+jfjucobo16
+
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 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.
Another concern is the lack of comparison with other existing methods. Such
a comparison should be provided.
---> JFC
+--> CG
For theses reasons, I do not recommend acceptance of this contribution in
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
+--> JFC (fait)
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
+--> JFC (fait)
It would be also interesting to see the comparison of the theoretical and simulated bounds on tau.
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
+--> PCH (fait)
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.
