Additional intro work and experimental setup (num exploits) work

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Noah L. Schrick 2023-04-04 19:17:24 -05:00
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7 changed files with 477 additions and 382 deletions

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file = {Attack Intent Analysis Method Based on Attack Path Graph:/home/noah/Zotero/storage/WDJ69WSH/Attack Intent Analysis Method Based on Attack Path Graph.pdf:application/pdf},
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@phdthesis{cook_rage_2018,
@mastersthesis{cook_rage_2018,
title = {{RAGE}: {The} {Rage} {Attack} {Graph} {Engine}},
author = {Cook, Kyle},
school = {The {University} of {Tulsa}},

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\bibitem{9678822}
N.~Dakhno, O.~Leshchenko, Y.~Kravchenko, A.~Dudnik, O.~Trush, and
V.~Khankishiev, ``Dynamic model of the spread of viruses in a computer
network using differential equations,'' in {\em 2021 IEEE 3rd International
Conference on Advanced Trends in Information Theory (ATIT)}, pp.~111--115,
2021.
\bibitem{7993827}
M.~Kwon, J.~Kwon, B.~Park, and H.~Park, ``An architecture of iptv networks
based on network coding,'' in {\em 2017 Ninth International Conference on
Ubiquitous and Future Networks (ICUFN)}, pp.~462--464, 2017.
\bibitem{8652334}
X.~Bai, M.~Liang, and S.~Zhu, ``A new routing scheme for large-scale computer
network,'' in {\em 2018 14th IEEE International Conference on Signal
Processing (ICSP)}, pp.~1019--1023, 2018.
\bibitem{baloyi_guidelines_2019}
N.~Baloyi and P.~Kotzé, ``Guidelines for {Data} {Privacy} {Compliance}: {A}
{Focus} on {Cyberphysical} {Systems} and {Internet} of {Things},'' in {\em
{SAICSIT} '19: {Proceedings} of the {South} {African} {Institute} of
{Computer} {Scientists} and {Information} {Technologists} 2019}, (Skukuza
South Africa), Association for Computing Machinery, 2019.
\bibitem{allman_complying_2006}
E.~Allman, ``Complying with {Compliance}: {Blowing} it off is not an option.,''
{\em ACM Queue}, vol.~4, no.~7, 2006.
\bibitem{j_hale_compliance_nodate}
{J. Hale}, P.~Hawrylak, and M.~Papa, ``Compliance {Method} for a
{Cyber}-{Physical} {System}.''
\newblock U.S. Patent Number 9,471,789, Oct. 18, 2016.
\bibitem{ou_scalable_2006}
X.~Ou, W.~F. Boyer, and M.~A. Mcqueen, ``A {Scalable} {Approach} to {Attack}
{Graph} {Generation},'' {\em CCS '06: Proceedings of the 13th ACM conference
on Computer and communications security}, pp.~336--345, 2006.
\bibitem{CPSIOT}
A.~T. Al~Ghazo, M.~Ibrahim, H.~Ren, and R.~Kumar, ``A2g2v: Automated attack
graph generator and visualizer,'' in {\em Proceedings of the 1st ACM MobiHoc
Workshop on Mobile IoT Sensing, Security, and Privacy}, Mobile IoT SSP'18,
(New York, NY, USA), Association for Computing Machinery, 2018.
\bibitem{ming_jo}
M.~Li, P.~Hawrylak, and J.~Hale, ``Strategies for practical hybrid attack graph
generation and analysis,'' {\em Digital Threats}, oct 2021.
\bibitem{cook_rage_2018}
K.~Cook, ``{RAGE}: {The} {Rage} {Attack} {Graph} {Engine},'' Master's thesis,
The {University} of {Tulsa}, 2018.
\bibitem{pacheco_introduction_2011}
P.~Pacheco, {\em An {Introduction} to {Parallel} {Programming}}.
\newblock Morgan Kaufmann, print~ed., 2011.
@ -60,11 +112,6 @@ J.~Siek, L.-Q. Lee, and A.~Lumsdaine, ``The {Boost} {Graph} {Library}, vers.
\newblock
{https://www.boost.org/doc/libs/1$\_$75$\_$0/libs/graph/doc/index.html}.
\bibitem{ou_scalable_2006}
X.~Ou, W.~F. Boyer, and M.~A. Mcqueen, ``A {Scalable} {Approach} to {Attack}
{Graph} {Generation},'' {\em CCS '06: Proceedings of the 13th ACM conference
on Computer and communications security}, pp.~336--345, 2006.
\bibitem{cook_scalable_2016}
K.~Cook, T.~Shaw, J.~Hale, and P.~Hawrylak, ``Scalable attack graph
generation,'' {\em Proceedings of the 11th Annual Cyber and Information

