Ajout exemple 3-cube pour algo Wild

[16dcc.git] / presPRNG.tex

diff --git a/presPRNG.tex b/presPRNG.tex
index a8b11b398931c37ce192e7f11bd618aa53ff5c76..fd0ce179a86378644551d7ecf6b7676c13fdd675 100644 (file)
--- a/presPRNG.tex
+++ b/presPRNG.tex
@@ -40,6 +40,7 @@
 \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}
@@ -114,11 +115,11 @@
 \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.
-\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}
@@ -158,7 +159,7 @@ 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:
-\includegraphics[width=0.45\textwidth]{iter_f0c}
+\includegraphics[width=0.45\textwidth]{images/iter_f0c}
 \end{itemize}
 \end{block}
 \end{frame}
@@ -171,10 +172,9 @@ 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.
-\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
-  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 
@@ -199,7 +199,7 @@ resulting Markov matrix is doubly stochastic.
   \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] 
@@ -457,6 +457,41 @@ Security and Cryptography, Vienna, Austria, 28-30 August, 2014, pp. 469--475}
   \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}
@@ -639,3 +674,8 @@ est $\frac{1}{\mathsf{N}-1}$ $\leadsto$ à intégrer.
 
 
 \end{document}
+
+%%% Local Variables:
+%%% mode: latex
+%%% TeX-master: t
+%%% End: