\item For cryptography: cryptographically secure
\item Successful pass on PRNG batteries of tests:
NIST\footnote{E.~Barker and A.~Roginsky.
-\newblock Draft {N}{I}{S}{T} special publication 800-131 recommendation for the
+ Draft {N}{I}{S}{T} special publication 800-131 recommendation for the
transitioning of cryptographic algorithms and key sizes, 2010.},
DieHARD\footnote{G.~Marsaglia.
-\newblock DieHARD: a battery of tests of randomness.
-\newblock {\em http://stat.fsu.edu/~geo/diehard.html}, 1996}
+ DieHARD: a battery of tests of randomness.
+ {\em http://stat.fsu.edu/~geo/diehard.html}, 1996}
\item Should have chaos properties
\end{itemize}
\end{itemize}
\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
+ 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.}:
+ Fundamentals of Computation Theory}, volume 6914 of {\em LNCS}, pages 126--137. Springer, 2011.}:
\begin{itemize}
\item with strongly connected iteration graph $\Gamma(f)$
\item with doubly stochastic Markov probability matrix
\begin{itemize}
\item Focus on the generation of Hamiltonian cycles in the
$n$-cube
- \item To find cyclic Gray codes.
+ \item Find cyclic Gray codes.
\end{itemize}
\end{block}
\footnote{Couchot, J., Héam, P., Guyeux, C., Wang, Q., Bahi, J. M. [2014]
