\maketitle
\begin{abstract}
-In this paper we present a new produce pseudo-random numbers generator (PRNG) on
+In this paper we present a new pseudo-random numbers generator (PRNG) on
graphics processing units (GPU). This PRNG is based on chaotic iterations. it
-is proven to be chaotic in the Devany's formulation. We propose an efficient
+is proven to be chaotic in the Devanay's formulation. We propose an efficient
implementation for GPU which succeeds to the {\it BigCrush}, the hardest
batteries of test of TestU01. Experimentations show that this PRNG can generate
about 20 billions of random numbers per second on Tesla C1060 and NVidia GTX280
Random numbers are used in many scientific applications and simulations. On
finite state machines, as computers, it is not possible to generate random
-numbers but only pseudo-random numbers. In practice, a good pseudo-random number
+numbers but only pseudo-random numbers. In practice, a good pseudo-random numbers
generator (PRNG) needs to verify some features to be used by scientists. It is
important to be able to generate pseudo-random numbers efficiently, the
generation needs to be reproducible and a PRNG needs to satisfy many usual
allows us to generated almost 20 billions of random numbers per second.
In order to establish that our PRNGs are chaotic according to the Devaney's
-formulation, we extend what we have proposed in~\cite{guyeux10}. Moreover, we
-define a new distance to measure the disorder in the chaos and we prove some
-interesting properties with this distance.
+formulation, we extend what we have proposed in~\cite{guyeux10}.
The rest of this paper is organised as follows. In Section~\ref{section:related
works} we review some GPU implementions of PRNG. Section~\ref{section:BASIC
implementation of our chaotic PRNG on a CPU. Section~\ref{sec:efficient prng
gpu} describes the GPU implementation of our chaotic PRNG. In
Section~\ref{sec:experiments} some experimentations are presented.
-Section~\ref{sec:de la relativité du désordre} describes the relativity of
-disorder. In Section~\ref{sec: chaos order topology} the proof that chaotic
-iterations can be described by iterations on a real interval is
-established. Finally, we give a conclusion and some perspectives.
+ Finally, we give a conclusion and some perspectives.
per joule. Concerning the GPU, authors can generate betweend 11 and 16GSample/s
with a GTX 280 GPU. The drawback of this work is that those PRNGs only succeed
the {\it Crush} test which is easier than the {\it Big Crush} test.
+
+Cuda has developped a library for the generation of random numbers called
+Curand~\cite{curand11}. Several PRNGs are implemented:
+Xorwow~\cite{Marsaglia2003} and some variants of Sobol. Some tests report that
+the fastest version provides 15GSample/s on the new Fermi C2050 card. Their
+PRNGs fail to succeed the whole tests of TestU01 on only one test.
\newline
\newline
To the best of our knowledge no GPU implementation have been proven to have chaotic properties.
an integer $b$, ensuring that the number of executed iterations is at least $b$
and at most $2b+1$; and an initial configuration $x^0$.
It returns the new generated configuration $x$. Internally, it embeds two
-\textit{XORshift}$(k)$ PRNGs \cite{Marsaglia2003} that returns integers
+\textit{XORshift}$(k)$ PRNGs~\cite{Marsaglia2003} that returns integers
uniformly distributed
into $\llbracket 1 ; k \rrbracket$.
\textit{XORshift} is a category of very fast PRNGs designed by George Marsaglia,
All the tests performed to pass the BigCrush of TestU01 succeeded. Different
number of threads, called \texttt{NumThreads} in our algorithm, have been tested
upto $10$ millions.
+\newline
+\newline
+{\bf QUESTION : on laisse cette remarque, je suis mitigé !!!}
\begin{remark}
Algorithm~\ref{algo:gpu_kernel} has the advantage to manipulate independent
-\section{Cryptanalysis of the Proposed PRNG}
+%% \section{Cryptanalysis of the Proposed PRNG}
-Mettre ici la preuve de PCH
+%% Mettre ici la preuve de PCH
%\section{The relativity of disorder}
%\label{sec:de la relativité du désordre}
\section{Conclusion}
+
+
+In this paper we have presented a new class of PRNGs based on chaotic
+iterations. We have proven that these PRNGs are chaotic in the sense of Devenay.
+
+An efficient implementation on GPU allows us to generate a huge number of pseudo
+random numbers per second (about 20Gsample/s). Our PRNGs succeed to pass the
+hardest batteries of test (TestU01).
+
+In future work we plan to extend our work in order to have cryptographically
+secure PRNGs because in some situations this property may be important.
+
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