\PCH{
{\bf Main contributions.} In this paper a new PRNG using chaotic iteration
-is defined. From a theoretical point of view, it is proved that it has fine
+is defined. From a theoretical point of view, it is proven that it has fine
topological chaotic properties and that it is cryptographically secured (when
the based PRNG is also cryptographically secured). From a practical point of
view, experiments point out a very good statistical behavior. Optimized
original implementation of this PRNG are also proposed and experimented.
-Pseudo-random numbers are generated at a rate of 20GSamples/s which is faster
+Pseudorandom numbers are generated at a rate of 20GSamples/s, which is faster
than in~\cite{conf/fpga/ThomasHL09,Marsaglia2003} (and with a better
statistical behavior). Experiments are also provided using BBS as the based
random generator. The generation speed is significantly weaker but, as far
\end{proposition}
\begin{proof}
-The proposition is proved by contraposition. Assume that $X$ is not
+The proposition is proven by contraposition. Assume that $X$ is not
secure. By Definition, there exists a polynomial time probabilistic
algorithm $D$, a positive polynomial $p$, such that for all $k_0$ there exists
$N\geq \frac{k_0}{2}$ satisfying
