X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/16dcc.git/blobdiff_plain/19a155db210ef35cc04c0184f35ffd12a014a855..e1fe6e435ee452003a7135763d26e2320756398c:/main.aux?ds=sidebyside diff --git a/main.aux b/main.aux deleted file mode 100644 index 0bd4d61..0000000 --- a/main.aux +++ /dev/null @@ -1,119 +0,0 @@ -\relax -\citation{915396,915385,5376454} -\citation{915396,915385} -\citation{5376454} -\citation{Marsaglia1996} -\citation{Nist10} -\citation{LEcuyerS07} -\citation{Devaney} -\select@language{english} -\@writefile{toc}{\select@language{english}} -\@writefile{lof}{\select@language{english}} -\@writefile{lot}{\select@language{english}} -\@writefile{toc}{\contentsline {section}{\tocsection {}{1}{Introduction}}{1}} -\citation{guyeuxTaiwan10,bcgr11:ip} -\citation{wbg10ip} -\citation{chgw14oip} -\citation{bcgr11:ip} -\citation{chgw14oip} -\citation{chgw14oip} -\citation{DBLP:conf/secrypt/CouchotHGWB14} -\@writefile{toc}{\contentsline {section}{\tocsection {}{2}{Preliminaries}}{3}} -\newlabel{sec:preliminaries}{{2}{3}} -\newlabel{eq:asyn}{{1}{3}} -\citation{bcgr11:ip} -\citation{bcgr11:ip} -\@writefile{lof}{\contentsline {figure}{\numberline {1}{\ignorespaces Iteration Graph $\Gamma (f^*)$ of the function $f^*$\relax }}{4}} -\providecommand*\caption@xref[2]{\@setref\relax\@undefined{#1}} -\newlabel{fig:iteration:f*}{{1}{4}} -\@writefile{loa}{\contentsline {algocf}{\numberline {1}{\ignorespaces Pseudo Code of the $\chi _{\textit {14Secrypt}}$ PRNG\relax }}{4}} -\newlabel{CI Algorithm}{{1}{4}} -\@writefile{toc}{\contentsline {section}{\tocsection {}{3}{Proof Of Chaos}}{4}} -\newlabel{sec:proofOfChaos}{{3}{4}} -\citation{Devaney} -\citation{Banks92} -\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{3.1}{Devaney's Chaotic Dynamical Systems}}{5}} -\newlabel{subsec:Devaney}{{3.1}{5}} -\newlabel{sensitivity}{{3.5}{5}} -\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{3.2}{A Metric Space for PRNG Iterations}}{5}} -\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{3.3}{A metric on $\mathcal {X}_{\mathsf {N},\mathcal {P}}$}}{6}} -\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{3.4}{$\Gamma _{\mathcal {P}}(f)$ as an extension of $\Gamma (f)$}}{8}} -\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{3.5}{Proofs of chaos}}{8}} -\newlabel{graphe1}{{2a}{9}} -\newlabel{sub@graphe1}{{a}{9}} -\newlabel{graphe2}{{2b}{9}} -\newlabel{sub@graphe2}{{b}{9}} -\@writefile{lof}{\contentsline {figure}{\numberline {2}{\ignorespaces Iterating $f_0:(x_1,x_2) \DOTSB \mapstochar \rightarrow (\overline {x_1}, \overline {x_2})$\relax }}{9}} -\newlabel{fig:itg}{{2}{9}} -\newlabel{prop:trans}{{3.8}{9}} -\citation{bcgr11:ip} -\citation{DBLP:conf/secrypt/CouchotHGWB14} -\@writefile{toc}{\contentsline {section}{\tocsection {}{4}{Functions with Strongly Connected $\Gamma _{\{b\}}(f)$}}{10}} -\newlabel{sec:SCCfunc}{{4}{10}} -\citation{bcgr11:ip} -\citation{Robinson:1981:CS,DBLP:journals/combinatorics/BhatS96,ZanSup04,Bykov2016} -\citation{DBLP:journals/combinatorics/BhatS96,ZanSup04} -\citation{Bykov2016} -\citation{ZanSup04,DBLP:journals/combinatorics/BhatS96} -\citation{Bykov2016} -\citation{ZanSup04} -\@writefile{toc}{\contentsline {section}{\tocsection {}{5}{(Locally) Balanced Hamiltonian Cycle}}{11}} -\newlabel{sec:hamilton}{{5}{11}} -\citation{Robinson:1981:CS} -\citation{DBLP:journals/combinatorics/BhatS96} -\citation{ZanSup04} -\citation{Robinson:1981:CS} -\citation{DBLP:journals/combinatorics/BhatS96} -\citation{ZanSup04} -\citation{ZanSup04} -\citation{ZanSup04} -\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{5.1}{Analysis of the Robinson-Cohn extension algorithm}}{12}} -\newlabel{item:nondet}{{1}{12}} -\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{5.2}{Balanced Codes}}{12}} -\newlabel{prop:balanced}{{5.1}{13}} -\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{5.3}{Toward a local uniform distribution of switches}}{13}} -\@writefile{toc}{\contentsline {section}{\tocsection {}{6}{Stopping Time}}{13}} -\newlabel{sec:hypercube}{{6}{13}} -\citation{LevinPeresWilmer2006} -\newlabel{eq:Markov:rairo}{{3}{15}} -\newlabel{lm:h}{{6.2}{15}} -\citation{proba} -\newlabel{prop:stop}{{6.4}{16}} -\newlabel{prop:lambda}{{6.5}{16}} -\newlabel{lm:stopprime}{{6.6}{17}} -\@writefile{toc}{\contentsline {section}{\tocsection {}{7}{Experiments}}{18}} -\newlabel{sec:prng}{{7}{18}} -\@writefile{loa}{\contentsline {algocf}{\numberline {2}{\ignorespaces Pseudo Code of the $\chi _{\textit {15Rairo}}$ PRNG\relax }}{18}} -\newlabel{CI Algorithm:2}{{2}{18}} -\@writefile{lot}{\contentsline {table}{\numberline {1}{\ignorespaces Functions with DSCC Matrix and smallest MT\relax }}{19}} -\newlabel{table:nc}{{1}{19}} -\bibstyle{alpha} -\bibdata{biblio} -\bibcite{Banks92}{BBCS92} -\@writefile{lot}{\contentsline {table}{\numberline {2}{\ignorespaces NIST SP 800-22 test results ($\mathbb {P}_T$)\relax }}{20}} -\newlabel{The passing rate}{{2}{20}} -\@writefile{toc}{\contentsline {section}{\tocsection {}{8}{Conclusion}}{20}} -\bibcite{bcgr11:ip}{BCGR11} -\bibcite{Nist10}{BR10} -\bibcite{DBLP:journals/combinatorics/BhatS96}{BS96} -\bibcite{Bykov2016}{Byk16} -\bibcite{chgw14oip}{CHG{$^{+}$}14a} -\bibcite{DBLP:conf/secrypt/CouchotHGWB14}{CHG{$^{+}$}14b} -\bibcite{5376454}{CMZ09} -\bibcite{Devaney}{Dev89} -\bibcite{guyeuxTaiwan10}{GWB10} -\bibcite{LevinPeresWilmer2006}{LPW06} -\bibcite{LEcuyerS07}{LS07} -\bibcite{Marsaglia1996}{Mar96} -\bibcite{proba}{MU05} -\bibcite{Robinson:1981:CS}{RC81} -\bibcite{915385}{SK01} -\bibcite{915396}{SPK01} -\bibcite{ZanSup04}{SZ04} -\bibcite{wbg10ip}{WBGF10} -\@writefile{toc}{\contentsline {section}{\tocsection {}{}{References}}{21}} -\newlabel{tocindent-1}{0pt} -\newlabel{tocindent0}{12.77466pt} -\newlabel{tocindent1}{17.77344pt} -\newlabel{tocindent2}{25.54932pt} -\newlabel{tocindent3}{0pt}