First of all, some chaotic iterations have to be done to generate a sequence
$\left(x^n\right)_{n\in\mathds{N}} \in \left(\mathds{B}^{32}\right)^\mathds{N}$
of Boolean vectors, which are the successive states of the iterated system.
-Some of these vectors will be randomly extracted and our pseudo-random bit
+Some of these vectors will be randomly extracted and our pseudorandom bit
flow will be constituted by their components. Such chaotic iterations are
realized as follows. Initial state $x^0 \in \mathds{B}^{32}$ is a Boolean
vector taken as a seed and chaotic strategy $\left(S^n\right)_{n\in\mathds{N}}\in
Such a procedure is equivalent to achieve chaotic iterations with
the Boolean vectorial negation $f_0$ and some well-chosen strategies.
Finally, some $x^n$ are selected
-by a sequence $m^n$ as the pseudo-random bit sequence of our generator.
+by a sequence $m^n$ as the pseudorandom bit sequence of our generator.
$(m^n)_{n \in \mathds{N}} \in \mathcal{M}^\mathds{N}$ is computed from $PRNG_1$, where $\mathcal{M}\subset \mathds{N}^*$ is a finite nonempty set of integers.
The basic design procedure of the New CI generator is summarized in Algorithm~\ref{Chaotic iteration1}.
}
\ENDFOR
\STATE$a\leftarrow{PRNG_1()}$\;
-\STATE$m\leftarrow{g(a)}$\;
-\STATE$k\leftarrow{m}$\;
+\STATE$k\leftarrow{g(a)}$\;
\WHILE{$i=0,\dots,k$}
\STATE$b\leftarrow{PRNG_2()~mod~\mathsf{N}}$\;
\begin{color}{red}
\section{Statistical Improvements Using Chaotic Iterations}
-\label{The generation of pseudo-random sequence}
+\label{The generation of pseudorandom sequence}
Let us now explain why we are reasonable grounds to believe that chaos
