From e0fb15d30798948e0555b424d5fb96d0377e4705 Mon Sep 17 00:00:00 2001 From: noah Date: Mon, 28 Mar 2022 03:01:25 -0500 Subject: [PATCH] Final edits --- Bibliography.bib | 36 +- Chapter1.aux | 11 +- Chapter1.tex | 2 +- Chapter2.aux | 9 + Chapter3.aux | 9 + Chapter3.tex | 2 +- Chapter4.aux | 9 + Chapter4.tex | 2 +- Chapter5.aux | 15 +- Chapter5.tex | 10 +- Chapter5_img/MPI-OpenMP-Blend.PNG | Bin 40892 -> 42681 bytes Chapter5_img/dup.drawio.png | Bin 63632 -> 63111 bytes Chapter5_img/horiz_task.drawio.png | Bin 145117 -> 160500 bytes Chapter6.aux | 11 +- Chapter6.tex | 8 +- Schrick-Noah_MS-Thesis.aux | 8 +- Schrick-Noah_MS-Thesis.bbl | 40 +- Schrick-Noah_MS-Thesis.bcf | 2483 ++++++++++++++++++++++++++++ Schrick-Noah_MS-Thesis.blg | 64 +- Schrick-Noah_MS-Thesis.log | 342 ++-- Schrick-Noah_MS-Thesis.pdf | Bin 2119796 -> 2130300 bytes Schrick-Noah_MS-Thesis.run.xml | 85 + Schrick-Noah_MS-Thesis.tex | 5 +- 23 files changed, 2904 insertions(+), 247 deletions(-) create mode 100644 Schrick-Noah_MS-Thesis.bcf create mode 100644 Schrick-Noah_MS-Thesis.run.xml diff --git a/Bibliography.bib b/Bibliography.bib index 9a59f7c..c92e80d 100644 --- a/Bibliography.bib +++ b/Bibliography.bib @@ -25,6 +25,7 @@ @misc{noauthor_parallel_nodate, title = {Parallel {BGL} {Parallel} {Boost} {Graph} {Library} - 1.75.0}, + authors = {Edmonds, Nick and Gregor, Douglas and Lumsdaine, Andrew}, url = {https://www.boost.org/doc/libs/1_75_0/libs/graph_parallel/doc/html/index.html}, } @@ -134,6 +135,7 @@ @phdthesis{cook_rage_2018, title = {{RAGE}: {The} {Rage} {Attack} {Graph} {Engine}}, author = {Cook, Kyle}, + school = {The {University} of {Tulsa}}, year = {2018}, file = {Kyle Cook Thesis:/home/noah/Zotero/storage/2SR28HM2/Kyle Cook Thesis.pdf:application/pdf}, } @@ -272,9 +274,11 @@ file = {Algorithm 447\: efficient algorithms for graph manipulation:/home/noah/Zotero/storage/ZZBQJLL3/Algorithm 447 efficient algorithms for graph manipulation.pdf:application/pdf}, } -@patent{j_hale_compliance_nodate, +@misc{j_hale_compliance_nodate, title = {Compliance {Method} for a {Cyber}-{Physical} {System}}, author = {{J. Hale} and Hawrylak, P. and Papa, M.}, + note = {U.S. Patent Number 9,471,789, Oct. 18, 2016.}, + number = {9471789}, file = {Complaince_Graph_US_Patent_9471789:/home/noah/Zotero/storage/55BZN4U7/Complaince_Graph_US_Patent_9471789.pdf:application/pdf}, } @@ -385,6 +389,7 @@ @phdthesis{louthan_hybrid_2011, title = {Hybrid {Attack} {Graphs} for {Modeling} {Cyber}-{Physical} {Systems}}, author = {Louthan, G}, + school = {The {University} of {Tulsa}}, year = {2011}, keywords = {icle}, file = {louthan_thesis:/home/noah/Zotero/storage/5SBCLYA3/louthan_thesis.pdf:application/pdf}, @@ -471,6 +476,7 @@ issn = {1595935185}, author = {Ou, Xinming and Boyer, Wayne F and Mcqueen, Miles A}, year = {2006}, + journal = {CCS '06: Proceedings of the 13th ACM conference on Computer and communications security}, keywords = {attack graphs, enterprise network security, logic-programming}, pages = {336--345}, file = {1180405.1180446:/home/noah/Zotero/storage/TJKHVC4R/1180405.1180446.pdf:application/pdf}, @@ -484,6 +490,7 @@ abstract = {This paper presents a graph-based approach to network vulnerability analysis. The method is flexible, allowing analysis of attacks from both outside and inside the network. It can analyze risks to a specific network asset, or examine the universe of possible consequences following a successful attack. The graph-based tool can identify the set of attack paths that have a high probability of success (or a low "effort" cost) for the attacker. The system could be used to test the effectiveness of making configuration changes, implementing an intrusion detection system, etc. The analysis system requires as input a database of common attacks, broken into atomic steps, specific network configuration and topology information, and an attacker profile. The attack information is "matched" with the network configuration information and an attacker profile to create a superset attack graph. Nodes identify a stage of attack, for example the class of machines the attacker has accessed and the user privilege level he or she has compromised. The arcs in the attack graph represent attacks or stages of attacks. By assigning probabilities of success on the arcs or costs representing level-of-effort for the attacker, various graph algorithms such as shortest-path algorithms can identify the attack paths with the highest probability of success.}, journal = {Proceedings New Security Paradigms Workshop}, author = {Phillips, Cynthia and Swiler, Laura Painton}, + note = {doi: 10.1145/310889.310919}, year = {1998}, keywords = {Attack graph, Computer security, Network vulnerability}, pages = {71--79}, @@ -530,12 +537,13 @@ file = {Application of Improved Dijkstra Algorithm in:/home/noah/Zotero/storage/T5RF74IL/Application of Improved Dijkstra Algorithm in.pdf:application/pdf}, } -@misc{schneier_modeling_1999, +@article{schneier_modeling_1999, title = {Modeling {Security} {Threats}}, url = {https://www.schneier.com/academic/archives/1999/12/attack_trees.html}, author = {Schneier, Bruce}, year = {1999}, - note = {Publication Title: Dr. Dobb's Journal}, + journal = {Dr. Dobb's Journal}, + note = {vol. 24, no.12} } @article{sheyner_automated_2002, @@ -654,7 +662,7 @@ isbn = {978-0-12-374260-5}, publisher = {Morgan Kaufmann}, author = {Pacheco, Peter}, - year = {2011}, + year = {2011} } @article{jost_comparing_nodate, @@ -1231,36 +1239,34 @@ @misc{lawrence_livermore_national_laboratory_mpip_nodate, - title = {mpiP}, + title = {mpi{P}, A light-weight {MPI} profiler}, shorttitle = {A light-weight {MPI} profiler.