-This paper is dedicated to the design of chaotic random generators
-and extends previous works proposed by some of the authors.
-We propose a theoretical framework proving both the chaotic properties and
-that the limit distribution is uniform.
-A theoretical bound on the stationary time is given and
-practical experiments show that the generators successfully pass
+
+Designing a pseudorandom number generator (PRNG) is a hard and complex task.
+Many recent works have consider chaotic functions as the basis of built
+PRNGs:
+the quality of the output would 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, it is not clear that embedding such kind of functions into a PRNG
+allows to get a chaotic output, which could be required for simulating
+some chaotic behaviours.
+
+In a previous work, some of the authors have proposed the idea of walking into a
+$\mathsf{N}$-cube where a balanced Hamiltonian cycle have 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.
+A upper bound of the length of the walk to obtain a uniform distribution is calculated.
+Finally practical experiments show that the generators successfully pass
