From 1ad3649fd6e60ffa7c238cf99b577c7cce7d7b26 Mon Sep 17 00:00:00 2001 From: cguyeux Date: Fri, 21 Sep 2012 10:10:39 +0200 Subject: [PATCH 1/1] fdlkjldfjs --- prng_gpu.tex | 22 ++++++++++++---------- supplementary.tex | 4 ++-- 2 files changed, 14 insertions(+), 12 deletions(-) diff --git a/prng_gpu.tex b/prng_gpu.tex index 32055e7..f357476 100644 --- a/prng_gpu.tex +++ b/prng_gpu.tex @@ -204,8 +204,8 @@ Section~\ref{sec:experiments}. 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 @@ -1638,13 +1638,13 @@ as it is shown in the next sections. 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 @@ -1653,7 +1653,7 @@ The standard definition 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 $uv$. @@ -1766,9 +1766,11 @@ proving that $H$ is not secure, which is a contradiction. -\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 @@ -2010,7 +2012,7 @@ on GPU can be useful in security context with the 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. diff --git a/supplementary.tex b/supplementary.tex index 012cfca..1fead57 100644 --- a/supplementary.tex +++ b/supplementary.tex @@ -311,7 +311,7 @@ have $d((S,E),(\tilde S,E))<\epsilon$. \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 @@ -717,7 +717,7 @@ integer. 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. -- 2.39.5