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.
\label{The generation of pseudorandom sequence}
-Let us now explain why we have reasonable ground to believe that chaos
+Let us explain in this annex why we have reasonable ground to believe that chaos
can improve statistical properties.
We will show in this section that chaotic properties as defined in the
mathematical theory of chaos are related to some statistical tests that can be found
A direct numerical application shows that this attacker
-cannot achieve its $(10^{12},0.2)$ distinguishing
+cannot achieve his $(10^{12},0.2)$ distinguishing
attack in that context.
