Fin

[prng_gpu.git] / prng_gpu.tex

diff --git a/prng_gpu.tex b/prng_gpu.tex
index 39cee4062e6752b541cd31361f951fce7f31e20d..f7499d98f7ab03016283032fde07ffb32364b842 100644 (file)
--- a/prng_gpu.tex
+++ b/prng_gpu.tex
@@ -1040,7 +1040,7 @@ not only sought in general to obtain chaos, but they are also required for rando
 \end{itemize}
 
 
 \end{itemize}
 
 

-We have proven in our previous works~\cite{} that chaotic iterations satisfying Theorem~\ref{Th:Caractérisation   des   IC   chaotiques} are, among other
+We have proven in our previous works~\cite{guyeux12:bc} that chaotic iterations satisfying Theorem~\ref{Th:Caractérisation   des   IC   chaotiques} are, among other

 things, strongly transitive, topologically mixing, chaotic as defined by Li and Yorke,
 and that they have a topological entropy and an exponent of Lyapunov both equal to $ln(\mathsf{N})$,
 where $\mathsf{N}$ is the size of the iterated vector.
 things, strongly transitive, topologically mixing, chaotic as defined by Li and Yorke,
 and that they have a topological entropy and an exponent of Lyapunov both equal to $ln(\mathsf{N})$,
 where $\mathsf{N}$ is the size of the iterated vector.


@@ -1279,7 +1279,7 @@ this generator will be simply referred as CIPRNG, or ``the proposed PRNG'', if t
 raise ambiguity.
 \end{color}
 
 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 
 \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
 
 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}
 
 \section{Efficient PRNGs based on Chaotic Iterations on GPU}
 \label{sec:efficient PRNG gpu}