intégration des remarques des relecteurs

[16dcc.git] / presPRNG.tex

diff --git a/presPRNG.tex b/presPRNG.tex
index a8b11b398931c37ce192e7f11bd618aa53ff5c76..dda026807860fb9d44c238c29a0de53b7b525ef2 100644 (file)
--- a/presPRNG.tex
+++ b/presPRNG.tex
@@ -18,6 +18,7 @@
 \usepackage[francais]{babel}
 \usepackage{rotating}
 \usepackage{algorithm2e}
 \usepackage[francais]{babel}
 \usepackage{rotating}
 \usepackage{algorithm2e}

+\usepackage{stmaryrd}

 
 \graphicspath{{Figures/}}
 
 
 \graphicspath{{Figures/}}
 


@@ -40,6 +41,7 @@
 \newcommand{\hauteur}[2]{\raisebox{0pt}[#1][-#1]{#2}}
 \def\oeuvre{\oe uvre }
 \def\oeuvrepv{\oe uvre}
 \newcommand{\hauteur}[2]{\raisebox{0pt}[#1][-#1]{#2}}
 \def\oeuvre{\oe uvre }
 \def\oeuvrepv{\oe uvre}

+\newcommand{\bleu}[1]{\color{blue}{#1}}

 
 %\newenvironment{myitemize}[1]{
 %%  \setlength{\topsep}{#1mm}
 
 %\newenvironment{myitemize}[1]{
 %%  \setlength{\topsep}{#1mm}


@@ -114,11 +116,11 @@
 \item For cryptography: cryptographically secure
 \item Successful pass on PRNG batteries of tests:
 NIST\footnote{E.~Barker and A.~Roginsky.
 \item For cryptography: cryptographically secure
 \item Successful pass on PRNG batteries of tests:
 NIST\footnote{E.~Barker and A.~Roginsky.

-\newblock Draft {N}{I}{S}{T} special publication 800-131 recommendation for the
+  Draft {N}{I}{S}{T} special publication 800-131 recommendation for the

   transitioning of cryptographic algorithms and key sizes, 2010.}, 
 DieHARD\footnote{G.~Marsaglia.
   transitioning of cryptographic algorithms and key sizes, 2010.}, 
 DieHARD\footnote{G.~Marsaglia.

-\newblock DieHARD: a battery of tests of randomness.
-\newblock {\em http://stat.fsu.edu/~geo/diehard.html}, 1996}
+ DieHARD: a battery of tests of randomness.
+ {\em http://stat.fsu.edu/~geo/diehard.html}, 1996}

 \item Should have chaos properties
 \end{itemize} 
 \end{itemize}
 \item Should have chaos properties
 \end{itemize} 
 \end{itemize}


@@ -143,6 +145,10 @@ return $x$\;
 %\end{scriptsize}
 \end{algorithm}
 \end{block}
 %\end{scriptsize}
 \end{algorithm}
 \end{block}

+$$
+F_f:  \Bool^{{\mathsf{N}}} \times \llbracket1;{\mathsf{N}} \rrbracket \to \Bool^{\mathsf{N}}, 
+F_f(x,i)=(x_1,\dots,x_{i-1},f_i(x),x_{i+1},\dots,x_{\mathsf{N}}).
+$$

   \end{frame}
 }
 
   \end{frame}
 }
 


@@ -158,7 +164,7 @@ f^*(x_1,x_2,x_3) =
 (x_2 \oplus x_3, \overline{x_1}\overline{x_3} + x_1\overline{x_2},
 \overline{x_1}\overline{x_3} + x_1x_2)$$
 \item Iteration graph $\Gamma(f^*)$ of this function:
 (x_2 \oplus x_3, \overline{x_1}\overline{x_3} + x_1\overline{x_2},
 \overline{x_1}\overline{x_3} + x_1x_2)$$
 \item Iteration graph $\Gamma(f^*)$ of this function:

-\includegraphics[width=0.45\textwidth]{iter_f0c}
+\includegraphics[width=0.45\textwidth]{images/iter_f0c}

 \end{itemize}
 \end{block}
 \end{frame}
 \end{itemize}
 \end{block}
 \end{frame}


@@ -171,10 +177,9 @@ f^*(x_1,x_2,x_3) =
 
 \begin{exampleblock}{Previous work}
 To provide a PRNG with the properties of Devaney's chaos and of succeeding NIST test: a (non-chaotic) PRNG + iterating a Boolean maps~\footnote{J. Bahi, J.-F. Couchot, C. Guyeux, and A. Richard.
 
 \begin{exampleblock}{Previous work}
 To provide a PRNG with the properties of Devaney's chaos and of succeeding NIST test: a (non-chaotic) PRNG + iterating a Boolean maps~\footnote{J. Bahi, J.-F. Couchot, C. Guyeux, and A. Richard.

