than in~\cite{conf/fpga/ThomasHL09,Marsaglia2003} (and with a better
statistical behavior). Experiments are also provided using BBS as the initial
random generator. The generation speed is significantly weaker.
-Note also that an original qualitative comparison between topological chaotic
-properties and statistical test is also proposed.
+%Note also that an original qualitative comparison between topological chaotic
+%properties and statistical test is also proposed.
We show in Section~\ref{sec:security analysis} that, if the inputted
generator is cryptographically secure, then it is the case too for the
generator provided by the post-treatment.
-A practical
-security evaluation is also outlined in Section~\ref{sec:Practicak evaluation}.
+%A practical
+%security evaluation is also outlined in Section~\ref{sec:Practicak evaluation}.
Such a proof leads to the proposition of a cryptographically secure and
chaotic generator on GPU based on the famous Blum Blum Shub
in Section~\ref{sec:CSGPU} and to an improvement of the
This section is dedicated to the security analysis of the
- proposed PRNGs, both from a theoretical and from a practical point of view.
+ proposed PRNGs.%, both from a theoretical and from a practical point of view.
-\subsection{Theoretical Proof of Security}
+%\subsection{Theoretical Proof of Security}
\label{sec:security analysis}
The standard definition
- of {\it indistinguishability} used is the classical one as defined for
+ of {\it indistinguishability} used here is the classical one as defined for
instance in~\cite[chapter~3]{Goldreich}.
This property shows that predicting the future results of the PRNG
cannot be done in a reasonable time compared to the generation time. It is important to emphasize that this
be broken in practice. But it also means that if the keys/seeds are large
enough, the system is secured.
As a complement, an example of a concrete practical evaluation of security
-is outlined in the next subsection.
+is outlined in Annex~\ref{A-sec:Practicak evaluation}.
In this section the concatenation of two strings $u$ and $v$ is classically
denoted by $uv$.
-\subsection{Practical Security Evaluation}
-\label{sec:Practicak evaluation}
-This subsection is given in Section~\ref{A-sec:Practicak evaluation} of the annex document.
+%\subsection{Practical Security Evaluation}
+%\label{sec:Practicak evaluation}
+%This subsection is given in Section
+A example of a practical security evaluation is outlined in
+Annex~\ref{A-sec:Practicak evaluation}.
%%RAF mis en annexe
proposed parameters, or if it is only a very fast
and statistically perfect generator on GPU, its
$(T,\varepsilon)-$security must be determined, and
-a formulation similar to Eq.\eqref{mesureConcrete}
+a formulation similar to Annex~\ref{A-sec:Practicak evaluation} %.Eq.\eqref{mesureConcrete}
must be established. Authors
hope to achieve this difficult task in a future
work.
