\section{Lyapunov exponent evaluation of a digital watermarking scheme proven to be secure~\cite{bfg12:ip}}

In this short paper, we have computed the Lyapunov exponent of the one bit 
watermarking scheme published in~\cite{gfb10:ip} (see Section~\ref{sec:iihmsp10}),
to improve our knowledge of its topological security.
To evaluate this Lyapunov exponent,
 chaotic iterations must be described by a differentiable function on $\mathds{R}$. 
To do so, 
a topological semiconjugacy between the phase space $\mathcal{X}$ and
$\mathds{R}$ must be written.
As this article is simply a rewriting in the digital watermarking field
of an unpublished result on chaotic iterations obtained during our 
thesis, we will not say any more about this publication.



