X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/prng_gpu.git/blobdiff_plain/beae8ac319dceb200d507fedc5ddb28c36078605..807fde0ea31c414c79ee3922e51251371e227185:/prng_gpu.tex?ds=inline

diff --git a/prng_gpu.tex b/prng_gpu.tex
index 3c6e281..db219a1 100644
--- a/prng_gpu.tex
+++ b/prng_gpu.tex
@@ -18,6 +18,8 @@
 \usepackage{tabularx}
 \usepackage{multirow}
 
+\usepackage{color}
+
 % Pour mathds : les ensembles IR, IN, etc.
 \usepackage{dsfont}
 
@@ -191,7 +193,11 @@ view, experiments point out a very good statistical behavior. An optimized
 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 BBS as the initial
+statistical behavior). Experiments are also provided using 
+\begin{color}{red} 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
 %properties and statistical tests is also proposed.
@@ -1483,6 +1489,13 @@ 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.
+\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 
@@ -2104,7 +2117,14 @@ behave chaotically, has finally been proposed.
 In future  work we plan to extend this research, building a parallel PRNG for  clusters or
 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. Finally, we
+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.
 
