X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/16dcc.git/blobdiff_plain/95808e0cc34f861214ab26eb69af0dbfb485774f..c9d6a79d174af327059607a3e0a1f23ab7921a49:/prng.tex

diff --git a/prng.tex b/prng.tex
index ea56fd4..4dbeea7 100644
--- a/prng.tex
+++ b/prng.tex
@@ -180,12 +180,25 @@ $\textcircled{e}$&151, 149, 19, 210, 144, 152, 141, 206, 13, 12, 171, 10, 201, 1
 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*}