\@writefile{toc}{\contentsline {section}{\tocsection {}{1}{Introduction}}{1}}
\citation{guyeuxTaiwan10,bcgr11:ip}
\citation{wbg10ip}
-\citation{chgw14oip}
+\citation{DBLP:conf/secrypt/CouchotHGWB14}
+\citation{bcgr11:ip}
\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{DBLP:conf/secrypt/CouchotHGWB14}
\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{CI Algorithm}{{1}{4}}
\@writefile{toc}{\contentsline {section}{\tocsection {}{3}{Proof Of Chaos}}{4}}
\newlabel{sec:proofOfChaos}{{3}{4}}
+\citation{bcgr11:ip}
\citation{Devaney}
\citation{Banks92}
\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{3.1}{Devaney's Chaotic Dynamical Systems}}{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}}
+\@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}
\citation{Robinson:1981:CS,DBLP:journals/combinatorics/BhatS96,ZanSup04,Bykov2016}
\citation{DBLP:journals/combinatorics/BhatS96,ZanSup04}
\citation{Bykov2016}
+\@writefile{toc}{\contentsline {section}{\tocsection {}{4}{Functions with Strongly Connected $\Gamma _{\{b\}}(f)$}}{11}}
+\newlabel{sec:SCCfunc}{{4}{11}}
+\@writefile{toc}{\contentsline {section}{\tocsection {}{5}{Balanced Hamiltonian Cycle}}{11}}
+\newlabel{sec:hamilton}{{5}{11}}
\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{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}}
+\citation{ZanSup04}
+\newlabel{item:u'}{{2}{13}}
+\newlabel{item:VW}{{3}{13}}
+\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{5.2}{Balanced Codes}}{13}}
\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}}
+\newlabel{eq:sys:zt1}{{3}{14}}
+\newlabel{eq:sys:zt2}{{4}{14}}
+\newlabel{eq:TCN:def}{{5}{15}}
+\@writefile{toc}{\contentsline {section}{\tocsection {}{6}{Stopping Time}}{15}}
+\newlabel{sec:hypercube}{{6}{15}}
\citation{LevinPeresWilmer2006}
-\newlabel{eq:Markov:rairo}{{3}{15}}
-\newlabel{lm:h}{{6.2}{15}}
+\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{6.1}{Formalizing the Random Walk}}{16}}
+\newlabel{sub:stop:formal}{{6.1}{16}}
+\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{6.2}{Upper bound of Stopping Time}}{17}}
+\newlabel{sub:stop:bound}{{6.2}{17}}
+\newlabel{eq:Markov:rairo}{{6}{17}}
+\newlabel{lm:h}{{6.2}{17}}
+\newlabel{prop:stop}{{6.4}{18}}
+\newlabel{prop:lambda}{{6.5}{18}}
\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}}
+\newlabel{lm:stopprime}{{6.6}{19}}
+\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{6.3}{Practical Evaluation of Stopping Times}}{20}}
+\newlabel{sub:stop:exp}{{6.3}{20}}
+\@writefile{loa}{\contentsline {algocf}{\numberline {2}{\ignorespaces Pseudo Code of the stoping time calculus\relax }}{20}}
+\newlabel{algo:stop}{{2}{20}}
+\@writefile{lot}{\contentsline {table}{\numberline {1}{\ignorespaces Average Stopping Time\relax }}{21}}
+\newlabel{table:stopping:moy}{{1}{21}}
+\@writefile{toc}{\contentsline {section}{\tocsection {}{7}{Experiments}}{21}}
+\newlabel{sec:prng}{{7}{21}}
+\@writefile{loa}{\contentsline {algocf}{\numberline {3}{\ignorespaces Pseudo Code of the $\chi _{\textit {15Rairo}}$ PRNG\relax }}{21}}
+\newlabel{CI Algorithm:2}{{3}{21}}
+\@writefile{lot}{\contentsline {table}{\numberline {2}{\ignorespaces Functions with DSCC Matrix and smallest MT\relax }}{22}}
+\newlabel{table:nc}{{2}{22}}
\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}}
+\@writefile{lot}{\contentsline {table}{\numberline {3}{\ignorespaces NIST SP 800-22 test results ($\mathbb {P}_T$)\relax }}{23}}
+\newlabel{The passing rate}{{3}{23}}
+\@writefile{toc}{\contentsline {section}{\tocsection {}{8}{Conclusion}}{23}}
\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{DBLP:conf/secrypt/CouchotHGWB14}{CHG{$^{+}$}14}
\bibcite{5376454}{CMZ09}
\bibcite{Devaney}{Dev89}
\bibcite{guyeuxTaiwan10}{GWB10}
\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}
+\@writefile{toc}{\contentsline {section}{\tocsection {}{}{References}}{24}}
