\rightarrow \{0,1\}^{\mathsf{N}}$).
These generators are $\textit{CIPRNG}_f^1(u)$
\cite{guyeuxTaiwan10,bcgr11:ip}, $\textit{CIPRNG}_f^2(u,v)$
-\cite{wbg10ip} and $\chi_{\textit{14Secrypt}}$
+\cite{wbg10ip}, and $\chi_{\textit{14Secrypt}}$
\cite{DBLP:conf/secrypt/CouchotHGWB14} where \textit{CI} means
\emph{Chaotic Iterations}. We have firstly proven in~\cite{bcgr11:ip}
that, to establish the chaotic nature of algorithm
However, the removed Hamiltonian cycle
has a great influence in the quality of the output.
-For instance, if this one one is not balanced (\textit{i.e.},
+For instance, if this one is not balanced (\textit{i.e.},
the number of changes in different bits are completely different),
some bits would be hard to switch.
This article shows an effective algorithm that efficiently
implements the previous scheme and provides thus functions issued
-from removing in the $\mathsf{N}$-cube a \emph{balanced} Hamiltonian cycle.
+from removing, in the $\mathsf{N}$-cube, a \emph{balanced} Hamiltonian cycle.
The length $b$ of the walk to reach a
distribution close to the uniform one would be dramatically long.
-
-The remainder of this article is organized as follows. The next
+This article, which
+is an extension of~\cite{DBLP:conf/secrypt/CouchotHGWB14},
+is organized as follows. The next
section is devoted to preliminaries, basic notations, and
terminologies regarding Boolean map iterations. Then, in
Section~\ref{sec:proofOfChaos}, Devaney's definition of chaos is
to obtain functions with awaited behavior. Main theorems are recalled
to make the document self-content.
The next section (Sect.~\ref{sec:hamilton}) presents an algorithm that
-implements this scheme and proves it always produces a solution.
-This is the second major contribution
-The later section
-(Sect.~\ref{sec:hypercube}) defines the theoretical framework to study
-the mixing-time, \textit{i.e.}, time until reaching a uniform
+implements this scheme and proves that it always produces a solution.
+This is the second major contribution.
+Then, Section~\ref{sec:hypercube} defines the theoretical framework to study
+the mixing-time, \textit{i.e.}, time until reaching an uniform
distribution. It proves that this one is at worth quadratic in the number
-of elements. Experiments show that the bound is practically largely much
-lower. This is the third major contribution. The
+of elements. Experiments show that the bound is in practice largely much
+lower. This is the third major contribution.
Section~\ref{sec:prng} gives practical results on evaluating the PRNG
against the NIST suite. This research work ends by a conclusion
section, where the contribution is summarized and intended future work
