process to minimize disk writing and reading. This also allows for leveraging the
performance benefits of memory operations, since graph computation relies less on processor speed and more on data dependency complexity, parallelism coarseness, and memory access time
 \cite{zhang_boosting_2017}, \cite{ainsworth_graph_2016}, \cite{berry_graph_2007}. The author of \cite{cook_rage_2018} does incorporate PostgreSQL as an initial and final storage mechanism to write the starting and resulting
 graph information, but no intermediate storage is otherwise conducted.
 
 While the design decision to not use intermediate storage maximizes performance for graph generation, it does suffer from a few complications. When generating large graphs, the system runs the risk 
 of running out of memory. This typically does not occur when generation is conducted on small graphs, and is especially true when relatively small graphs are generated on an HPC 
 system with substantial amounts of memory. However, when running on local systems or when the graph is large, memory can quickly be depleted due to state space explosion. The memory depletion is due to two primary
 memory consumption points: the frontier which contains all of the states that still need to be explored, and the graph instance which holds all of the states and their information,
 as well as all of the edges.

 The frontier quickly becomes a problem point with large graphs that have a large height value, and contain many layers before reaching leaf nodes. During the generation process, RAGE works on a Breadth-First Search approach, and new states
 are continuously discovered each time a state from the frontier is explored. In almost all cases, this means that for every state that is removed from the frontier, several more are added, leading to an ever-growing
 frontier that can not be adequately reduced for large networks. Simultaneously, the graph instance continues to grow as states are explored. When the network contains numerous assets, each with their own large sets of 
 qualities, the size of each state becomes noticeably larger. With some graphs containing millions of nodes and billions of edges like those mentioned by the authors of \cite{zhang_boosting_2017}, it becomes increasingly
 unlikely that the graph can be fully contained within system memory.

 \TUsubsection{Maximizing Performance with Intermediate Database Storage}
 Rather than a static implementation of storing to the database on disk at a set interval or a set size, the goal was to dynamically store to the database only when necessary. This would allow for proper utilization of systems with greater memory, and would reduce fine-tuning of a maximum size variable before database writes on different systems. Since there is an associated cost with preparing
 the writes to disk, the communication cost across nodes, the writing to disk itself, and a cost for retrieving items from disk, it is desirable to store as much in memory for as long as possible and only write when necessary. When 
 running RAGE, a new argument can be passed \textit{(-a $<$double$>$)} to specify the amount of memory the tool should use before writing to disk. This argument is a value between 0 and 0.99 to specify a percentage.
 This double is immediately reduced by 10\%. For instance, if 0.6 is passed, it is immediately reduced to 0.5. This acts as a buffer for PostgreSQL. Since queries will consume a variable amount of memory through parsing or preparation,
 an additional 10\% is saved as a precaution. This can be changed later as needed or desired for future optimizations. Specific to the graph data, the statement is made that the frontier is allowed to consume half of the allocated memory,
 and that the graph instance is allowed to consume the other half.

 To decide when to store to the database instead of memory, two separate checks are made. The first check is for the frontier. If the size of the frontier consumes equal to or more than the allowed allocated memory, then all new states
 are stored into a new table in the database called “unexplored states”. Each new state from this point forward is stored in the table, regardless of if room is freed in the frontier. This is to ensure proper ordering of the FIFO queue.
 The only time new states are stored directly into the frontier is when the unexplored states table is empty. Once the frontier has been completely emptied, new states are then pulled from the database into the frontier. To pull from
 the database, the parent loop for the generator process has been altered. Instead of a while loop for when the frontier is not empty, it has been adjusted to when the frontier is not empty or the unexplored states table is not empty. Due
 to C++ using short-circuit evaluation where the first argument is completely evaluated before processing the second, some performance is gained. The performance gained is due to not having to pass a SQL statement to disk to check the size of the unexplored states table unless the frontier is empty. The original generation design stored new states
 into the frontier during the critical section to avoid testing on already-explored states. To follow this design decision, writing new states to the database is also performed during the critical section.

 For the graph instance, a check in the critical section determines if the size of the graph instance consumes more than its allocated share of the memory. If it does, the edges, network states, and network state items are written to the database,
 and are then removed from memory.

 However, a new issue arose with database storage. The original design was to save staging, preparation, and communication cost by writing all the data in one query (as in, writing all of the network states in one query, all the network
 state items in one query, and all the edges in one query). While this was best option in terms of performance, it was also not scalable. Building the SQL queries themselves quickly began depleting the already constrained memory with large storage
 requests. As a result, the storage process would consume too much memory and crash the generator tool. To combat this, all queries had to be broken up into multiple queries. As previously mentioned, an extra 10\% buffer was saved 
 for the storage process. SQL query strings are now built until they consume the 10\% buffer, where they are then processed by PostgreSQL, cleared, and the query building process resumes.

 \TUsubsection{Portability}
 The intermediate database storage is greatly advantageous in increasing the portability of RAGE across various systems, while still allowing for performance benefits. By allowing for a user-defined argument, users can safely assign
 a value that allows for other processes and for the host OS to continue their workloads. While the ``total memory" component currently utilizes the Linux \textit{sysconf()} function, this is not rigid and is easily adjustable. When 
 working on a High-Performance Computing cluster, using this function could lead to difficulties since multiple users may be working on the same nodes, which prevents RAGE from fully using all system memory. This could be prevented 
 by using a job scheduler argument such as Slurm's ``--exclusive" option, but this may not be desirable. Instead, a user could pass in the amount of total memory to use (and can be reused from a job scheduler's memory allocation
 request option), and the intermediate database storage process would function in the same fashion.


\TUsection{Relational Operators} \label{sec:relops}
As discussed in Section \ref{sec:compops}, many of the graphs previously generated by RAGE comprise of states with an established set of qualities and values. These typically have included $``compliance$\_$vio=true/false"$,
$``root=true/false"$, or other general $``true/false"$ values or $``version=X"$ qualities. To further expand the dynamism of graph generation, it is important to distinguish when a quality has a value that satisfies a
relational comparison to an exploit. An example application for attack graphs can be seen through CVE-2019-10747, where "set-value is vulnerable to Prototype Pollution in versions lower than 3.0.1" \cite{CVE-2019-10747}. An example compliance graph application using the aforementioned car example can be seen in the Toyota Corolla Maintenance Schedule, which states an engine coolant replacement should be conducted after 24,000 miles. Prior to the implementation
of relational operators, to determine whether this exploit was applicable to a network state, multiple exploit qualities must be enumerated for all versions prior to 3.0.1. This would mean that the exploit needed to check if 
\textit{version=3.0.0}, or \textit{version=2.0.0}, or \textit{version=1.0.0}, or \textit{version=0.4.3}, etc. For the compliance graph exploit check, this could lead to even worse scaling where checks needed to be conducted at a much more granular level like \textit{engine$\_$coolant$\_$miles=24001}, or \textit{engine$\_$coolant$\_$miles=24002}, or \textit{engine$\_$coolant$\_$miles=24003}, etc. This becomes increasingly tedious when there are many checks to perform, and this not only reduces readability, but is also more
prone to human error when creating the exploit files. Relational operators work to alleviate these difficulties.

To implement the relational operators, operator overloads were placed into the Quality class. At the time of writing, the following are implemented: $==$, $<$, $>$, $\leq$, $\geq$. However, these operators do not take up room in the 
encoding scheme, so additional operators can be freely implemented as needed. The overloads ensure that the Quality asset IDs and Quality names match, and then compares the Quality values based on the operator in question.