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@ -55,10 +55,11 @@ Attack Graph; Compliance Graph; MPI; High-Performance Computing; Cybersecurity;
As the size of computer networks continues to grow, cybersecurity analysts are tasked to mitigate risk with increasing difficulty. The authors of \cite{9678822}, \cite{7993827}, and \cite{8652334} discuss how the rapidly expanding network sizes bring about drastic changes along with the requirement to shift and refocus to accommodate the expansion. This includes presenting novel architectures to support the ever-growing IPTV networks, examinations of computer viruses through epidemiology modeling, and evaluations of new routing schemes. In recent years, a greater usage of cyber-physical systems and a growing adoption of the Internet of Things (IoT) also contributes to an increased need for risk mitigation across varying types of networks, as discussed by the authors of \cite{baloyi_guidelines_2019}, \cite{allman_complying_2006}, and \cite{j_hale_compliance_nodate}. One approach for analyzing the large number of hosts and growing lists of exploits is to automate the generation of attack or compliance graphs for later use. Attack and compliance graphs are directed acyclic graphs (DAGs) that typically represent one or many systems as nodes in a graph, and any changes that could be made to them as edges. The automation of these graphs has been used and presented by authors such as \cite{ou_scalable_2006}, \cite{CPSIOT}, and \cite{ming_jo}. The graph generators will take system information and exploits to check for as input, and will exhaustively draw all possible ways that the systems may be at risk of a cybersecurity attack or at risk of violating a compliance regulation or mandate. If a system is able to be modified through a setting change (regardless of intent), have its compliance standing altered, or have a policy updated, an edge is drawn from that node to a new node with the changed system properties. This process is repeated until all possible alterations are identified and represented in the resulting attack or compliance graph.
Difficulties
Due to the expansion in network size, and with the inclusion of IoT and cyber-physical devices, the generation of attack and compliance graph quickly becomes difficult with the large number of assets needed to be processed. In addition, the number of regulatory and compliance checks, the large number of exploit and vulnerability entries available, and any custom internal standard checks or zero-day scripting causes a state space explosion in the graph generation process. As a result, these graphs become infeasible to generate and process serially.
This work attempts to further those efforts and extend RAGE to function on distributed computing environments to take advantage of the increased computing power using message-passing. As mentioned by the author of \cite{pacheco_introduction_2011}, MPI is the most widely used message-passing API, and one goal of this work was to utilize an API that was not only familiar and accessible, but versatile and powerful for parallelizing RAGE for distributed computing platforms. This work discusses a task parallelism approach for the generation process, and uses OpenMPI for the MPI implementation.
The attack and compliance graph generation is a viable process to parallelize and deploy on High-Performance Computing (HPC) environments, and related parallel and speedup works are discussed in Section \ref{sec:rel_works}. This work presents an extension to RAGE (RAGE Attack Graph Engine \cite{cook_rage_2018}) to function on distributed computing environments to take advantage of the increased computing power using message-passing. As mentioned by the author of \cite{pacheco_introduction_2011}, MPI is a widely used message-passing API, and one goal of this work was to utilize an API that was not only familiar and accessible, but versatile and powerful for parallelizing RAGE for distributed computing platforms. This work discusses a task parallelism approach for the generation process, and uses OpenMPI for the MPI implementation.
\section{Related Works}
\section{Related Works} \label{sec:rel_works}
For architectural and hardware techniques for general graph generation improvement, the authors of \cite{ainsworth_graph_2016} discuss the high cache miss rate, and how general prefetching
does not increase the prediction rate due to nonsequential graph structures and data-dependent access patterns. However, the authors continue to discuss that generation algorithms are known in advance, so explicit tuning of the hardware prefetcher to follow the traversal order pattern can lead to better performance. The authors were able to achieve over 2x performance improvement of a breadth-first search approach with this method.
Another hardware approach is to make use of accelerators. The authors of \cite{yao_efficient_2018} present an approach for minimizing the slowdown caused by the underlying graph atomic functions. By using the atomic function patterns, the authors utilized pipeline stages where vertex updates can be processed in parallel dynamically.
@ -228,6 +229,15 @@ In order to capture a comprehensive image of the tasking approach's impact on pe
\end{table}
\subsection{Number of Exploits}
Task 1 loops through the number of exploits and checks each exploit against the list of assets to see if an exploit is applicable at the current state. As the number of exploits grows, the time taken for Task 1 will increase accordingly. The exploit list used by Task 1 does not need to be applicable to the current asset or state, or even to any asset or any state. Regardless of if the exploit is applicable or not, Task 1 still loops through the entirety of the exploit list to check if any exploit may be applicable. Therefore, to prevent state-space explosion but still gather valid results, each exploit list in the tests contained a set of exploits that could be applicable, and all remaining exploits were not applicable. The not applicable exploits were created in a fashion similar to that seen in Figure \ref{fig:NA-exp}. By creating a multitude of not applicable exploits, the exploit list is able to be artificially increased, which ensures that the resulting graph maintains the same number of states, edges, and identical properties. For the experimental setup, the original exploit list begins with a size of 6, and artificially doubles in size until a final set of graphs is generated using an exploit size of 49,152 exploits.
\begin{figure}[htp]
\centering
\includegraphics[scale=0.5]{"./images/NA.png"}
\vspace{.2truein} \centerline{}
\caption{Example of a Not Applicable Exploit for the MPI Tasking Testing}
\label{fig:NA-exp}
\end{figure}
\subsection{Applicability of Exploits}
@ -253,13 +263,7 @@ In terms of efficiency, 2 compute nodes offer the greatest value since the speed
Figures \ref{fig:Tasking-RT}, \ref{fig:Tasking-Spd}, and \ref{fig:Tasking-Eff} display the results of the tasking approach for runtime in milliseconds, speedup, and efficiency respectively in table format.
\begin{figure}[htp]
\centering
\includegraphics[scale=0.5]{"./images/NA.png"}
\vspace{.2truein} \centerline{}
\caption{Example of a Not Applicable Exploit for the MPI Tasking Testing}
\label{fig:NA-exp}
\end{figure}
\begin{figure}
\centering