+\begin{abstract}
+ Designing a pseudorandom number generator (PRNG) is a
+difficult and complex task. Many recent works have considered chaotic
+functions as the basis of built PRNGs: the quality of the output would
+indeed
+be an obvious consequence of some chaos properties. However, there is
+no direct reasoning that goes from chaotic functions to uniform
+distribution of the output.
+Moreover,
+embedding such kind of functions into a PRNG does not necessarily
+allow to get a chaotic output,
+which could be required for simulating some chaotic behaviors.
+
+In a previous work, some of the authors have proposed the idea of
+walking into a $\mathsf{N}$-cube where a balanced Hamiltonian cycle
+has been removed as the basis of a chaotic PRNG. In this article, all
+the difficult issues observed in the previous work have been
+tackled. The chaotic behavior of the whole PRNG is proven. The
+construction of the balanced Hamiltonian cycle is theoretically and
+practically solved. An upper bound of the expected length of the walk
+to obtain a uniform distribution is calculated. Finally practical
+experiments show that the generators successfully pass the classical
+statistical tests.
+\end{abstract}
+
+
+\keywords{Pseudorandom Numbers Generator, Chaotic iterations, Random Walk}
+
