new version for parallel computing

[prng_gpu.git] / prng_gpu.tex

diff --git a/prng_gpu.tex b/prng_gpu.tex
index 0ab28a170efca640d062d65a664bcf8fc7507550..b3a844a113d6826ba9d14acc7219f966e32520c1 100644 (file)
--- a/prng_gpu.tex
+++ b/prng_gpu.tex
@@ -1,5 +1,6 @@
 %\documentclass{article}
-\documentclass[10pt,journal,letterpaper,compsoc]{IEEEtran}
+%\documentclass[10pt,journal,letterpaper,compsoc]{IEEEtran}
+\documentclass[preprint,12pt]{elsarticle}
 \usepackage[utf8]{inputenc}
 \usepackage[T1]{fontenc}
 \usepackage{fullpage}
@@ -48,7 +49,7 @@
 Guyeux, and Pierre-Cyrille Héam\thanks{Authors in alphabetic order}}
    
 
-\IEEEcompsoctitleabstractindextext{
+%\IEEEcompsoctitleabstractindextext{
 \begin{abstract}
 In this paper we present a new pseudorandom number generator (PRNG) on
 graphics processing units  (GPU). This PRNG is based  on the so-called chaotic iterations.  It
@@ -63,12 +64,12 @@ A chaotic version of the Blum-Goldwasser asymmetric key encryption scheme is fin
 
 
 \end{abstract}
-}
+%}
 
 \maketitle
 
-\IEEEdisplaynotcompsoctitleabstractindextext
-\IEEEpeerreviewmaketitle
+%\IEEEdisplaynotcompsoctitleabstractindextext
+%\IEEEpeerreviewmaketitle
 
 
 \section{Introduction}
@@ -1128,7 +1129,7 @@ a^1 & \text{if}~  z^{n-1} = 0 .\end{array} \right. \end{array}\end{equation}
 
 
 \begin{table}
-\renewcommand{\arraystretch}{1.3}
+%\renewcommand{\arraystretch}{1}
 \caption{TestU01 Statistical Test Failures}
 \label{TestU011}
 \centering
@@ -1150,7 +1151,7 @@ Failures          &       &261            &146    &0       \\
 
 
 \begin{table}
-\renewcommand{\arraystretch}{1.3}
+%\renewcommand{\arraystretch}{1}
 \caption{TestU01 Statistical Test Failures for Old CI algorithms ($\mathsf{N}=4$)}
 \label{TestU01 for Old CI}
 \centering
@@ -1189,7 +1190,7 @@ TestU01~\cite{LEcuyerS07}, which encompasses the two other batteries.
 
 \label{Results and discussion}
 \begin{table*}
-\renewcommand{\arraystretch}{1.3}
+%\renewcommand{\arraystretch}{1}
 \caption{NIST and DieHARD tests suite passing rates for PRNGs without CI}
 \label{NIST and DieHARD tests suite passing rate the for PRNGs without CI}
 \centering
@@ -1235,7 +1236,7 @@ However 8 tests have been improved (with no deflation for the other results).
 
 
 \begin{table*}
-\renewcommand{\arraystretch}{1.3}
+%\renewcommand{\arraystretch}{1.3}
 \caption{NIST and DieHARD tests suite passing rates for PRNGs with CI}
 \label{NIST and DieHARD tests suite passing rate the for single CIPRNGs}
 \centering
@@ -1264,7 +1265,7 @@ Thus rapid and perfect PRNGs, regarding the NIST and DieHARD batteries, can be o
 using chaotic iterations on defective generators.
 
 \begin{table*}
-\renewcommand{\arraystretch}{1.3}
+%\renewcommand{\arraystretch}{1.3}
 \caption{Number of $\oplus$ operations to pass the whole NIST and DieHARD batteries}
 \label{threshold}
 \centering
@@ -1571,7 +1572,7 @@ As a  comparison,   Listing~\ref{algo:seqCIPRNG}  leads   to the  generation of
 
 \begin{figure}[htbp]
 \begin{center}
-  \includegraphics[width=\columnwidth]{curve_time_xorlike_gpu.pdf}
+  \includegraphics[scale=0.7]{curve_time_xorlike_gpu.pdf}
 \end{center}
 \caption{Quantity of pseudorandom numbers generated per second with the xorlike-based PRNG}
 \label{fig:time_xorlike_gpu}
@@ -1590,7 +1591,7 @@ reduction.
 
 \begin{figure}[htbp]
 \begin{center}
-  \includegraphics[width=\columnwidth]{curve_time_bbs_gpu.pdf}
+  \includegraphics[scale=0.7]{curve_time_bbs_gpu.pdf}
 \end{center}
 \caption{Quantity of pseudorandom numbers generated per second using the BBS-based PRNG}
 \label{fig:time_bbs_gpu}
@@ -2045,14 +2046,14 @@ her new public key will be $(S^0, N)$.
 
 To encrypt his message, Bob will compute
 %%RAPH : ici, j'ai mis un simple $
-%\begin{equation}
-$c = \left(m_0 \oplus (b_0 \oplus S^0), m_1 \oplus (b_0 \oplus b_1 \oplus S^0), \hdots, \right.$
-$ \left. m_{L-1} \oplus (b_0 \oplus b_1 \hdots \oplus b_{L-1} \oplus S^0) \right)$
-%%\end{equation}
-instead of $\left(m_0 \oplus b_0, m_1 \oplus b_1, \hdots, m_{L-1} \oplus b_{L-1} \right)$. 
+\begin{equation*}
+c = \left(m_0 \oplus (b_0 \oplus S^0), m_1 \oplus (b_0 \oplus b_1 \oplus S^0), \hdots, \right.
+ \left. m_{L-1} \oplus (b_0 \oplus b_1 \hdots \oplus b_{L-1} \oplus S^0) \right)
+\end{equation*}
+instead of $$\left(m_0 \oplus b_0, m_1 \oplus b_1, \hdots, m_{L-1} \oplus b_{L-1} \right)$$. 
 
 The same decryption stage as in Blum-Goldwasser leads to the sequence 
-$\left(m_0 \oplus S^0, m_1 \oplus S^0, \hdots, m_{L-1} \oplus S^0 \right)$.
+$$\left(m_0 \oplus S^0, m_1 \oplus S^0, \hdots, m_{L-1} \oplus S^0 \right)$$.
 Thus, with a simple use of $S^0$, Alice can obtain the plaintext.
 By doing so, the proposed generator is used in place of BBS, leading to
 the inheritance of all the properties presented in this paper.