+Review 1
+
+The author first prove the chaotic behaviour of a family of pseudorandom
+number generators (PRNG) introduced in a previous work by the same authors.
+These PRNGs are based on iterating continuous functions on a discrete domain.
+The paper first recalls Devaney’s definition of chaos and presents the proof of
+the main results. Next, the authors study the stopping time, i.e. the time until
+a uniform distribution is reached. Finally, they evaluate the PRNG against the
+NIST suite.
+Review 1
+
+The paper is globally well organized and many examples are provided to
+help the understanding. Unfortunately, it does not always make it easy to read.
+Some definition are quite hard to understand,
+as for example the metric defined in section 3.3.
+
+--> CG
+
+The overall presentation might be greatly improved.
+Another concern is the lack of comparison with other existing methods. Such
+a comparison should be provided.
+
+--> JFC
+
+
+For theses reasons, I do not recommend acceptance of this contribution in
+its current sate.
+
+
+Review 2:
+
+Some concerns must be noted on the practical side. It is unclear how the algorithm improves the randomness properties, as the results of the randomness test suite is not compared to that of the input PRNG. If that had been a perfect RNG, only 8 bits would have been enough to generate 8 bits, in this case we need 582 bits according to Table 1. This difference has to be justified.
+
+--> JFC
+
+The removal of the Hamiltonian cycle adds an interesting twist to the N-cube, but the importance of this complication is not emphasized properly.
+
+--> JFC
+
+It would be also interesting to see the comparison of the theoretical and simulated bounds on tau.
+
+--> JFC
+
+
+What is more, there are some basic mathematical errors that should not appear in such a paper. On page 6-7, a metric is defined. For the terms u, first per digit absolute difference is introduced, which then suddenly switches to absolute difference of the whole numbers! E.g., for 915 and 277, the first would give |9-2|, |1-7|, |7-5| = 7 6 2, while the other one is |972-277| = 695, which is just not the same.
+
+--> CG
+
+
+Also, in the proof of Lemma 5.3., bitwise uniform randomness is shown (already questionably), which is not sufficient for having a stationary distribution overall. Take for example X such that it is (0,0,...,0) or (1,1,...1) with probability 0.5 each. This is bitwise uniformly random, but is clearly not uniform on the whole cube.
+
+--> PCH
+
+
+The level of English is borderline acceptable, it should be checked more carefully. For example, it is unclear why examples are "running". In the middle of page we find "With all this material" for which "Based on this setup" or something similar would be more appropriate; bottom of page 10 says "Basically, let consider" instead of "Basically, let us consider", and so on.
+
+--> JFC
+
+
+Based on all these observations the reviewer considers the paper not to be acceptable in the current form.
