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\begin{document}
%% \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
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)
-\end{color}
as the initial
random generator. The generation speed is significantly weaker.
%Note also that an original qualitative comparison between topological chaotic
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.
-\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
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}.
-\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
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.
-\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.
+\section*{Acknowledgment}
+This work is partially funded by the Labex ACTION program (contract ANR-11-LABX-01-01).
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