This battery can be found in the well-known TestU01 package~\cite{LEcuyerS07}.
Chaos, for its part, refers to the well-established definition of a
chaotic dynamical system proposed by Devaney~\cite{Devaney}.
-
+\begin{color}{red}
+More precisely, each time we performed a test on a PRNG, we ran it
+twice in order to observe if all p-values are inside [0.01, 0.99]. In
+fact, we observed that few p-values (less than ten) are sometimes
+outside this interval but inside [0.001, 0.999], so that is why a
+second run allows us to confirm that the values outside are not for
+the same test. With this approach all our PRNGs pass the {\it
+ BigCrush} successfully and all p-values are at least once inside
+[0.01, 0.99].
+\end{color}
In a previous work~\cite{bgw09:ip,guyeux10} we have proposed a post-treatment on PRNGs making them behave
as a chaotic dynamical system. Such a post-treatment leads to a new category of
two PRNGs as inputs. These two generators are mixed with chaotic iterations,
leading thus to a new PRNG that
\begin{color}{red}
-should improves the statistical properties of each
+should improve the statistical properties of each
generator taken alone.
Furthermore, the generator obtained by this way possesses various chaos properties that none of the generators used as input
present.
\bigskip
\textit{The authors should include a summary of test measurements showing their method passes the test sets mentioned (NIST, Diehard, TestU01) instead of the one sentence saying it passed that is in section 1.}
-\begin{color}{red} Raph, c'est pour toi ça.\end{color}
+\begin{color}{red} In section 1, we have added a small summary of test measurements performed with BigCrush of TestU01.
+As other tests (NIST, Diehard, SmallCrush and Crush of TestU01 ) are deemed less selective, in this paper we did not use them.
+\end{color}
\bigskip
