main.aux

   1 \relax
   2 \citation{915396,915385,5376454}
   3 \citation{915396,915385}
   4 \citation{5376454}
   5 \citation{Marsaglia1996}
   6 \citation{Nist10}
   7 \citation{LEcuyerS07}
   8 \citation{Devaney}
   9 \select@language{english}
  10 \@writefile{toc}{\select@language{english}}
  11 \@writefile{lof}{\select@language{english}}
  12 \@writefile{lot}{\select@language{english}}
  13 \@writefile{toc}{\contentsline {section}{\tocsection {}{1}{Introduction}}{1}}
  14 \citation{guyeuxTaiwan10,bcgr11:ip}
  15 \citation{wbg10ip}
  16 \citation{chgw14oip}
  17 \citation{bcgr11:ip}
  18 \citation{chgw14oip}
  19 \citation{chgw14oip}
  20 \citation{DBLP:conf/secrypt/CouchotHGWB14}
  21 \@writefile{toc}{\contentsline {section}{\tocsection {}{2}{Preliminaries}}{3}}
  22 \newlabel{sec:preliminaries}{{2}{3}}
  23 \newlabel{eq:asyn}{{1}{3}}
  24 \citation{bcgr11:ip}
  25 \citation{bcgr11:ip}
  26 \@writefile{lof}{\contentsline {figure}{\numberline {1}{\ignorespaces Iteration Graph $\Gamma (f^*)$ of the function $f^*$\relax }}{4}}
  27 \providecommand*\caption@xref[2]{\@setref\relax\@undefined{#1}}
  28 \newlabel{fig:iteration:f*}{{1}{4}}
  29 \@writefile{loa}{\contentsline {algocf}{\numberline {1}{\ignorespaces Pseudo Code of the $\chi _{\textit  {14Secrypt}}$ PRNG\relax }}{4}}
  30 \newlabel{CI Algorithm}{{1}{4}}
  31 \@writefile{toc}{\contentsline {section}{\tocsection {}{3}{Proof Of Chaos}}{4}}
  32 \newlabel{sec:proofOfChaos}{{3}{4}}
  33 \citation{Devaney}
  34 \citation{Banks92}
  35 \@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{3.1}{Devaney's Chaotic Dynamical Systems}}{5}}
  36 \newlabel{subsec:Devaney}{{3.1}{5}}
  37 \newlabel{sensitivity}{{3.5}{5}}
  38 \@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{3.2}{A Metric Space for PRNG Iterations}}{5}}
  39 \@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{3.3}{A metric on $\mathcal  {X}_{\mathsf  {N},\mathcal  {P}}$}}{6}}
  40 \@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{3.4}{$\Gamma _{\mathcal  {P}}(f)$ as an extension of $\Gamma (f)$}}{8}}
  41 \@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{3.5}{Proofs of chaos}}{8}}
  42 \newlabel{graphe1}{{2a}{9}}
  43 \newlabel{sub@graphe1}{{a}{9}}
  44 \newlabel{graphe2}{{2b}{9}}
  45 \newlabel{sub@graphe2}{{b}{9}}
  46 \@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}}
  47 \newlabel{fig:itg}{{2}{9}}
  48 \newlabel{prop:trans}{{3.8}{9}}
  49 \citation{bcgr11:ip}
  50 \citation{DBLP:conf/secrypt/CouchotHGWB14}
  51 \@writefile{toc}{\contentsline {section}{\tocsection {}{4}{Functions with Strongly Connected $\Gamma _{\{b\}}(f)$}}{10}}
  52 \newlabel{sec:SCCfunc}{{4}{10}}
  53 \citation{bcgr11:ip}
  54 \citation{Robinson:1981:CS,DBLP:journals/combinatorics/BhatS96,ZanSup04,Bykov2016}
  55 \citation{DBLP:journals/combinatorics/BhatS96,ZanSup04}
  56 \citation{Bykov2016}
  57 \citation{ZanSup04,DBLP:journals/combinatorics/BhatS96}
  58 \citation{Bykov2016}