-\newblock On the link between strongly connected iteration graphs and chaotic
+ On the link between strongly connected iteration graphs and chaotic

   Boolean discrete-time dynamical systems, {\em
   Boolean discrete-time dynamical systems, {\em

-  Fundamentals of Computation Theory}, volume 6914 of {\em Lecture Notes in
-  Computer Science}, pages 126--137. Springer Berlin Heidelberg, 2011.}:
+  Fundamentals of Computation Theory}, volume 6914 of {\em LNCS}, pages 126--137. Springer, 2011.}:

 \begin{itemize}
 \item with strongly connected iteration graph $\Gamma(f)$
 \item with doubly stochastic Markov probability matrix 
 \begin{itemize}
 \item with strongly connected iteration graph $\Gamma(f)$
 \item with doubly stochastic Markov probability matrix 


@@ -199,7 +204,7 @@ resulting Markov matrix is doubly stochastic.
   \begin{itemize}
   \item  Focus on the generation of Hamiltonian cycles in the 
     $n$-cube
   \begin{itemize}
   \item  Focus on the generation of Hamiltonian cycles in the 
     $n$-cube

-  \item To find cyclic Gray codes.
+  \item Find cyclic Gray codes.

   \end{itemize}
 \end{block}
 \footnote{Couchot, J., Héam, P., Guyeux, C., Wang, Q.,  Bahi, J. M. [2014] 
   \end{itemize}
 \end{block}
 \footnote{Couchot, J., Héam, P., Guyeux, C., Wang, Q.,  Bahi, J. M. [2014] 


@@ -457,6 +462,41 @@ Security and Cryptography, Vienna, Austria, 28-30 August, 2014, pp. 469--475}
   \end{frame}
 }
 
   \end{frame}
 }
 

+\frameselect{true}{
+  \begin{frame}
+    \frametitle{Exemple sur le 3-cube}
+    
+    \begin{center}
+      \vspace{-.75em}
+      \includegraphics[width=.3\textwidth]{3-cube.pdf}
+      \vspace{-.75em}
+    \end{center}
+
+    \begin{block}{}
+      \small
+      \vspace{-1.5em}
+      \begin{center}
+        \begin{equation*}
+          \begin{array}[h]{c|cccccccccccc}
+            \text{arêtes}  & 1         & 2         & 3   & 4   & 5   & 6 & 7   & 8 & 9 & 10 & 11  & 12 \\
+            \hline
+            \text{init}    & 2         & 2         & 2   & 2   & 2   & 2 & 2   & 2 & 2 & 2  & 2   & 2  \\
+            \hline
+            \text{ajout a} & d_1       & d_1       & 2   & 2   & d_1  & 2 & 2   & 2 & 2 & 2  & 2   & 2  \\
+            \hline
+            \text{ajout b} & \alert{1} & \bleu{g_1} & 2   & \bleu{g_2} & \bleu{g_1}  & 2 & 2   & 2 & 2 & 2  & \bleu{g_2} & 2  \\
+                           & \alert{0} & \bleu{1}         & 2   & \bleu{1}   & \bleu{1}   & 2 & 2   & 2 & 2 & 2  & \bleu{1}   & 2  \\
+            \hline
+            \text{ajout c} & 1         & \alert{1} & \bleu{g_3} & g_2 & \bleu{0}   & 2 & \bleu{g_3} & 2 & 2 & 2  & g_2 & 2  \\
+                           & 1         & \alert{0} & \bleu{1}   & g_2 & \bleu{1}   & 2 & \bleu{1}   & 2 & 2 & 2  & g_2 & 2  \\
+                           & 0         & 1         & \bleu{g_3} & 1   & 1   & 2 & \bleu{g_3} & 2 & 2 & 2  & 1   & 2  \\
+          \end{array}
+        \end{equation*}
+      \end{center}
+    \end{block}
+  \end{frame}
+}
+

 \frameselect{true}{
   \begin{frame}
     \frametitle{Adaptation au contexte de N-cube}
 \frameselect{true}{
   \begin{frame}
     \frametitle{Adaptation au contexte de N-cube}


@@ -638,4 +678,26 @@ est $\frac{1}{\mathsf{N}-1}$ $\leadsto$ à intégrer.
 }
 
 
 }
 
 

+  \begin{frame}
+    \frametitle{Perspectives}
+\begin{itemize}
+\item Qu'est-ce qu'un $\mathsf{N}$-cube?
+\item Justifier les trois arrêtes sortantes du n{\oe}ud $010$ de la figure~1. 
+\item Illustrer à l'aide d'un graphe le fait que la fonction $f^*$, définie au milieu de la~page~3  est un 3-cube privé d'un cycle hamiltonien.
+\item Pourquoi l'extension de Robinson-Cohn (page 11) n'est-elle pas un algorithme? A quoi sert la démonstration de la section 5.2?
+\item Quel est l'objectif de la section~6? 
+Ordonner les lemmes et théorèmes de cette section pour dégager le résultat 
+final. 
+\item Expliquer toutes les informations que l'on peut trouver dans la seconde 
+ligne du tableau de la page 18 (ligne portant le libéllé \og function \textcircled{a}\fg{}.
+\end{itemize}
+\end{frame}
+
+
+

 \end{document}
 \end{document}

+
+%%% Local Variables:
+%%% mode: latex
+%%% TeX-master: t
+%%% End: