autres modifs

[prng_gpu.git] / prng_gpu.tex

diff --git a/prng_gpu.tex b/prng_gpu.tex
index 6ae1ef67161d651368535d85c39290de57654398..e90d0c241698897332ab973a12b42f73eefc0229 100644 (file)
--- a/prng_gpu.tex
+++ b/prng_gpu.tex
@@ -18,7 +18,7 @@
 \usepackage{tabularx}
 \usepackage{multirow}
 
 \usepackage{tabularx}
 \usepackage{multirow}
 

-\usepackage{color}
+%\usepackage{color}

 
 % Pour mathds : les ensembles IR, IN, etc.
 \usepackage{dsfont}
 
 % Pour mathds : les ensembles IR, IN, etc.
 \usepackage{dsfont}


@@ -40,7 +40,7 @@
 \newcommand{\BN}{\mathds{B}^\mathsf{N}}
 \let\sur=\overline
 
 \newcommand{\BN}{\mathds{B}^\mathsf{N}}
 \let\sur=\overline
 

-\newcommand{\alert}[1]{\begin{color}{blue}\textit{#1}\end{color}}
+%\newcommand{\alert}[1]{\begin{color}{blue}\textit{#1}\end{color}}

 
 \begin{document}
 
 
 \begin{document}
 


@@ -58,7 +58,7 @@
 %% \ead{pierre-cyrille.heam@univ-fcomte.fr}
 
 \author{Christophe Guyeux \and  Rapha\"{e}l Couturier \and    Pierre-Cyrille Héam \and Jacques M. Bahi\\
 %% \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}
+FEMTO-ST Institute, UMR  6174 CNRS,\\ University of Bourgogne Franche Comte, Belfort, France}

 
 \maketitle
 
 
 \maketitle
 


@@ -194,9 +194,8 @@ original implementation of this PRNG is also proposed and experimented.
 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 
 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 

-\begin{color}{red} the well-known Blum-Blum-Shub
+ the well-known Blum-Blum-Shub

 (BBS) 
 (BBS) 

-\end{color}

 as the initial
 random generator. The generation speed is significantly weaker.
 %Note also that an original qualitative comparison between topological chaotic
 as the initial
 random generator. The generation speed is significantly weaker.
 %Note also that an original qualitative comparison between topological chaotic


@@ -724,11 +723,9 @@ the list of cells to update in the state $x^n$ of the system (represented
 as an integer having $\mathsf{N}$ bits too). More precisely, the $k-$th 
 component of this state (a binary digit) changes if and only if the $k-$th 
 digit in the binary decomposition of $S^n$ is 1.
 as an integer having $\mathsf{N}$ bits too). More precisely, the $k-$th 
 component of this state (a binary digit) changes if and only if the $k-$th 
 digit in the binary decomposition of $S^n$ is 1.

-\begin{color}{red} 

 Obviously, when $S$ is periodic of period $p$, then $x$ is periodic too of
 period either $p$ or $2p$, depending on the fact that, after $p$ iterations,
 the state of the system may or not be the same as before these iterations.
 Obviously, when $S$ is periodic of period $p$, then $x$ is periodic too of
 period either $p$ or $2p$, depending on the fact that, after $p$ iterations,
 the state of the system may or not be the same as before these iterations.

-\end{color}

 
 The single basic component presented in Eq.~\ref{equation Oplus} is of 
 ordinary use as a good elementary brick in various PRNGs. It corresponds
 
 The single basic component presented in Eq.~\ref{equation Oplus} is of 
 ordinary use as a good elementary brick in various PRNGs. It corresponds


@@ -1494,13 +1491,12 @@ then   the  memory   required   to  store all of the  internals   variables  of
 PRNGs\footnote{we multiply this number by $2$ in order to count 32-bits numbers}
 and  the pseudorandom  numbers generated by  our  PRNG,  is  equal to  $100,000\times  ((4+5+6)\times
 2+(1+100))=1,310,000$ 32-bits numbers, that is, approximately $52$Mb.
 PRNGs\footnote{we multiply this number by $2$ in order to count 32-bits numbers}
 and  the pseudorandom  numbers generated by  our  PRNG,  is  equal to  $100,000\times  ((4+5+6)\times
 2+(1+100))=1,310,000$ 32-bits numbers, that is, approximately $52$Mb.

-\begin{color}{red}

 Remark that the only requirement regarding the seed regarding the security of our PRNG is
 that it must be randomly picked. Indeed, the asymptotic security of BBS guarantees
 that, as the seed length increases, no polynomial time statistical test can 
 distinguish the pseudorandom sequences from truly random sequences with non-negligible probability,
 see, \emph{e.g.},~\cite{Sidorenko:2005:CSB:2179218.2179250}.
 Remark that the only requirement regarding the seed regarding the security of our PRNG is
 that it must be randomly picked. Indeed, the asymptotic security of BBS guarantees
 that, as the seed length increases, no polynomial time statistical test can 
 distinguish the pseudorandom sequences from truly random sequences with non-negligible probability,
 see, \emph{e.g.},~\cite{Sidorenko:2005:CSB:2179218.2179250}.

-\end{color}
+

 
 This generator is able to pass the whole BigCrush battery of tests, for all
 the versions that have been tested depending on their number of threads 
 
 This generator is able to pass the whole BigCrush battery of tests, for all
 the versions that have been tested depending on their number of threads 


@@ -2123,16 +2119,16 @@ In future  work we plan to extend this research, building a parallel PRNG for  c
 grid computing. Topological properties of the various proposed generators will be investigated,
 and the use of other categories of PRNGs as input will be studied too. The improvement
 of Blum-Goldwasser will be deepened.
 grid computing. Topological properties of the various proposed generators will be investigated,
 and the use of other categories of PRNGs as input will be studied too. The improvement
 of Blum-Goldwasser will be deepened.

-\begin{color}{red}

 Another aspect to consider might be different accelerator-based systems like 
 Intel Xeon Phi cards and speed measurements using such cards: as heterogeneity of
 supercomputers tends to increase using other accelerators than GPGPUs,
 a Xeon Phi solution might be interesting to investigate.
 Another aspect to consider might be different accelerator-based systems like 
 Intel Xeon Phi cards and speed measurements using such cards: as heterogeneity of
 supercomputers tends to increase using other accelerators than GPGPUs,
 a Xeon Phi solution might be interesting to investigate.

-\end{color}

  Finally, we
 will try to enlarge the quantity of pseudorandom numbers generated per second either
 in a simulation context or in a cryptographic one.
 
  Finally, we
 will try to enlarge the quantity of pseudorandom numbers generated per second either
 in a simulation context or in a cryptographic one.
 

+\section*{Acknowledgment}
+This work is  partially funded by the Labex ACTION program (contract ANR-11-LABX-01-01).

 
 
 \bibliographystyle{plain} 
 
 
 \bibliographystyle{plain}