}, - url = {https://software.llnl.gov/mpiP/}, + note = {https://software.llnl.gov/mpiP/}, author = {{Lawrence Livermore National Laboratory}}, } @misc{noauthor_sarbanes-oxley_2002, title = {Sarbanes-{Oxley} {Act} of 2002}, - url = {https://www.govinfo.gov/content/pkg/PLAW-107publ204/html/PLAW-107publ204.htm}, - year = {2002}, + note = {Pub. L. No. 107-204. 2002 [Online]. Available: https://www.govinfo.gov/content/pkg/PLAW-107publ204/html/PLAW-107publ204.htm}, } @misc{noauthor_health_1996, title = {Health {Insurance} {Portability} and {Accountability} {Act} of 1996}, - url = {https://www.govinfo.gov/content/pkg/PLAW-104publ191/html/PLAW-104publ191.htm}, - year = {1996}, + note = {Pub. L. No. 104-191. 1996 [Online]. Available: https://www.govinfo.gov/content/pkg/PLAW-104publ191/html/PLAW-104publ191.htm}, } -@online{EUdataregulations2018, - title = {REGULATION (EU) 2016/679 OF THE EUROPEAN PARLIAMENT AND OF THE COUNCIL +@misc{EUdataregulations2018, + title = {Regulation (EU) 2016/679 of the {European} {Parliament} and of THE {Council} of 27}, - url = {https://eur-lex.europa.eu/legal-content/EN/TXT/PDF/?uri=CELEX:32016R0679}, + note = {Available: https://eur-lex.europa.eu/legal-content/EN/TXT/PDF/?uri=CELEX:32016R0679}, author = {The European Parliment and the Council of the European Union}, date = {2016-04-27} } @misc{PCI, - title = {Payment Card Industry (PCI) Data Security Standard}, - url = {https://www.pcisecuritystandards.org/documents/PCI_DSS_v3-2-1.pdf}, + title = {Payment {Card} {Industry} {(PCI)} {Data} {Security} {Standard}}, + note = {{Available: https://www.pcisecuritystandards.org/documents/PCI$\_$DSS$\_$v3-2-1.pdf}}, month = may, year = {2018}, author = {PCI Security Standards Council} diff --git a/Chapter1.aux b/Chapter1.aux index 64267d6..88a8ee3 100644 --- a/Chapter1.aux +++ b/Chapter1.aux @@ -21,7 +21,7 @@ \citation{PCI} \citation{cook_rage_2018} \@writefile{toc}{\contentsline {subsection}{\numberline {1.2.2}\it Defining Compliance Graphs}{3}{}\protected@file@percent } -\newlabel{CG-alter}{{1.2.2}{3}} +\newlabel{sec:CG-alter}{{1.2.2}{3}} \@writefile{toc}{\contentsline {subsection}{\numberline {1.2.3}\it Difficulties of Compliance Graphs}{3}{}\protected@file@percent } \newlabel{sec:CG-diff}{{1.2.3}{3}} \@writefile{toc}{\contentsline {section}{\numberline {1.3}\bf Objectives and Contributions}{4}{}\protected@file@percent } @@ -47,6 +47,15 @@ \setcounter{continuedfloat}{0} \setcounter{subfigure}{0} \setcounter{subtable}{0} +\setcounter{float@type}{8} +\setcounter{algorithm}{0} +\setcounter{ALG@line}{0} +\setcounter{ALG@rem}{0} +\setcounter{ALG@nested}{0} +\setcounter{ALG@Lnr}{2} +\setcounter{ALG@blocknr}{10} +\setcounter{ALG@storecount}{0} +\setcounter{ALG@tmpcounter}{0} \setcounter{lofdepth}{1} \setcounter{lotdepth}{1} } diff --git a/Chapter1.tex b/Chapter1.tex index 5abd7e2..f48087c 100644 --- a/Chapter1.tex +++ b/Chapter1.tex @@ -27,7 +27,7 @@ A few alterations are required for attack graph generators to function as compli are discussed in Section \ref{CG-alter}. Compliance requirements are broad and varying, and can function as safety regulations, maintenance compliance, or any other regulatory compliance. In the same fashion as attack graphs, compliance graphs are exhaustive, and future system states can be analyzed to determine appropriate steps that need to be taken for preventative measures \cite{j_hale_compliance_nodate}. -\TUsubsection{Defining Compliance Graphs} \label{CG-alter} +\TUsubsection{Defining Compliance Graphs} \label{sec:CG-alter} The common encodings of attack graph properties have different encoding definitions in compliance graphs. The nodes of an attack graph typically represent the system state that includes the qualities and topologies of all assets in the network as they pertain to cybersecurity postures. Nodes of a compliance graphs also represent the system state, however they include the qualities and topologies of all assets in the network as they pertain to compliance regulation. For instance, a quality for a vehicle's maintenance compliance could be described as: \textit{car:months\_since\_oil\_change=6}, or \textit{car:miles\_since\_oil\_change=10,000}. diff --git a/Chapter2.aux b/Chapter2.aux index 83350c2..0d7766b 100644 --- a/Chapter2.aux +++ b/Chapter2.aux @@ -51,6 +51,15 @@ \setcounter{continuedfloat}{0} \setcounter{subfigure}{0} \setcounter{subtable}{0} +\setcounter{float@type}{8} +\setcounter{algorithm}{0} +\setcounter{ALG@line}{0} +\setcounter{ALG@rem}{0} +\setcounter{ALG@nested}{0} +\setcounter{ALG@Lnr}{2} +\setcounter{ALG@blocknr}{10} +\setcounter{ALG@storecount}{0} +\setcounter{ALG@tmpcounter}{0} \setcounter{lofdepth}{1} \setcounter{lotdepth}{1} } diff --git a/Chapter3.aux b/Chapter3.aux index 82cac21..8b550ef 100644 --- a/Chapter3.aux +++ b/Chapter3.aux @@ -49,6 +49,15 @@ \setcounter{continuedfloat}{0} \setcounter{subfigure}{0} \setcounter{subtable}{0} +\setcounter{float@type}{8} +\setcounter{algorithm}{0} +\setcounter{ALG@line}{0} +\setcounter{ALG@rem}{0} +\setcounter{ALG@nested}{0} +\setcounter{ALG@Lnr}{2} +\setcounter{ALG@blocknr}{10} +\setcounter{ALG@storecount}{0} +\setcounter{ALG@tmpcounter}{0} \setcounter{lofdepth}{1} \setcounter{lotdepth}{1} } diff --git a/Chapter3.tex b/Chapter3.tex index 26519ef..677ee4e 100644 --- a/Chapter3.tex +++ b/Chapter3.tex @@ -114,7 +114,7 @@ performance benefits of memory operations, since graph computation relies less o \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 +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. diff --git a/Chapter4.aux b/Chapter4.aux index 953774f..81bbf76 100644 --- a/Chapter4.aux +++ b/Chapter4.aux @@ -55,6 +55,15 @@ \setcounter{continuedfloat}{0} \setcounter{subfigure}{0} \setcounter{subtable}{0} +\setcounter{float@type}{8} +\setcounter{algorithm}{0} +\setcounter{ALG@line}{0} +\setcounter{ALG@rem}{0} +\setcounter{ALG@nested}{0} +\setcounter{ALG@Lnr}{2} +\setcounter{ALG@blocknr}{10} +\setcounter{ALG@storecount}{0} +\setcounter{ALG@tmpcounter}{0} \setcounter{lofdepth}{1} \setcounter{lotdepth}{1} } diff --git a/Chapter4.tex b/Chapter4.tex index 8378474..448fb08 100644 --- a/Chapter4.tex +++ b/Chapter4.tex @@ -7,7 +7,7 @@ have inseparable features, the generation process forcibly separates features to One example of an inseparable feature is time. If two different assets are identical and no constraints dictate otherwise, the two assets cannot proceed through times at different rates. For example, if two cars were manufactured at the same -moment, one of these cars cannot proceed multiple time steps into the future while the other remains at its current time step - each car must step through time at the same rate. +moment, one of these cars cannot proceed multiple time steps into the future while the other remains at its current time step; each car must step through time at the same rate. However, the generation of attack graphs and compliance graphs examines the possibilities that one car ages by one time step, while the other car does not, or vice versa. This results in an attack graph that can be seen in Figure \ref{fig:non-sync_ex}, which is a partial attack graph showing the separation of the time feature. All shaded states are considered unattainable, since all of these states comprise of assets that have advanced time at different rates. It is noticeable that not only are the unattainable states themselves a wasteful generation, diff --git a/Chapter5.aux b/Chapter5.aux index 66aa012..fc50779 100644 --- a/Chapter5.aux +++ b/Chapter5.aux @@ -29,12 +29,12 @@ \newlabel{fig:Task1-Case2}{{5.5}{36}} \@writefile{toc}{\contentsline {subsubsection}{Task 4 and Task 5}{36}{}\protected@file@percent } \newlabel{sec:T4T5}{{5.3.2}{36}} -\newlabel{table:tasking-tag}{{\caption@xref {table:tasking-tag}{ on input line 104}}{37}} \@writefile{lot}{\contentsline {table}{\numberline {5.1}{\ignorespaces MPI Tags for the MPI Tasking Approach\relax }}{37}{}\protected@file@percent } +\newlabel{table:tasking-tag}{{5.1}{37}} \@writefile{toc}{\contentsline {subsubsection}{MPI Tags}{37}{}\protected@file@percent } \newlabel{sec:tasking-tag}{{5.3.2}{37}} \@writefile{toc}{\contentsline {subsection}{\numberline {5.3.3}\it Performance Expectations and Use Cases}{37}{}\protected@file@percent } -\newlabel{Task-perf-expec}{{5.3.3}{37}} +\newlabel{sec:Task-perf-expec}{{5.3.3}{37}} \@writefile{toc}{\contentsline {subsection}{\numberline {5.3.4}\it Results}{38}{}\protected@file@percent } \newlabel{sec:Tasking-Results}{{5.3.4}{38}} \@writefile{lof}{\contentsline {figure}{\numberline {5.6}{\ignorespaces Example of a Not Applicable Exploit for the MPI Tasking Testing\relax }}{39}{}\protected@file@percent } @@ -57,8 +57,8 @@ \@writefile{toc}{\contentsline {subsection}{\numberline {5.4.3}\it Performance Expectations and Use Cases}{44}{}\protected@file@percent } \newlabel{sec:perf_expec_subg}{{5.4.3}{44}} \citation{lawrence_livermore_national_laboratory_mpip_nodate} -\newlabel{table:subg-tag}{{\caption@xref {table:subg-tag}{ on input line 192}}{45}} \@writefile{lot}{\contentsline {table}{\numberline {5.2}{\ignorespaces MPI Tags for the MPI Subgraphing Approach\relax }}{45}{}\protected@file@percent } +\newlabel{table:subg-tag}{{5.2}{45}} \@writefile{toc}{\contentsline {subsection}{\numberline {5.4.4}\it Results}{45}{}\protected@file@percent } \newlabel{sec:Subgraphing-Results}{{5.4.4}{45}} \@writefile{lof}{\contentsline {figure}{\numberline {5.10}{\ignorespaces First iteration results of MPI Subgraphing in terms of Runtime\relax }}{46}{}\protected@file@percent } @@ -95,6 +95,15 @@ \setcounter{continuedfloat}{0} \setcounter{subfigure}{0} \setcounter{subtable}{0} +\setcounter{float@type}{8} +\setcounter{algorithm}{0} +\setcounter{ALG@line}{0} +\setcounter{ALG@rem}{0} +\setcounter{ALG@nested}{0} +\setcounter{ALG@Lnr}{2} +\setcounter{ALG@blocknr}{10} +\setcounter{ALG@storecount}{0} +\setcounter{ALG@tmpcounter}{0} \setcounter{lofdepth}{1} \setcounter{lotdepth}{1} } diff --git a/Chapter5.tex b/Chapter5.tex index fbfc4d7..fa25e55 100644 --- a/Chapter5.tex +++ b/Chapter5.tex @@ -101,7 +101,7 @@ Intermediate database operations, though not frequent and may never occur for sm \TUsubsubsection{MPI Tags} \label{sec:tasking-tag} To ensure that the intended message is received by each node, the MPI message envelopes have their tag fields specified. When a node sends a message, it specifies a tag that corresponds with the data and intent for which it is sent. The tag values were arbitrarily chosen, and tags can be added to the existing list or removed as desired. When receiving a message, a node can specify to only look for messages that have an envelope with a matching tag field. Not only do tags ensure that nodes are receiving the correct messages, they also reduce complexity for program design. Table \ref{table:tasking-tag} displays the list of tags used for the MPI Tasking approach. -\begin{table}[] \label{table:tasking-tag} +\begin{table}[] \centering \begin{tabular}{|l|l|} \hline @@ -125,9 +125,10 @@ To ensure that the intended message is received by each node, the MPI message en 50 & NetworkState to Store in Task 5 \\ \hline \end{tabular} \caption{MPI Tags for the MPI Tasking Approach} + \label{table:tasking-tag} \end{table} -\TUsubsection{Performance Expectations and Use Cases} \label{Task-perf-expec} +\TUsubsection{Performance Expectations and Use Cases} \label{sec:Task-perf-expec} Due to the amount of communication between nodes to distribute the necessary data through all stages of the tasking pipeline, this approach is not expected to outperform the serial approach in all cases. This tasking approach was specifically designed to reduce the computation time when the generation of each individual state increases in time. This approach does not offer any guarantees of processing through the frontier at an increased rate; it's main objective is to distribute the workload of individual state generation. As discussed in Section \ref{sec:Intro}, the amount of entries in the National Vulnerability database and any custom vulnerability testing to ensure adequate examination of all assets in the network sums to large number of exploits in the exploit list. Likewise for compliance graphs and compliance examinations, Section \ref{sec:CG-diff} discussed that the number of compliance checks for SOX, HIPAA, GDPR, PCI DSS, and/or any other regulatory compliance also sums to a large number of compliance checks in the exploit list. Since the generation of each state is largely dependent on the number of exploits present in the exploit list, this approach is best-suited for when the exploit list grows in size. As will be later discussed, it is also hypothesized that this approach is well-suited when many database operations occur. \TUsubsection{Results} \label{sec:Tasking-Results} @@ -135,7 +136,7 @@ A series of tests were conducted on the platform described at the beginning of S The results of the Tasking Approach can be seen in Figure \ref{fig:Spd-Eff-Task}. In terms of speedup, when the number of entries in the exploit list is small, the serial approach has better performance. This is expected due to the communication cost requiring more time than it does to generate a state, as discussed in Section \ref{sec:Task-perf-expec}. However, as the number of items in the exploit list increase, the Tasking Approach quickly begins to outperform the serial approach. It is notable that even when the tasking pipeline is not fully saturated (when there are less compute nodes assigned than tasks), the performance is still approximately equal to that of the serial approach. The other noticeable feature is that as more compute nodes are assigned, the speedup continues to increase. -In terms of efficiency, 2 compute nodes offer the greatest value since the speedup using 2 compute nodes is approximately 1.0 as the exploit list size increases. While the 2 compute node option does offer the greatest efficiency, it does not provide any speedup on any of the testing cases conducted. Similarly, testing with 3, 4, and 5 compute nodes were relatively high compared to the "fully saturated pipeline" testing counterparts, but they also did not provide any speedup on any of the testing cases conducted. The results also demonstrate that an odd number of compute nodes in a fully saturated pipeline has better efficiency that an even number of compute nodes. When referring to Figure \ref{fig:node-alloc}, when there is an odd number number of compute nodes, Task 1 is allocated more nodes than Task 2. In the testing conducted, Task 1 was responsible for iterating through an increased size of the exploit list, so more nodes is advantageous in distributing the workload. However, since many exploits were not applicable, Task 2 had a lower workload where only 6 exploits could be applicable. This will be further elaborated upon in Section \ref{sec:FW}, but it is expected that efficiency will increase for real networks, since nodes in Task 2 will see a realistic workload. +In terms of efficiency, 2 compute nodes offer the greatest value since the speedup using 2 compute nodes is approximately 1.0 as the exploit list size increases. While the 2 compute node option does offer the greatest efficiency, it does not provide any speedup on any of the testing cases conducted. Similarly, testing with 3, 4, and 5 compute nodes were relatively high compared to the ``fully saturated pipeline" testing counterparts, but they also did not provide any speedup on any of the testing cases conducted. The results also demonstrate that an odd number of compute nodes in a fully saturated pipeline has better efficiency that an even number of compute nodes. When referring to Figure \ref{fig:node-alloc}, when there is an odd number number of compute nodes, Task 1 is allocated more nodes than Task 2. In the testing conducted, Task 1 was responsible for iterating through an increased size of the exploit list, so more nodes is advantageous in distributing the workload. However, since many exploits were not applicable, Task 2 had a lower workload where only 6 exploits could be applicable. This will be further elaborated upon in Section \ref{sec:FW}, but it is expected that efficiency will increase for real networks, since nodes in Task 2 will see a realistic workload. \begin{figure}[htp] \centering @@ -189,7 +190,7 @@ A node dedicated to database operations is also present in this approach. The wo \TUsubsubsection{MPI Tags} Similar to Section \ref{sec:tasking-tag} that discussed the usage of MPI Tags for the tasking approach, the subgraphing approach also made use of MPI Tags. Table \ref{table:subg-tag} displays the integers and descriptions of the tags used for this approach. -\begin{table}[] \label{table:subg-tag} +\begin{table}[] \centering \begin{tabular}{|l|l|} \hline @@ -207,6 +208,7 @@ Similar to Section \ref{sec:tasking-tag} that discussed the usage of MPI Tags fo 99 & Generation Finalize Signal \\ \hline \end{tabular} \caption{MPI Tags for the MPI Subgraphing Approach} + \label{table:subg-tag} \end{table} \TUsubsection{Performance Expectations and Use Cases} \label{sec:perf_expec_subg} diff --git a/Chapter5_img/MPI-OpenMP-Blend.PNG b/Chapter5_img/MPI-OpenMP-Blend.PNG index 170d48a77865f203891d85d5cb2c7abdfc169918..601c7e692ee17bee3917ce1d1d413df7807a61bf 100644 GIT binary patch literal 42681 zcmeFZ2~<9gg^pBh#^7}0t6D$za8t;Id$K?_y6Dc$GHD^ zwf0gfZtzVIqZW5fmXNa{+7^@zg+-J26hylz9LIa=2W9 zTPR)cv}D_nO2fb(b?V?24t~AUUw7>(;TIrd2yl-{;G6LsKxeIsfF_S+2AQ`et#eue z>Tm-ZH3Hwhd;%zTClqMZ_Y`RTEzKR2G<#C`MV5_DLQ6pVw~0WbtH8IFhbs+1ff%4s 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\@writefile{toc}{\contentsline {section}{\numberline {6.2}\bf Future Work}{55}{}\protected@file@percent } \newlabel{sec:FW}{{6.2}{55}} \@writefile{lof}{\contentsline {figure}{\numberline {6.1}{\ignorespaces Possible Method for Blending MPI and OpenMP for Task 2 of the MPI Tasking Approach\relax }}{56}{}\protected@file@percent } -\newlabel{fig:Subg_base}{{6.1}{56}} +\newlabel{fig:OMP_MPI_Blend}{{6.1}{56}} \@setckpt{Chapter6}{ \setcounter{page}{58} \setcounter{equation}{0} @@ -27,6 +27,15 @@ \setcounter{continuedfloat}{0} \setcounter{subfigure}{0} \setcounter{subtable}{0} +\setcounter{float@type}{8} +\setcounter{algorithm}{0} +\setcounter{ALG@line}{0} +\setcounter{ALG@rem}{0} +\setcounter{ALG@nested}{0} +\setcounter{ALG@Lnr}{2} +\setcounter{ALG@blocknr}{10} +\setcounter{ALG@storecount}{0} +\setcounter{ALG@tmpcounter}{0} \setcounter{lofdepth}{1} \setcounter{lotdepth}{1} } diff --git a/Chapter6.tex b/Chapter6.tex index 38e1214..3259f96 100644 --- a/Chapter6.tex +++ b/Chapter6.tex @@ -4,22 +4,22 @@ This thesis presented various extensions to an attack graph generator, RAGE, to Chapter \ref{ch:Sync-Fire} presents the synchronous firing feature, which is successfully able to reduce the state space and runtime of the generation process when assets have inseparable features. This feature does not lose any substantive information from a network and its resulting graph; the graph is able to remain exhaustive and still capture all necessary information. The results are promising, and greater reductions are expected when a greater number of assets share inseparable features, as discussed in Section \ref{sec:FW}. -Chapter \ref{ch:MPI} presented two approaches for utilizing MPI for extension to the distributed computing platform space. One approach was a task parallelism approach discussed in Section \ref{sec:MPI-Tasking}, and promising results were observed when the generation of each state increased in computation requirements. The second approach was a data parallelism approach discussed in Section \ref{sec:MPI_Subgraphing}. While results were not promising for this approach, future works can be conducted to optimize and avoid the difficulties of duplicate work and communication overhead. +Chapter \ref{ch:MPI} presented two approaches for utilizing MPI for extension to the distributed computing platform space. One approach was a task parallelism approach discussed in Section \ref{sec:Tasking-Approach}, and promising results were observed when the generation of each state increased in computation requirements. The second approach was a data parallelism approach discussed in Section \ref{sec:Subgraphing_Approach}. While results were not promising for this approach, future works can be conducted to optimize and avoid the difficulties of duplicate work and communication overhead. Throughout this thesis and its works, RAGE has demonstrated its extensions to support compliance graph generation. Section \ref{sec:CG-alter} discussed the alterations required for attack graph generators to support compliance graphs, and example compliance graphs have been generated in the results seen in Sections \ref{sec:Sync-Results}, \ref{sec:Tasking-Results}, and \ref{sec:Subgraphing-Results}. \TUsection{Future Work} \label{sec:FW} There are multiple avenues that future works and research can be conducted. One such investigation involves examining the effect of the synchronous firing feature with more assets belonging to groups. As the number of assets with inseparable features increases, more permutations consisting of unattainable states in a graph would exist. Since more assets can devolve and grow increasingly out of sync, the reduction rate when using the synchronous firing feature is likely to increase. -Another avenue is to improve and further test the MPI Tasking approach discussed in Section \ref{sec:MPI-Tasking}. One improvement approach involves blending OpenMP and MPI. For Task 2 specifically, an example diagram was created that displays a possible approach at leveraging both OpenMP and MPI, and this can be seen in Figure \ref{fig:OMP_MPI_Blend}. Similar techniques could likely