new version for parallel computing

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{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}
 \usepackage[utf8]{inputenc}
 \usepackage[T1]{fontenc}
 \usepackage{fullpage}


@@ -48,7 +49,7 @@
 Guyeux, and Pierre-Cyrille Héam\thanks{Authors in alphabetic order}}
    
 
 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
 \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}
 
 
 \end{abstract}

-}
+%}

 
 \maketitle
 
 
 \maketitle
 

-\IEEEdisplaynotcompsoctitleabstractindextext
-\IEEEpeerreviewmaketitle
+%\IEEEdisplaynotcompsoctitleabstractindextext
+%\IEEEpeerreviewmaketitle

 
 
 \section{Introduction}
 
 
 \section{Introduction}


@@ -1128,7 +1129,7 @@ a^1 & \text{if}~  z^{n-1} = 0 .\end{array} \right. \end{array}\end{equation}
 
 
 \begin{table}
 
 
 \begin{table}

-\renewcommand{\arraystretch}{1.3}
+%\renewcommand{\arraystretch}{1}

 \caption{TestU01 Statistical Test Failures}
 \label{TestU011}
 \centering
 \caption{TestU01 Statistical Test Failures}
 \label{TestU011}
 \centering


@@ -1150,7 +1151,7 @@ Failures          &       &261            &146    &0       \\
 
 
 \begin{table}
 
 
 \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
 \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*}
 
 \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
 \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*}
 
 
 \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
 \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*}
 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
 \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}
 
 \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}
 \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}
 
 \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}
 \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 $
 
 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 
 
 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.
 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.