and on an iteration process called ``chaotic
iterations'' on which the post-treatment is based.
The proposed PRNG and its proof of chaos are given in Section~\ref{sec:pseudorandom}.
-
-Section~\ref{The generation of pseudorandom sequence} illustrates the statistical
-improvement related to the chaotic iteration based post-treatment, for
-our previously released PRNGs and a new efficient
+Section~\ref{sec:efficient PRNG} %{The generation of pseudorandom sequence} %illustrates the statistical
+%improvement related to the chaotic iteration based post-treatment, for
+%our previously released PRNGs and
+ contains a new efficient
implementation on CPU.
-
Section~\ref{sec:efficient PRNG
gpu} describes and evaluates theoretically the GPU implementation.
Such generators are experimented in
\begin{theorem}
\label{t:chaos des general}
- The general chaotic iterations defined by
- \begin{equation}
- x_i^n=\left\{
- \begin{array}{ll}
- x_i^{n-1} & \text{ if } i \notin \mathcal{S}^n \\
- \left(f(x^{n-1})\right)_{S^n} & \text{ if }i \in \mathcal{S}^n.
- \end{array}\right.
- \label{general CIs}
- \end{equation}
+ The general chaotic iterations defined in Equation~\ref{eq:generalIC}
satisfy
the Devaney's property of chaos.
\end{theorem}
%%RAF : mis en supplementary
-\section{Statistical Improvements Using Chaotic Iterations}
-\label{The generation of pseudorandom sequence}
-The content is this section is given in Section~\ref{A-The generation of pseudorandom sequence} of the annex document.
-
+%\section{Statistical Improvements Using Chaotic Iterations}
+%\label{The generation of pseudorandom sequence}
+%The content is this section is given in Section~\ref{A-The generation of pseudorandom sequence} of the annex document.
+The reasons to desire chaos to achieve randomness are given in Annex~\ref{A-The generation of pseudorandom sequence}.
%% \label{The generation of pseudorandom sequence}
%% raise ambiguity.
-\subsection{First Efficient Implementation of a PRNG based on Chaotic Iterations}
+\section{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