  59 \citation{ZanSup04}
  60 \@writefile{toc}{\contentsline {section}{\tocsection {}{5}{(Locally) Balanced Hamiltonian Cycle}}{11}}
  61 \newlabel{sec:hamilton}{{5}{11}}
  62 \citation{Robinson:1981:CS}
  63 \citation{DBLP:journals/combinatorics/BhatS96}
  64 \citation{ZanSup04}
  65 \citation{Robinson:1981:CS}
  66 \citation{DBLP:journals/combinatorics/BhatS96}
  67 \citation{ZanSup04}
  68 \citation{ZanSup04}
  69 \citation{ZanSup04}
  70 \@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{5.1}{Analysis of the Robinson-Cohn extension algorithm}}{12}}
  71 \newlabel{item:nondet}{{1}{12}}
  72 \@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{5.2}{Balanced Codes}}{12}}
  73 \newlabel{prop:balanced}{{5.1}{13}}
  74 \@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{5.3}{Toward a local uniform distribution of switches}}{13}}
  75 \@writefile{toc}{\contentsline {section}{\tocsection {}{6}{Stopping Time}}{13}}
  76 \newlabel{sec:hypercube}{{6}{13}}
  77 \citation{LevinPeresWilmer2006}
  78 \newlabel{eq:Markov:rairo}{{3}{15}}
  79 \newlabel{lm:h}{{6.2}{15}}
  80 \citation{proba}
  81 \newlabel{prop:stop}{{6.4}{16}}
  82 \newlabel{prop:lambda}{{6.5}{16}}
  83 \newlabel{lm:stopprime}{{6.6}{17}}
  84 \@writefile{toc}{\contentsline {section}{\tocsection {}{7}{Experiments}}{18}}
  85 \newlabel{sec:prng}{{7}{18}}
  86 \@writefile{loa}{\contentsline {algocf}{\numberline {2}{\ignorespaces Pseudo Code of the $\chi _{\textit  {15Rairo}}$ PRNG\relax }}{18}}
  87 \newlabel{CI Algorithm:2}{{2}{18}}
  88 \@writefile{lot}{\contentsline {table}{\numberline {1}{\ignorespaces Functions with DSCC Matrix and smallest MT\relax }}{19}}
  89 \newlabel{table:nc}{{1}{19}}
  90 \bibstyle{alpha}
  91 \bibdata{biblio}
  92 \bibcite{Banks92}{BBCS92}
  93 \@writefile{lot}{\contentsline {table}{\numberline {2}{\ignorespaces NIST SP 800-22 test results ($\mathbb  {P}_T$)\relax }}{20}}
  94 \newlabel{The passing rate}{{2}{20}}
  95 \@writefile{toc}{\contentsline {section}{\tocsection {}{8}{Conclusion}}{20}}
  96 \bibcite{bcgr11:ip}{BCGR11}
  97 \bibcite{Nist10}{BR10}
  98 \bibcite{DBLP:journals/combinatorics/BhatS96}{BS96}
  99 \bibcite{Bykov2016}{Byk16}
 100 \bibcite{chgw14oip}{CHG{$^{+}$}14a}
 101 \bibcite{DBLP:conf/secrypt/CouchotHGWB14}{CHG{$^{+}$}14b}
 102 \bibcite{5376454}{CMZ09}
 103 \bibcite{Devaney}{Dev89}
 104 \bibcite{guyeuxTaiwan10}{GWB10}
 105 \bibcite{LevinPeresWilmer2006}{LPW06}
 106 \bibcite{LEcuyerS07}{LS07}
 107 \bibcite{Marsaglia1996}{Mar96}
 108 \bibcite{proba}{MU05}
 109 \bibcite{Robinson:1981:CS}{RC81}
 110 \bibcite{915385}{SK01}
 111 \bibcite{915396}{SPK01}
 112 \bibcite{ZanSup04}{SZ04}
 113 \bibcite{wbg10ip}{WBGF10}
 114 \@writefile{toc}{\contentsline {section}{\tocsection {}{}{References}}{21}}
 115 \newlabel{tocindent-1}{0pt}
 116 \newlabel{tocindent0}{12.77466pt}
 117 \newlabel{tocindent1}{17.77344pt}
 118 \newlabel{tocindent2}{25.54932pt}
 119 \newlabel{tocindent3}{0pt}