last version

[prng_gpu.git] / prng_gpu.tex

diff --git a/prng_gpu.tex b/prng_gpu.tex
index 807f6dfa2c56eecdeb0a522ca445b8db83f5398c..3c6e281a0243d69a29765acf87e2b4ce81f97e3d 100644 (file)
--- a/prng_gpu.tex
+++ b/prng_gpu.tex
@@ -1,6 +1,6 @@
-%\documentclass{article}
+\documentclass{article}
 %\documentclass[10pt,journal,letterpaper,compsoc]{IEEEtran}
-\documentclass[preprint,12pt]{elsarticle}
+%\documentclass[preprint,12pt]{elsarticle}
 \usepackage[utf8]{inputenc}
 \usepackage[T1]{fontenc}
 \usepackage{fullpage}
@@ -40,15 +40,28 @@
 
 \newcommand{\alert}[1]{\begin{color}{blue}\textit{#1}\end{color}}
 
-
+\begin{document}
 
 \title{Efficient and Cryptographically Secure Generation of Chaotic Pseudorandom Numbers on GPU}
-\begin{document}
 
-\author{Jacques M. Bahi, Rapha\"{e}l Couturier,  Christophe
-Guyeux, and Pierre-Cyrille Héam*\\ FEMTO-ST Institute, UMR  6174 CNRS,\\ University of Franche-Comt\'{e}, Besan\c con, France\\ * Authors in alphabetic order}
-   
 
+%% \author{Jacques M. Bahi}
+%% \ead{jacques.bahi@univ-fcomte.fr}
+%% \author{ Rapha\"{e}l Couturier \corref{cor1}}
+%% \ead{raphael.couturier@univ-fcomte.fr}
+%% \cortext[cor1]{Corresponding author}
+%% \author{  Christophe Guyeux}
+%% \ead{christophe.guyeux@univ-fcomte.fr}
+%% \author{ Pierre-Cyrille Héam }
+%% \ead{pierre-cyrille.heam@univ-fcomte.fr}
+
+\author{Christophe Guyeux \and  Rapha\"{e}l Couturier \and    Pierre-Cyrille Héam \and Jacques M. Bahi\\
+FEMTO-ST Institute, UMR  6174 CNRS,\\ University of Franche Comte, Belfort, France}
+
+\maketitle
+
+
+%\begin{frontmatter}
 %\IEEEcompsoctitleabstractindextext{
 \begin{abstract}
 In this paper we present a new pseudorandom number generator (PRNG) on
@@ -65,8 +78,11 @@ A chaotic version of the Blum-Goldwasser asymmetric key encryption scheme is fin
 
 \end{abstract}
 %}
+%\begin{keyword}
+%   pseudo random number\sep parallelization\sep GPU\sep cryptography\sep chaos
+%\end{keyword}
+%\end{frontmatter}
 
-\maketitle
 
 %\IEEEdisplaynotcompsoctitleabstractindextext
 %\IEEEpeerreviewmaketitle
@@ -177,8 +193,8 @@ Pseudorandom numbers are generated at a rate of 20GSamples/s, which is faster
 than in~\cite{conf/fpga/ThomasHL09,Marsaglia2003} (and with a better
 statistical behavior). Experiments are also provided using BBS as the initial
 random generator. The generation speed is significantly weaker.
-Note also that an original qualitative comparison between topological chaotic
-properties and statistical tests is also proposed.
+%Note also that an original qualitative comparison between topological chaotic
+%properties and statistical tests is also proposed.
 
 
 
@@ -1786,14 +1802,7 @@ Let $\varepsilon > 0$.
 $\mathcal{D}$ is called a $(T,\varepsilon)-$distinguishing attack on pseudorandom
 generator $G$ if
 
-\begin{flushleft}
-$\left| Pr[\mathcal{D}(G(k)) = 1 \mid k \in_R \{0,1\}^\ell ]\right.$
-\end{flushleft}
-
-\begin{flushright}
-$ - \left. Pr[\mathcal{D}(s) = 1 \mid s \in_R \mathds{B}^M ]\right| \geqslant \varepsilon,$
-\end{flushright}
-
+$$\left| Pr[\mathcal{D}(G(k)) = 1 \mid k \in_R \{0,1\}^\ell ]\right. - \left. Pr[\mathcal{D}(s) = 1 \mid s \in_R \mathds{B}^M ]\right| \geqslant \varepsilon,$$
 \noindent where the probability is taken over the internal coin flips of $\mathcal{D}$, and the notation
 ``$\in_R$'' indicates the process of selecting an element at random and uniformly over the
 corresponding set.