X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/prng_gpu.git/blobdiff_plain/a0cdbfd7933130eaba676883427b46743a6cf7ea..1ac8792cbffd85b53eb50d99f0f70e7d2bf2eb3f:/prng_gpu.tex?ds=inline

diff --git a/prng_gpu.tex b/prng_gpu.tex
index 39cee40..f985e03 100644
--- a/prng_gpu.tex
+++ b/prng_gpu.tex
@@ -1279,7 +1279,7 @@ this generator will be simply referred as CIPRNG, or ``the proposed PRNG'', if t
 raise ambiguity.
 \end{color}
 
-\subsection{Efficient Implementation of a PRNG based on Chaotic Iterations}
+\subsection{First Efficient Implementation of a PRNG based on Chaotic Iterations}
 \label{sec:efficient PRNG}
 %
 %Based on the proof presented in the previous section, it is now possible to 
@@ -1358,7 +1358,13 @@ works with 32-bits, we use the command \texttt{(unsigned int)}, that selects the
 
 Thus producing a pseudorandom number needs 6 xor operations with 6 32-bits numbers
 that  are provided by  3 64-bits  PRNGs.  This  version successfully  passes the
-stringent BigCrush battery of tests~\cite{LEcuyerS07}.
+stringent BigCrush battery of tests~\cite{LEcuyerS07}. 
+\begin{color}{red}At this point, we thus
+have defined an efficient and statistically unbiased generator. Its speed is
+directly related to the use of linear operations, but for the same reason,
+this fast generator cannot be proven as secure.
+\end{color}
+
 
 \section{Efficient PRNGs based on Chaotic Iterations on GPU}
 \label{sec:efficient PRNG gpu}
