From: couchot <couchot@localhost.localdomain>
Date: Wed, 29 Jun 2016 20:04:05 +0000 (+0200)
Subject: modif abstract
X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/16dcc.git/commitdiff_plain/d509acd9cc478541bd9cf2f33686e60f3b77cce5?ds=inline;hp=-c

modif abstract
---

d509acd9cc478541bd9cf2f33686e60f3b77cce5
diff --git a/main.pdf b/main.pdf
index b70a2cd..58e266f 100644
Binary files a/main.pdf and b/main.pdf differ
diff --git a/main.tex b/main.tex
index f772c80..f49eef6 100644
--- a/main.tex
+++ b/main.tex
@@ -528,16 +528,45 @@
 % in the abstract or keywords.
 
 
+% \begin{abstract}
+% This paper is dedicated to the design of chaotic random generators
+% and extends previous works proposed by some of the authors.
+% We propose a theoretical framework proving both the chaotic properties and
+% that the limit distribution is uniform.
+% A theoretical bound on the stationary time is given and
+% practical experiments show that the generators successfully pass
+% the classical statistical tests.
+% \end{abstract}
+
 \begin{abstract}
-This paper is dedicated to the design of chaotic random generators
-and extends previous works proposed by some of the authors.
-We propose a theoretical framework proving both the chaotic properties and
-that the limit distribution is uniform.
-A theoretical bound on the stationary time is given and
-practical experiments show that the generators successfully pass
+
+Designing a pseudorandom number generator (PRNG) is a hard and complex task.
+Many recent works have consider chaotic functions as the basis of built 
+PRNGs:
+the quality of the output would be an obvious consequence of some chaos 
+properties.  
+However, there is no direct reasoning that goes from chaotic functions to 
+uniform distribution of the output. 
+Moreover, it is not clear that embedding such kind of functions into a PRNG
+allows to get a chaotic output, which could be required for simulating 
+some chaotic behaviours.
+
+In a previous work, some of the authors have proposed the idea of walking into a 
+$\mathsf{N}$-cube where a balanced Hamiltonian cycle have been removed 
+as the basis of a chaotic PRNG.
+In this article, all the difficult issues observed in the previous work have been tackled.
+The chaotic behavior of the whole PRNG is proven.
+The construction of the balanced Hamiltonian cycle is  theoretically and practically solved.
+A upper bound of the length of the walk to obtain a uniform distribution is calculated.
+Finally practical experiments show that the generators successfully pass 
 the classical statistical tests.
+
+
 \end{abstract}
 
+
+
+
 % Note that keywords are not normally used for peerreview papers.
 % \begin{IEEEkeywords}
 % IEEE, IEEEtran, journal, \LaTeX, paper, template.
diff --git a/prng.tex b/prng.tex
index b4f2059..8acfce7 100644
--- a/prng.tex
+++ b/prng.tex
@@ -186,7 +186,7 @@ achieve to pass the NIST battery of tests.
 
 
 
-\begin{table} 
+\begin{table*} 
 \renewcommand{\arraystretch}{1.3}
 \begin{center}
 \begin{scriptsize}
@@ -217,7 +217,7 @@ Linear Complexity& 0.719 (1.0)& 0.739 (0.99)& 0.759 (0.98)& 0.122 (0.97)& 0.514
 \end{center}
 \caption{NIST SP 800-22 test results ($\mathbb{P}_T$)}
 \label{The passing rate}
-\end{table}
+\end{table*}
 
 
 %%% Local Variables: