From 46d6a307ef54aaa29e31036ba77cdec7aeccc27e Mon Sep 17 00:00:00 2001 From: noah Date: Mon, 2 May 2022 15:17:51 -0500 Subject: [PATCH] Finishing Intro and Related Works --- Report/Bibliography.bib | 37 ++++++++++++ Report/Schrick-Noah_CS-7863_Final-Report.aux | 55 ++++++++++------- Report/Schrick-Noah_CS-7863_Final-Report.bbl | 31 ++++++++++ Report/Schrick-Noah_CS-7863_Final-Report.blg | 60 ++++++++++--------- Report/Schrick-Noah_CS-7863_Final-Report.log | 60 ++++++++----------- Report/Schrick-Noah_CS-7863_Final-Report.pdf | Bin 103964 -> 110956 bytes Report/Schrick-Noah_CS-7863_Final-Report.tex | 5 ++ Report/Schrick-Noah_CS-7863_Final-Report.toc | 36 +++++------ 8 files changed, 181 insertions(+), 103 deletions(-) diff --git a/Report/Bibliography.bib b/Report/Bibliography.bib index 65ae0c7..479b4ad 100644 --- a/Report/Bibliography.bib +++ b/Report/Bibliography.bib @@ -179,6 +179,13 @@ year = {2013}, } +@phdthesis{ming_diss, + title = {{A} {System} for {Attack} {Graph} {Generation} and {Analysis}}, + author = {Li, Ming}, + school = {The {University} of {Tulsa}}, + year = {2021}, +} + @article{edmonds_design_nodate, title = {Design of a {Large}-{Scale} {Hybrid}-{Parallel} {Graph} {Library}}, journal = {International Conference for High Performance Computing, Student Research Symposium}, @@ -1280,5 +1287,35 @@ of 27}, author = {PCI Security Standards Council} } +@article{centrality_causal, + title = {Node centrality measures are a poor substitute for causal inference}, + volume = {9}, + issn = {6846}, + doi = {10.1038/s41598-019-43033-9}, + journal = {Scientific Reports}, + author = {Dablander, Fabian and Hinne, Max}, + year = {2019}, +} +@inproceedings{Mieghem2018DirectedGA, + title={Directed graphs and mysterious complex eigenvalues}, + author={Piet Van Mieghem}, + year={2018} +} +@article{Guo2017HermitianAM, + title={Hermitian Adjacency Matrix of Digraphs and Mixed Graphs}, + author={Krystal Guo and Bojan Mohar}, + journal={Journal of Graph Theory}, + year={2017}, + volume={85} +} + +@article{Brualdi2010SpectraOD, + title={Spectra of digraphs}, + author={Richard A. Brualdi}, + journal={Linear Algebra and its Applications}, + year={2010}, + volume={432}, + pages={2181-2213} +} \ No newline at end of file diff --git a/Report/Schrick-Noah_CS-7863_Final-Report.aux b/Report/Schrick-Noah_CS-7863_Final-Report.aux index dabb889..3fd6781 100644 --- a/Report/Schrick-Noah_CS-7863_Final-Report.aux +++ b/Report/Schrick-Noah_CS-7863_Final-Report.aux @@ -1,36 +1,49 @@ \relax \providecommand\babel@aux[2]{} \@nameuse{bbl@beforestart} +\babel@aux{nil}{} \citation{phillips_graph-based_1998} \citation{schneier_modeling_1999} -\babel@aux{nil}{} \citation{j_hale_compliance_nodate} \citation{baloyi_guidelines_2019} \citation{allman_complying_2006} \@writefile{toc}{\contentsline {section}{\numberline {1}Introduction}{2}{}\protected@file@percent } \@writefile{toc}{\contentsline {subsection}{\numberline {1.1}Attack Graphs}{2}{}\protected@file@percent } \@writefile{toc}{\contentsline {subsection}{\numberline {1.2}Compliance Graphs}{2}{}\protected@file@percent } +\citation{Mieghem2018DirectedGA} +\citation{Mieghem2018DirectedGA} +\citation{ming_diss} +\citation{Guo2017HermitianAM} +\citation{Mieghem2018DirectedGA} +\citation{Brualdi2010SpectraOD} +\@writefile{toc}{\contentsline {subsection}{\numberline {1.3}Difficulties of Compliance Graph Analysis}{3}{}\protected@file@percent } +\@writefile{toc}{\contentsline {section}{\numberline {2}Related Works}{3}{}\protected@file@percent } +\@writefile{toc}{\contentsline {section}{\numberline {3}Experimental Networks}{4}{}\protected@file@percent } +\@writefile{toc}{\contentsline {section}{\numberline {4}Centralities}{5}{}\protected@file@percent } +\@writefile{toc}{\contentsline {subsection}{\numberline {4.1}Introduction}{5}{}\protected@file@percent } +\@writefile{toc}{\contentsline {subsection}{\numberline {4.2}Degree}{5}{}\protected@file@percent } +\@writefile{toc}{\contentsline {subsection}{\numberline {4.3}Betweenness}{5}{}\protected@file@percent } +\@writefile{toc}{\contentsline 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Analysis}{5}{}\protected@file@percent } +\@writefile{toc}{\contentsline {section}{\numberline {8}Conclusions and Future Work}{5}{}\protected@file@percent } \bibdata{Bibliography} \bibcite{phillips_graph-based_1998}{1} -\@writefile{toc}{\contentsline {subsection}{\numberline {1.3}Difficulties of Compliance Graph Analysis}{4}{}\protected@file@percent } -\@writefile{toc}{\contentsline {section}{\numberline {2}Related Works}{4}{}\protected@file@percent } -\@writefile{toc}{\contentsline {section}{\numberline {3}Experimental Networks}{4}{}\protected@file@percent } -\@writefile{toc}{\contentsline {section}{\numberline {4}Centralities}{4}{}\protected@file@percent } -\@writefile{toc}{\contentsline {subsection}{\numberline {4.1}Introduction}{4}{}\protected@file@percent } -\@writefile{toc}{\contentsline {subsection}{\numberline {4.2}Degree}{4}{}\protected@file@percent } -\@writefile{toc}{\contentsline {subsection}{\numberline {4.3}Betweenness}{4}{}\protected@file@percent } -\@writefile{toc}{\contentsline {subsection}{\numberline {4.4}Katz}{4}{}\protected@file@percent } -\@writefile{toc}{\contentsline {subsection}{\numberline {4.5}K-Path Edge}{4}{}\protected@file@percent } -\@writefile{toc}{\contentsline {subsection}{\numberline {4.6}Adapted Page Rank}{4}{}\protected@file@percent } -\@writefile{toc}{\contentsline {section}{\numberline {5}Transitive Closure}{4}{}\protected@file@percent } -\@writefile{toc}{\contentsline {subsection}{\numberline {5.1}Introduction}{4}{}\protected@file@percent } -\@writefile{toc}{\contentsline {subsection}{\numberline {5.2}Application}{4}{}\protected@file@percent } -\@writefile{toc}{\contentsline {section}{\numberline {6}Dominant Tree}{4}{}\protected@file@percent } -\@writefile{toc}{\contentsline {subsection}{\numberline {6.1}Introduction}{4}{}\protected@file@percent } -\@writefile{toc}{\contentsline {subsection}{\numberline {6.2}Application}{4}{}\protected@file@percent } -\@writefile{toc}{\contentsline {section}{\numberline {7}Results and Result Analysis}{4}{}\protected@file@percent } -\@writefile{toc}{\contentsline {section}{\numberline {8}Conclusions and Future Work}{4}{}\protected@file@percent } -\@writefile{toc}{\contentsline {section}{Bibliography}{4}{}\protected@file@percent } \bibcite{schneier_modeling_1999}{2} +\bibcite{j_hale_compliance_nodate}{3} +\bibcite{baloyi_guidelines_2019}{4} +\bibcite{allman_complying_2006}{5} +\bibcite{Mieghem2018DirectedGA}{6} +\bibcite{ming_diss}{7} +\bibcite{Guo2017HermitianAM}{8} +\bibcite{Brualdi2010SpectraOD}{9} \bibstyle{ieeetr} -\gdef \@abspage@last{5} +\@writefile{toc}{\contentsline {section}{Bibliography}{6}{}\protected@file@percent } +\gdef \@abspage@last{6} diff --git a/Report/Schrick-Noah_CS-7863_Final-Report.bbl b/Report/Schrick-Noah_CS-7863_Final-Report.bbl index 303d778..eb3860b 100644 --- a/Report/Schrick-Noah_CS-7863_Final-Report.bbl +++ b/Report/Schrick-Noah_CS-7863_Final-Report.bbl @@ -10,4 +10,35 @@ C.~Phillips and L.~P. Swiler, ``A graph-based system for network-vulnerability B.~Schneier, ``Modeling {Security} {Threats},'' {\em Dr. Dobb's Journal}, 1999. \newblock vol. 24, no.12. +\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} + {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{Mieghem2018DirectedGA} +P.~V. Mieghem, ``Directed graphs and mysterious complex eigenvalues,'' 2018. + +\bibitem{ming_diss} +M.~Li, {\em {A} {System} for {Attack} {Graph} {Generation} and {Analysis}}. +\newblock PhD thesis, The {University} of {Tulsa}, 2021. + +\bibitem{Guo2017HermitianAM} +K.~Guo and B.~Mohar, ``Hermitian adjacency matrix of digraphs and mixed + graphs,'' {\em Journal of Graph Theory}, vol.~85, 2017. + +\bibitem{Brualdi2010SpectraOD} +R.~A. Brualdi, ``Spectra of digraphs,'' {\em Linear Algebra and its + Applications}, vol.~432, pp.~2181--2213, 2010. + \end{thebibliography} diff --git a/Report/Schrick-Noah_CS-7863_Final-Report.blg b/Report/Schrick-Noah_CS-7863_Final-Report.blg index 4450f72..dbe2f82 100644 --- a/Report/Schrick-Noah_CS-7863_Final-Report.blg +++ b/Report/Schrick-Noah_CS-7863_Final-Report.blg @@ -3,44 +3,46 @@ Capacity: max_strings=200000, hash_size=200000, hash_prime=170003 The top-level auxiliary file: Schrick-Noah_CS-7863_Final-Report.aux The style file: ieeetr.bst Database file #1: Bibliography.bib -You've used 2 entries, +Warning--empty booktitle in Mieghem2018DirectedGA +You've used 9 entries, 1876 wiz_defined-function locations, - 491 strings with 3842 characters, -and the built_in function-call counts, 464 in all, are: -= -- 49 -> -- 12 + 534 strings with 4972 characters, +and the built_in function-call counts, 1708 in all, are: += -- 166 +> -- 55 < -- 0 -+ -- 5 -- -- 3 -* -- 28 -:= -- 76 -add.period$ -- 4 -call.type$ -- 2 -change.case$ -- 2 ++ -- 23 +- -- 14 +* -- 104 +:= -- 261 +add.period$ -- 12 +call.type$ -- 9 +change.case$ -- 8 chr.to.int$ -- 0 -cite$ -- 2 -duplicate$ -- 24 -empty$ -- 45 -format.name$ -- 3 -if$ -- 110 +cite$ -- 10 +duplicate$ -- 97 +empty$ -- 187 +format.name$ -- 14 +if$ -- 414 int.to.chr$ -- 0 -int.to.str$ -- 2 -missing$ -- 2 -newline$ -- 11 -num.names$ -- 2 -pop$ -- 4 +int.to.str$ -- 9 +missing$ -- 7 +newline$ -- 34 +num.names$ -- 9 +pop$ -- 36 preamble$ -- 1 purify$ -- 0 quote$ -- 0 -skip$ -- 13 +skip$ -- 42 stack$ -- 0 -substring$ -- 24 -swap$ -- 8 +substring$ -- 60 +swap$ -- 23 text.length$ -- 0 text.prefix$ -- 0 top$ -- 0 type$ -- 0 -warning$ -- 0 -while$ -- 5 -width$ -- 3 -write$ -- 24 +warning$ -- 1 +while$ -- 14 +width$ -- 10 +write$ -- 88 +(There was 1 warning) diff --git a/Report/Schrick-Noah_CS-7863_Final-Report.log b/Report/Schrick-Noah_CS-7863_Final-Report.log index d27c69f..a2199d9 100644 --- a/Report/Schrick-Noah_CS-7863_Final-Report.log +++ b/Report/Schrick-Noah_CS-7863_Final-Report.log @@ -1,4 +1,4 @@ -This is pdfTeX, Version 3.141592653-2.6-1.40.24 (TeX Live 2022/Arch Linux) (preloaded format=pdflatex 2022.4.29) 2 MAY 2022 12:56 +This is pdfTeX, Version 3.141592653-2.6-1.40.24 (TeX Live 2022/Arch Linux) (preloaded format=pdflatex 2022.4.29) 2 MAY 2022 15:13 entering extended mode restricted \write18 enabled. %&-line parsing enabled. @@ -278,33 +278,21 @@ LaTeX Font Info: External font `cmex10' loaded for size \tf@toc=\write3 \openout3 = `Schrick-Noah_CS-7863_Final-Report.toc'. + [1 +{/var/lib/texmf/fonts/map/pdftex/updmap/pdftex.map}] Overfull \hbox (21.08397pt too wide) in paragraph at lines 33--34 []\OT1/cmr/m/n/10 To address the rising risks of computing and threats to cyber security, vulnerability [] -[1 -{/var/lib/texmf/fonts/map/pdftex/updmap/pdftex.map}] Overfull \hbox (3.02843pt too wide) in paragraph at lines 35--36 []\OT1/cmr/m/n/10 Attack graphs begin with a root node that contains all the cu rrent information [] -LaTeX Warning: Citation `j_hale_compliance_nodate' on page 2 undefined on input - line 38. - - -LaTeX Warning: Citation `baloyi_guidelines_2019' on page 2 undefined on input l -ine 38. - - -LaTeX Warning: Citation `allman_complying_2006' on page 2 undefined on input li -ne 38. - - Overfull \hbox (2.19508pt too wide) in paragraph at lines 38--39 []\OT1/cmr/m/n/10 Compliance graphs are an alternate form of attack graphs, uti lized specifically @@ -328,33 +316,35 @@ Overfull \hbox (2.69524pt too wide) in paragraph at lines 40--41 n, the information [] -[2] (./Schrick-Noah_CS-7863_Final-Report.bbl [3] -Overfull \vbox (137.26349pt too high) has occurred while \output is active [] +[2] +Overfull \hbox (18.35255pt too wide) in paragraph at lines 43--44 +\OT1/cmr/m/n/10 adjacency matrix present in directed graphs. 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While security and compliance statuses are related, the information that is analyzed in compliance graphs is focused less on certain security properties, and is expanded to also examine administrative policies and properties of systems. Since compliance and regulation is broad and can vary by industry and application, the information to analyze can range from safety regulations, maintenance compliance, or any other regulatory compliance. However, the graph structure of compliance graphs is identical to that of attack graphs, where edges represent a modification to the systems, and nodes represent all current information in the system. \subsection{Difficulties of Compliance Graph Analysis} +Analysis of directed graphs is not as simple as their undirected counterparts, and attack and compliance graphs are directed acyclic graphs. The primary contributor to the increased difficulty is due to the asymmetric adjacency matrix present in directed graphs. With undirected graphs, simplifications can be made in the analysis process both computationally and conceptually. Since the ``in" degrees are equal to the ``out" degrees, less work is required both in terms of parsing the adjacency matrix, but also in terms of determining importance of nodes. As the author of \cite{Mieghem2018DirectedGA} discusses, the difficulty of directed graphs also extends to the graph Laplacian, where the definition for asymmetric adjacency matrices is not uniquely defined, and is based on either row or column sums computing to zero, but both cannot. The author of \cite{Mieghem2018DirectedGA} continues to discuss that directed graphs lead to complex eigenvalues, and can lead to adjacency matrices that are unable to be diagonalized. These challenges require different approaches for typical clustering or centrality measures. \section{Related Works} +The author of \cite{ming_diss} presents three centrality measures that were applied to various attack graphs. The centrality measures implemented were Katz, K-path Edge, and Adapted PageRank. Each of these centrality measures are applicable to the directed format of attack graphs, and conclusions can be drawn regarding patching schemes for preventing exploits. As an approach for avoiding complex eigenvalues, the authors of \cite{Guo2017HermitianAM} present work examining directed, undirected, and mixed graphs using its Hermitian adjacency matrix. Other works, such as that discussed by the author of \cite{Mieghem2018DirectedGA} include mathematical manipulation of directed graph spectra (originally presented by the author of \cite{Brualdi2010SpectraOD}) with Schur's Theorem to bound eigenvalues and allow for explicit computation, which can then be used for additional analysis metrics. \section{Experimental Networks} +The work conducted in this approach \section{Centralities} \subsection{Introduction} @@ -65,6 +68,8 @@ The semantics of compliance graphs are similar to that of attack graphs, but wit \section{Conclusions and Future Work} +\clearpage + \addcontentsline{toc}{section}{Bibliography} \bibliography{Bibliography} \bibliographystyle{ieeetr} diff --git a/Report/Schrick-Noah_CS-7863_Final-Report.toc b/Report/Schrick-Noah_CS-7863_Final-Report.toc index 1214b1f..e51cfa1 100644 --- a/Report/Schrick-Noah_CS-7863_Final-Report.toc +++ b/Report/Schrick-Noah_CS-7863_Final-Report.toc @@ -2,22 +2,22 @@ \contentsline {section}{\numberline {1}Introduction}{2}{}% \contentsline {subsection}{\numberline {1.1}Attack Graphs}{2}{}% \contentsline {subsection}{\numberline {1.2}Compliance Graphs}{2}{}% -\contentsline {subsection}{\numberline {1.3}Difficulties of Compliance Graph Analysis}{4}{}% -\contentsline {section}{\numberline {2}Related Works}{4}{}% +\contentsline {subsection}{\numberline {1.3}Difficulties of Compliance Graph Analysis}{3}{}% +\contentsline {section}{\numberline {2}Related Works}{3}{}% \contentsline {section}{\numberline {3}Experimental Networks}{4}{}% -\contentsline {section}{\numberline {4}Centralities}{4}{}% -\contentsline {subsection}{\numberline {4.1}Introduction}{4}{}% -\contentsline {subsection}{\numberline {4.2}Degree}{4}{}% -\contentsline {subsection}{\numberline {4.3}Betweenness}{4}{}% -\contentsline {subsection}{\numberline {4.4}Katz}{4}{}% -\contentsline {subsection}{\numberline {4.5}K-Path Edge}{4}{}% -\contentsline {subsection}{\numberline {4.6}Adapted Page Rank}{4}{}% -\contentsline {section}{\numberline {5}Transitive Closure}{4}{}% -\contentsline {subsection}{\numberline {5.1}Introduction}{4}{}% -\contentsline {subsection}{\numberline {5.2}Application}{4}{}% -\contentsline {section}{\numberline {6}Dominant Tree}{4}{}% -\contentsline {subsection}{\numberline {6.1}Introduction}{4}{}% -\contentsline {subsection}{\numberline {6.2}Application}{4}{}% -\contentsline {section}{\numberline {7}Results and Result Analysis}{4}{}% -\contentsline {section}{\numberline {8}Conclusions and Future Work}{4}{}% -\contentsline {section}{Bibliography}{4}{}% +\contentsline {section}{\numberline {4}Centralities}{5}{}% +\contentsline {subsection}{\numberline {4.1}Introduction}{5}{}% +\contentsline {subsection}{\numberline {4.2}Degree}{5}{}% +\contentsline {subsection}{\numberline {4.3}Betweenness}{5}{}% +\contentsline {subsection}{\numberline {4.4}Katz}{5}{}% +\contentsline {subsection}{\numberline {4.5}K-Path Edge}{5}{}% +\contentsline {subsection}{\numberline {4.6}Adapted Page Rank}{5}{}% +\contentsline {section}{\numberline {5}Transitive Closure}{5}{}% +\contentsline {subsection}{\numberline {5.1}Introduction}{5}{}% +\contentsline {subsection}{\numberline {5.2}Application}{5}{}% +\contentsline {section}{\numberline {6}Dominant Tree}{5}{}% +\contentsline {subsection}{\numberline {6.1}Introduction}{5}{}% +\contentsline {subsection}{\numberline {6.2}Application}{5}{}% +\contentsline {section}{\numberline {7}Results and Result Analysis}{5}{}% +\contentsline {section}{\numberline {8}Conclusions and Future Work}{5}{}% +\contentsline {section}{Bibliography}{6}{}%