\begin{block}{Motivation}
Automatically generating a large class of PRNGs
  with chaos and statistical properties
\end{block}

\begin{exampleblock}{Previous work}
To provide a PRNG with the properties of Devaney's chaos and of succeeding NIST test: a (non-chaotic) PRNG + iterating a Boolean maps\footnote{J. Bahi, J.-F. Couchot, C. Guyeux, and A. Richard.
\newblock On the link between strongly connected iteration graphs and chaotic
  Boolean discrete-time dynamical systems, {\em
  Fundamentals of Computation Theory}, volume 6914 of {\em Lecture Notes in
  Computer Science}, pages 126--137. Springer Berlin Heidelberg, 2011.}
\begin{itemize}
\item with strongly connected iteration graph (sufficient)
\item with doubly stochastic Markov probability matrix  (necessary and sufficient)
\end{itemize}
\end{exampleblock}