Excellent excellent work!''
\medskip
-In practice the seeds are generated using ISAAC which is a cryptographic PRNG. So the security of our seeds lies on the security of ISAAC. We think that this is enough to consider that our seeds are sufficiently secure.
+{\it In practice the seeds are generated using ISAAC which is a cryptographic PRNG. So the security of our seeds lies on the security of ISAAC. We think that this is enough to consider that our seeds are sufficiently secure.}
\end{enumerate}
longer period of the resultant generator compared to any of the input generators.''
\medskip
-We have added the following text in Section 4.2:\\
+{\it We have added the following text in Section 4.2:\\
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 than before these iterations.
+the state of the system may or not be the same than before these iterations.}
\end{enumerate}
reworked by a native speaker.''
\medskip
-The paper has been reread by a native speaker
+{\it The paper has been reread by a native speaker.}
\item ``The mathematical introductions are short and concise, enabling a reader to gather all relevant knowledge directly from this publication.
This always raises the question of novelty of the paper, as new aspects are arising only at a later stage in the paper itself
While working through the paper a few minor questions arised:
- page 7, Algorithm 3: is the increment of i in the while loop implicit, or where is it incremented?''
-In fact this is implicit with the ''while'' instruction.
+{\it In fact this is implicit with the ''while'' instruction.}
\item ``In Algorithm 5 and 6 threadIdx is written sometimes as threadId''
- We have uniformized that
+{\it We have uniformized that.}
\item ``Page 19, Algorithm 6: there are 8 random numbers and their corresponding 8 states. You state that only a few of them are used, which is reflected in the algorithm itself. Are always the same ones used, or do you also rotate there?''
- In practice, 8 BBS random numbers are used but for each of them only the four last bits are used. So we used $8 \times 4=32$ bits. If we chose a bigger number of BBS, the computation would slower. That is why we have used 8 BBS which seems to be a good trade-off.
+{\it In practice, 8 BBS random numbers are used but for each of them only the four last bits are used. So we used $8 \times 4=32$ bits. If we chose a bigger number of BBS, the computation would slower. That is why we have used 8 BBS which seems to be a good trade-off.}
\item ``In the references starting on page 21, some references need a bit more work. Probably BibTeX did some magic there and needs
to be tweaked manually. Example Ref [7] nist needs to be NIST.''
- We have corrected that.
+{\it We have corrected that.}
\item ``Another nice aspect to consider in future might be different accelerator-based systems such as Intel Xeon Phi cards and speed measurements
using such cards. As supercomputers tend to get more and more heterogeneous (Tianhe-2, Stampede) using other accelerators than GPGPUs,
a Xeon Phi solution might be very beneficial for the community.''
- Thank you for this remark, we have added that in the future work.
+{\it Thank you for this remark, we have added that in the future work.}
\item ``With the strong mathematical focus, the authors could also think about submitting this paper to a different, more
mathematically oriented journal, as the focus on supercomputers and supercomputing capabilities is not as strong in this paper.
Nevertheless, I recommend the paper for publication.''
-In fact there are different parts in this paper, we have chosen the Journal of Supercomputing because, for previous submissions to this journal, we had interesting reviews and because this journal has a wide audience and is of really high standards.
+{\it In fact there are different parts in this paper, we have chosen the Journal of Supercomputing because, for previous submissions to this journal, we had interesting reviews and because this journal has a wide audience and is of really high standards.}
\end{enumerate}
\usepackage{tabularx}
\usepackage{multirow}
-\usepackage{color}
+%\usepackage{color}
% Pour mathds : les ensembles IR, IN, etc.
\usepackage{dsfont}
\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}
%% \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).
\bibliographystyle{plain}
