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*}