be implemented for Task 1, and other techniques could be devised for these tasks and for Tasks 3, 4, and 5. Further testing can be conducted to examine the effectiveness of MPI Tasking when generating large networks with many applicable exploits at any given state. This would allow Task 2 to have a greater workload, where increased speedups are likely to be attained over the serial approach. +Another avenue is to improve and further test the MPI Tasking approach discussed in Section \ref{sec:Tasking-Approach}. One improvement approach involves blending OpenMP and MPI. For Task 2 specifically, an example diagram was created that displays a possible approach at leveraging both OpenMP and MPI, and this can be seen in Figure \ref{fig:OMP_MPI_Blend}. Similar techniques could likely be implemented for Task 1, and other techniques could be devised for these tasks and for Tasks 3, 4, and 5. Further testing can be conducted to examine the effectiveness of MPI Tasking when generating large networks with many applicable exploits at any given state. This would allow Task 2 to have a greater workload, where increased speedups are likely to be attained over the serial approach. \begin{figure}[htp] \includegraphics[width=\linewidth]{"./Chapter5_img/MPI-OpenMP-Blend.PNG"} \vspace{.2truein} \centerline{} \caption{Possible Method for Blending MPI and OpenMP for Task 2 of the MPI Tasking Approach} - \label{fig:Subg_base} + \label{fig:OMP_MPI_Blend} \end{figure} -Many research avenues exist for the MPI Subgraphing approach seen in Section \ref{sec:MPI_Subgraphing}. The results collected in this work were not promising, and many alterations can be attempted. Duplicate states are the primary problem point of this approach, and using a DHT increased the communication cost to a large degree. Alternate methods for addressing this issue can be devised. While it did not improve the results in this work, parameter tuning with this approach can be performed in regards to the depth limit value and the metric for when a worker node does not have a queue marker. This work used a random metric, but more intelligent strategies could be devised. +Many research avenues exist for the MPI Subgraphing approach seen in Section \ref{sec:Subgraphing_Approach}. The results collected in this work were not promising, and many alterations can be attempted. Duplicate states are the primary problem point of this approach, and using a DHT increased the communication cost to a large degree. Alternate methods for addressing this issue can be devised. While it did not improve the results in this work, parameter tuning with this approach can be performed in regards to the depth limit value and the metric for when a worker node does not have a queue marker. This work used a random metric, but more intelligent strategies could be devised. Drastic results are not likely to occur, but various MPI parameter tunings can be performed for both the MPI Tasking and Subgraphing approaches. For instance, this work utilized the parameters for binding to and mapping by NUMA. This is seemingly the most common approach, and MPI balances the workload of NUMA nodes automatically when these parameters are used. Many other options exists for these parameters, and many other parameters exist that can be examined. In addition, comparisons between OpenMPI, MPICH, and MVAPICH can be conducted to see if there is any noticeable, consistent improvement. diff --git a/Schrick-Noah_MS-Thesis.aux b/Schrick-Noah_MS-Thesis.aux index 2b82170..ce8680a 100644 --- a/Schrick-Noah_MS-Thesis.aux +++ b/Schrick-Noah_MS-Thesis.aux @@ -28,14 +28,14 @@ \bibcite{j_hale_compliance_nodate}{6} \bibcite{baloyi_guidelines_2019}{7} \bibcite{allman_complying_2006}{8} -\bibcite{noauthor_sarbanes-oxley_2002}{9} -\bibcite{noauthor_health_1996}{10} -\bibcite{EUdataregulations2018}{11} \@writefile{toc}{{\hfill \ }} \@writefile{toc}{\contentsline {section}{\hspace {-\parindent }NOMENCLATURE}{58}{}\protected@file@percent } \@writefile{toc}{\addvspace {10pt}} \@writefile{toc}{\contentsline {section}{\hspace {-\parindent }BIBLIOGRAPHY}{58}{}\protected@file@percent } \@writefile{toc}{{\hfill \ }} +\bibcite{noauthor_sarbanes-oxley_2002}{9} +\bibcite{noauthor_health_1996}{10} +\bibcite{EUdataregulations2018}{11} \bibcite{PCI}{12} \bibcite{cook_rage_2018}{13} \bibcite{berry_graph_2007}{14} @@ -55,5 +55,7 @@ \bibcite{li_combining_2019}{28} \bibcite{CVE-2019-10747}{29} \bibcite{louthan_hybrid_2011}{30} +\bibcite{pacheco_introduction_2011}{31} +\bibcite{lawrence_livermore_national_laboratory_mpip_nodate}{32} \bibstyle{ieeetr} \gdef \@abspage@last{71} diff --git a/Schrick-Noah_MS-Thesis.bbl b/Schrick-Noah_MS-Thesis.bbl index 9e4914c..7833e88 100644 --- a/Schrick-Noah_MS-Thesis.bbl +++ b/Schrick-Noah_MS-Thesis.bbl @@ -4,14 +4,16 @@ C.~Phillips and L.~P. Swiler, ``A graph-based system for network-vulnerability analysis,'' {\em Proceedings New Security Paradigms Workshop}, vol.~Part F1292, pp.~71--79, 1998. +\newblock doi: 10.1145/310889.310919. \bibitem{schneier_modeling_1999} -B.~Schneier, ``Modeling {Security} {Threats},'' 1999. -\newblock Publication Title: Dr. Dobb's Journal. +B.~Schneier, ``Modeling {Security} {Threats},'' {\em Dr. Dobb's Journal}, 1999. +\newblock vol. 24, no.12. \bibitem{ou_scalable_2006} X.~Ou, W.~F. Boyer, and M.~A. Mcqueen, ``A {Scalable} {Approach} to {Attack} - {Graph} {Generation},'' pp.~336--345, 2006. + {Graph} {Generation},'' {\em CCS '06: Proceedings of the 13th ACM conference + on Computer and communications security}, pp.