keywords = {circuit testing, counters, gray codes, hamming distance, transition counts, uniform distance},
}
+
+
+@article{matsumoto1998mersenne,
+ title={Mersenne twister: a 623-dimensionally equidistributed uniform pseudo-random number generator},
+ author={Matsumoto, Makoto and Nishimura, Takuji},
+ journal={ACM Transactions on Modeling and Computer Simulation (TOMACS)},
+ volume={8},
+ number={1},
+ pages={3--30},
+ year={1998},
+ publisher={ACM}
+}
\ No newline at end of file
We have exhibit an efficient method to compute such a balanced Hamiltonian
cycle. This method is an algebraic solution of an undeterministic
approach~\cite{ZanSup04} and has a low complexity.
-Thanks to this solution, many chaotic functions can be generated.
-
+According to the author knowledge, this is the first time a full
+automatic method to provide chaotic PRNGs is given.
+Practically speaking, this approach preserves the security properties of
+the embedded PRNG, even if it remains quite cost expensive.
We furthermore have exhibited a upper bound on the number of iterations
Let us first discuss about results against the NIST test suite.
In our experiments, 100 sequences (s = 100) of 1,000,000 bits are generated and tested.
If the value $\mathbb{P}_T$ of any test is smaller than 0.0001, the sequences are considered to be not good enough
-and the generator is unsuitable. Table~\ref{The passing rate} shows $\mathbb{P}_T$ of sequences based on discrete
-chaotic iterations using different schemes. If there are at least two statistical values in a test, this test is
+and the generator is unsuitable.
+
+Table~\ref{The passing rate} shows $\mathbb{P}_T$ of sequences based
+on $\chi_{\textit{16HamG}}$ using different functions, namely
+$\textcircled{a}$,\ldots, $\textcircled{e}$.
+In this algorithm implementation,
+the embedded PRNG \textit{Random} is the default Python PRNG, \textit{i.e.},
+the Mersenne Twister Algorithm~\cite{matsumoto1998mersenne}.
+Implementations for $\mathsf{N}=4, \dots, 8$ of this algorithm is evaluated
+through the NIST test suite and results are given in columns
+$\textit{MT}_4$, \ldots, $\textit{MT}_8$.
+If there are at least two statistical values in a test, this test is
marked with an asterisk and the average value is computed to characterize the statistics.
-We can see in Table \ref{The passing rate} that all the rates are greater than 97/100, \textit{i.e.}, all the generators
-achieve to pass the NIST battery of tests.
+We first can see in Table \ref{The passing rate} that all the rates
+are greater than 97/100, \textit{i.e.}, all the generators
+achieve to pass the NIST battery of tests.
+It can be noticed that adding chaos properties for Mersenne Twister
+algorithm does not reduce its security aginst this statistical tests.
\begin{table*}
+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.
