Merge branch 'master' of ssh://bilbo.iut-bm.univ-fcomte.fr/16dcc

[16dcc.git] / main.aux

diff --git a/main.aux b/main.aux
index 9cfaa3d00646f6c701127c6b9302db459ad4c9f5..0bd4d611def5da4811adfd65946c11d159577440 100644 (file)
--- a/main.aux
+++ b/main.aux
@@ -18,7 +18,7 @@
 \citation{chgw14oip}
 \citation{chgw14oip}
 \citation{DBLP:conf/secrypt/CouchotHGWB14}
 \citation{chgw14oip}
 \citation{chgw14oip}
 \citation{DBLP:conf/secrypt/CouchotHGWB14}

-\@writefile{toc}{\contentsline {section}{\tocsection {}{2}{\uppercase {Preliminaries}}}{3}}
+\@writefile{toc}{\contentsline {section}{\tocsection {}{2}{Preliminaries}}{3}}

 \newlabel{sec:preliminaries}{{2}{3}}
 \newlabel{eq:asyn}{{1}{3}}
 \citation{bcgr11:ip}
 \newlabel{sec:preliminaries}{{2}{3}}
 \newlabel{eq:asyn}{{1}{3}}
 \citation{bcgr11:ip}


@@ -38,46 +38,67 @@
 \@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 {}{3.2}{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{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}}

-\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{3.5}{Proofs of chaos}}{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}
 \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{DBLP:conf/secrypt/CouchotHGWB14}
-\@writefile{toc}{\contentsline {section}{\tocsection {}{5}{Stopping Time}}{11}}
-\newlabel{sec:hypercube}{{5}{11}}
+\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}
 \citation{LevinPeresWilmer2006}

-\newlabel{eq:Markov:rairo}{{3}{13}}
-\newlabel{lm:h}{{5.2}{13}}
+\newlabel{eq:Markov:rairo}{{3}{15}}
+\newlabel{lm:h}{{6.2}{15}}

 \citation{proba}
 \citation{proba}

-\newlabel{prop:stop}{{5.4}{14}}
-\newlabel{prop:lambda}{{5.5}{14}}
-\newlabel{lm:stopprime}{{5.6}{15}}
-\@writefile{toc}{\contentsline {section}{\tocsection {}{6}{Experiments}}{15}}
-\newlabel{sec:prng}{{6}{15}}
-\@writefile{loa}{\contentsline {algocf}{\numberline {2}{\ignorespaces Pseudo Code of the $\chi _{\textit  {15Rairo}}$ PRNG\relax }}{16}}
-\newlabel{CI Algorithm:2}{{2}{16}}
-\@writefile{lot}{\contentsline {table}{\numberline {1}{\ignorespaces Functions with DSCC Matrix and smallest MT\relax }}{17}}
-\newlabel{table:nc}{{1}{17}}
-\@writefile{toc}{\contentsline {section}{\tocsection {}{7}{Conclusion}}{17}}
+\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}
 \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{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{chgw14oip}{CHG{$^{+}$}14a}
 \bibcite{DBLP:conf/secrypt/CouchotHGWB14}{CHG{$^{+}$}14b}

-\@writefile{lot}{\contentsline {table}{\numberline {2}{\ignorespaces NIST SP 800-22 test results ($\mathbb  {P}_T$)\relax }}{18}}
-\newlabel{The passing rate}{{2}{18}}
-\@writefile{toc}{\contentsline {section}{\tocsection {}{}{References}}{18}}

 \bibcite{5376454}{CMZ09}
 \bibcite{Devaney}{Dev89}
 \bibcite{guyeuxTaiwan10}{GWB10}
 \bibcite{5376454}{CMZ09}
 \bibcite{Devaney}{Dev89}
 \bibcite{guyeuxTaiwan10}{GWB10}


@@ -85,11 +106,14 @@
 \bibcite{LEcuyerS07}{LS07}
 \bibcite{Marsaglia1996}{Mar96}
 \bibcite{proba}{MU05}
 \bibcite{LEcuyerS07}{LS07}
 \bibcite{Marsaglia1996}{Mar96}
 \bibcite{proba}{MU05}

+\bibcite{Robinson:1981:CS}{RC81}

 \bibcite{915385}{SK01}
 \bibcite{915396}{SPK01}
 \bibcite{915385}{SK01}
 \bibcite{915396}{SPK01}

+\bibcite{ZanSup04}{SZ04}

 \bibcite{wbg10ip}{WBGF10}
 \bibcite{wbg10ip}{WBGF10}

+\@writefile{toc}{\contentsline {section}{\tocsection {}{}{References}}{21}}

 \newlabel{tocindent-1}{0pt}
 \newlabel{tocindent-1}{0pt}

-\newlabel{tocindent0}{13.28564pt}
-\newlabel{tocindent1}{18.39551pt}
-\newlabel{tocindent2}{26.57129pt}
+\newlabel{tocindent0}{12.77466pt}
+\newlabel{tocindent1}{17.77344pt}
+\newlabel{tocindent2}{25.54932pt}

 \newlabel{tocindent3}{0pt}
 \newlabel{tocindent3}{0pt}