~336--345, 2006. \bibitem{sheyner_automated_2002} O.~Sheyner, J.~Haines, S.~Jha, R.~Lippmann, and J.~Wing, ``Automated @@ -27,6 +29,7 @@ J.~Zhang, S.~Khoram, and J.~Li, ``Boosting the performance of {FPGA}-based \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{baloyi_guidelines_2019} N.~Baloyi and P.~Kotzé, ``Guidelines for {Data} {Privacy} {Compliance}: {A} @@ -40,22 +43,30 @@ E.~Allman, ``Complying with {Compliance}: {Blowing} it off is not an option.,'' {\em ACM Queue}, vol.~4, no.~7, 2006. \bibitem{noauthor_sarbanes-oxley_2002} -``Sarbanes-{Oxley} {Act} of 2002,'' 2002. +``Sarbanes-{Oxley} {Act} of 2002.'' +\newblock Pub. L. No. 107-204. 2002 [Online]. Available: + https://www.govinfo.gov/content/pkg/PLAW-107publ204/html/PLAW-107publ204.htm. \bibitem{noauthor_health_1996} -``Health {Insurance} {Portability} and {Accountability} {Act} of 1996,'' 1996. +``Health {Insurance} {Portability} and {Accountability} {Act} of 1996.'' +\newblock Pub. L. No. 104-191. 1996 [Online]. Available: + https://www.govinfo.gov/content/pkg/PLAW-104publ191/html/PLAW-104publ191.htm. \bibitem{EUdataregulations2018} T.~E. Parliment and the Council of~the European~Union, ``Regulation (eu) - 2016/679 of the european parliament and of the council of 27.'' + 2016/679 of the {European} {Parliament} and of the {Council} of 27.'' +\newblock Available: + https://eur-lex.europa.eu/legal-content/EN/TXT/PDF/?uri=CELEX:32016R0679. \bibitem{PCI} -P.~S.~S. Council, ``Payment card industry (pci) data security standard,'' May - 2018. +P.~S.~S. Council, ``Payment {Card} {Industry} {(PCI)} {Data} {Security} + {Standard},'' May 2018. +\newblock {Available: + https://www.pcisecuritystandards.org/documents/PCI$\_$DSS$\_$v3-2-1.pdf}. \bibitem{cook_rage_2018} K.~Cook, {\em {RAGE}: {The} {Rage} {Attack} {Graph} {Engine}}. -\newblock PhD thesis, 2018. +\newblock PhD thesis, The {University} of {Tulsa}, 2018. \bibitem{berry_graph_2007} J.~Berry and B.~Hendrickson, ``Graph {Analysis} with {High} {Performance} @@ -143,6 +154,15 @@ M.~Li, P.~Hawrylak, and J.~Hale, ``Combining {OpenCL} and {MPI} to support \bibitem{louthan_hybrid_2011} G.~Louthan, {\em Hybrid {Attack} {Graphs} for {Modeling} {Cyber}-{Physical} {Systems}}. -\newblock PhD thesis, 2011. +\newblock PhD thesis, The {University} of {Tulsa}, 2011. + +\bibitem{pacheco_introduction_2011} +P.~Pacheco, {\em An {Introduction} to {Parallel} {Programming}}. +\newblock Morgan Kaufmann, print~ed., 2011. + +\bibitem{lawrence_livermore_national_laboratory_mpip_nodate} +{Lawrence Livermore National Laboratory}, ``mpi{P}, a light-weight {MPI} + profiler.'' +\newblock https://software.llnl.gov/mpiP/. \end{thebibliography} diff --git a/Schrick-Noah_MS-Thesis.bcf b/Schrick-Noah_MS-Thesis.bcf new file mode 100644 index 0000000..8dacf97 --- /dev/null +++ b/Schrick-Noah_MS-Thesis.bcf @@ -0,0 +1,2483 @@ + + + + + + output_encoding + utf8 + + + input_encoding + utf8 + + + debug + 0 + + + mincrossrefs + 2 + + + minxrefs + 2 + + + sortcase + 1 + + + sortupper + 1 + + + + + + + alphaothers + + + + + labelalpha + 0 + + + labelnamespec + shortauthor + author + shorteditor + editor + translator + + + labeltitle + 0 + + + labeltitlespec + shorttitle + title + maintitle + + + labeltitleyear + 0 + + + labeldateparts + 0 + + + labeldatespec + date + year + eventdate + origdate + urldate + nodate + + + julian + 0 + + + gregorianstart + 1582-10-15 + + + maxalphanames + 3 + + + maxbibnames + 3 + + + maxcitenames + 3 + + + maxsortnames + 3 + + + maxitems + 3 + + + minalphanames + 1 + + + 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author + journaltitle + title + + + + book + mvbook + + author + title + + + + inbook + bookinbook + suppbook + + author + title + booktitle + + + + booklet + + + author + editor + + title + + + + collection + reference + mvcollection + mvreference + + editor + title + + + + incollection + suppcollection + inreference + + author + editor + title + booktitle + + + + dataset + + title + + + + manual + + title + + + + misc + software + + title + + + + online + + title + + url + doi + eprint + + + + + patent + + author + title + number + + + + periodical + + editor + title + + + + proceedings + mvproceedings + + title + + + + inproceedings + + author + title + booktitle + + + + report + + author + title + type + institution + + + + thesis + + author + title + type + institution + + + + unpublished + + author + title + + + + + isbn + + + issn + + + ismn + + + gender + + + + + + + Bibliography.bib + + + phillips_graph-based_1998 + schneier_modeling_1999 + ou_scalable_2006 + sheyner_automated_2002 + ou_scalable_2006 + zhang_boosting_2017 + j_hale_compliance_nodate + baloyi_guidelines_2019 + allman_complying_2006 + j_hale_compliance_nodate + j_hale_compliance_nodate + noauthor_sarbanes-oxley_2002 + noauthor_health_1996 + EUdataregulations2018 + PCI + cook_rage_2018 + berry_graph_2007 + berry_graph_2007 + zhang_boosting_2017 + ainsworth_graph_2016 + berry_graph_2007 + ainsworth_graph_2016 + ainsworth_graph_2016 + yao_efficient_2018 + zhang_boosting_2017 + dai_fpgp_2016 + arifuzzaman_fast_2015 + yu_construction_2018 + liakos_memory-optimized_2016 + liakos_memory-optimized_2016 + liakos_memory-optimized_2016 + balaji_graph_2016 + noauthor_overview_nodate + noauthor_boost_nodate + ou_scalable_2006 + cook_scalable_2016 + li_concurrency_2019 + li_concurrency_2019 + 9150145 + 7087377 + cook_rage_2018 + cook_rage_2018 + li_concurrency_2019 + li_combining_2019 + zhang_boosting_2017 + ainsworth_graph_2016 + berry_graph_2007 + cook_rage_2018 + zhang_boosting_2017 + CVE-2019-10747 + louthan_hybrid_2011 + louthan_hybrid_2011 + louthan_hybrid_2011 + louthan_hybrid_2011 + louthan_hybrid_2011 + cook_rage_2018 + cook_rage_2018 + louthan_hybrid_2011 + pacheco_introduction_2011 + li_concurrency_2019 + 9150145 + 7087377 + li_concurrency_2019 + lawrence_livermore_national_laboratory_mpip_nodate + phillips_graph-based_1998 + schneier_modeling_1999 + ou_scalable_2006 + sheyner_automated_2002 + zhang_boosting_2017 + j_hale_compliance_nodate + baloyi_guidelines_2019 + allman_complying_2006 + noauthor_sarbanes-oxley_2002 + noauthor_health_1996 + EUdataregulations2018 + PCI + cook_rage_2018 + berry_graph_2007 + ainsworth_graph_2016 + yao_efficient_2018 + dai_fpgp_2016 + arifuzzaman_fast_2015 + yu_construction_2018 + liakos_memory-optimized_2016 + balaji_graph_2016 + noauthor_overview_nodate + noauthor_boost_nodate + cook_scalable_2016 + li_concurrency_2019 + 9150145 + 7087377 + li_combining_2019 + CVE-2019-10747 + louthan_hybrid_2011 + pacheco_introduction_2011 + lawrence_livermore_national_laboratory_mpip_nodate + + + + + presort + + + sortkey + + + sortname + author + editor + translator + sorttitle + title + + + sorttitle + title + + + sortyear + year + + + volume + 0 + + + + + + diff --git a/Schrick-Noah_MS-Thesis.blg b/Schrick-Noah_MS-Thesis.blg index 9e70492..a46af98 100644 --- a/Schrick-Noah_MS-Thesis.blg +++ b/Schrick-Noah_MS-Thesis.blg @@ -9,52 +9,44 @@ A level-1 auxiliary file: Chapter5.aux A level-1 auxiliary file: Chapter6.aux The style file: ieeetr.bst Database file #1: Bibliography.bib -Warning--entry type for "j_hale_compliance_nodate" isn't style-file defined ---line 275 of file Bibliography.bib -Warning--entry type for "EUdataregulations2018" isn't style-file defined ---line 1253 of file Bibliography.bib -Warning--empty journal in ou_scalable_2006 -Warning--empty school in cook_rage_2018 -Warning--empty school in louthan_hybrid_2011 -You've used 30 entries, +You've used 32 entries, 1876 wiz_defined-function locations, - 624 strings with 9065 characters, -and the built_in function-call counts, 6551 in all, are: -= -- 612 -> -- 261 + 642 strings with 9940 characters, +and the built_in function-call counts, 6904 in all, are: += -- 666 +> -- 269 < -- 0 -+ -- 100 -- -- 70 -* -- 425 -:= -- 911 -add.period$ -- 30 -call.type$ -- 30 -change.case$ -- 28 ++ -- 104 +- -- 72 +* -- 432 +:= -- 966 +add.period$ -- 37 +call.type$ -- 32 +change.case$ -- 30 chr.to.int$ -- 0 -cite$ -- 33 -duplicate$ -- 333 -empty$ -- 695 -format.name$ -- 70 -if$ -- 1606 +cite$ -- 32 +duplicate$ -- 351 +empty$ -- 732 +format.name$ -- 72 +if$ -- 1704 int.to.chr$ -- 0 -int.to.str$ -- 30 -missing$ -- 19 -newline$ -- 96 -num.names$ -- 26 -pop$ -- 148 +int.to.str$ -- 32 +missing$ -- 22 +newline$ -- 110 +num.names$ -- 28 +pop$ -- 160 preamble$ -- 1 purify$ -- 0 quote$ -- 0 -skip$ -- 227 +skip$ -- 216 stack$ -- 0 substring$ -- 347 -swap$ -- 108 +swap$ -- 111 text.length$ -- 0 text.prefix$ -- 0 top$ -- 0 type$ -- 0 -warning$ -- 3 -while$ -- 60 -width$ -- 32 -write$ -- 250 -(There were 5 warnings) +warning$ -- 0 +while$ -- 62 +width$ -- 34 +write$ -- 282 diff --git a/Schrick-Noah_MS-Thesis.log b/Schrick-Noah_MS-Thesis.log index f1963c7..a6b51fa 100644 --- a/Schrick-Noah_MS-Thesis.log +++ b/Schrick-Noah_MS-Thesis.log @@ -1,4 +1,4 @@ -This is pdfTeX, Version 3.141592653-2.6-1.40.23 (TeX Live 2021/Arch Linux) (preloaded format=pdflatex 2022.3.21) 28 MAR 2022 00:06 +This is pdfTeX, Version 3.141592653-2.6-1.40.23 (TeX Live 2021/Arch Linux) (preloaded format=pdflatex 2022.3.21) 28 MAR 2022 03:00 entering extended mode restricted \write18 enabled. %&-line parsing enabled. @@ -81,45 +81,82 @@ Package caption Info: Standard document class detected. \c@subfigure=\count196 \c@subtable=\count197 ) -(/usr/share/texmf-dist/tex/latex/tocloft/tocloft.sty +(/usr/share/texmf-dist/tex/latex/algorithms/algorithm.sty +Package: algorithm 2009/08/24 v0.1 Document Style `algorithm' - floating enviro +nment + 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Pub. L. No. 107-204. 2002 [O +n-line]. Avail- + [] + + +Underfull \hbox (badness 10000) in paragraph at lines 46--49 +\OT1/cmr/m/n/12 able: https://www.govinfo.gov/content/pkg/PLAW-107publ204/html/ +PLAW- + [] + + +Underfull \hbox (badness 1137) in paragraph at lines 51--54 +[]\OT1/cmr/m/n/12 ``Health In-sur-ance Porta-bil-ity and Ac-count-abil-ity Act +of 1996.'' Pub. L. No. + [] + + +Underfull \hbox (badness 2119) in paragraph at lines 51--54 +\OT1/cmr/m/n/12 104-191. 1996 [On-line]. 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a/Schrick-Noah_MS-Thesis.tex b/Schrick-Noah_MS-Thesis.tex index dbe0725..fa836ff 100644 --- a/Schrick-Noah_MS-Thesis.tex +++ b/Schrick-Noah_MS-Thesis.tex @@ -92,7 +92,8 @@ \usepackage{boxedminipage} \usepackage{graphicx} \usepackage{subcaption} - +\usepackage{algorithm} +\usepackage[noend]{algpseudocode} % Added by Richard D Redner 2017-08-16 % If, in the List of Tables or List of Figures, the figure/table numbers @@ -154,7 +155,7 @@ \fifthmember{} % as needed \sixthmember{} % as needed -\numofpages{65} % number of pages in the document +\numofpages{71} % number of pages in the document \numofchapters=6 % number of chapters in the document \lastchapter{Conclusions and Future Works} % the title of the last numbered chapter \numofabstractwords{196} % number of words in the abstract