X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/prng_gpu.git/blobdiff_plain/5e488f8546b2d4aaeefee70e1adfa87435312a6f..9fb4290afcf7de31edb7dda484ba7a2fedadaafb:/prng_gpu.tex

diff --git a/prng_gpu.tex b/prng_gpu.tex
index 25214fd..bc06797 100644
--- a/prng_gpu.tex
+++ b/prng_gpu.tex
@@ -180,8 +180,8 @@ 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 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.
 
 
 
@@ -192,12 +192,11 @@ The remainder of this paper  is organized as follows. In Section~\ref{section:re
   and on an iteration process called ``chaotic
 iterations'' on which the post-treatment is based. 
 The proposed PRNG and its proof of chaos are given in  Section~\ref{sec:pseudorandom}.
-
-Section~\ref{The generation of pseudorandom sequence} illustrates the statistical
-improvement related to the chaotic iteration based post-treatment, for
-our previously released PRNGs and a new efficient 
+Section~\ref{sec:efficient PRNG} %{The generation of pseudorandom sequence} %illustrates the statistical
+%improvement related to the chaotic iteration based post-treatment, for
+%our previously released PRNGs and
+ contains a new efficient 
 implementation on CPU.
-
  Section~\ref{sec:efficient PRNG
   gpu}   describes and evaluates theoretically  the  GPU   implementation. 
 Such generators are experimented in 
@@ -205,8 +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
@@ -726,15 +725,7 @@ investigated in Annex~\ref{A-deuxiÃ¨me def}, leading to the following result.
 
  \begin{theorem}
  \label{t:chaos des general}
-  The general chaotic iterations defined by
- \begin{equation}
-   x_i^n=\left\{
- \begin{array}{ll}
-   x_i^{n-1} &  \text{ if  } i \notin \mathcal{S}^n \\
-   \left(f(x^{n-1})\right)_{S^n} & \text{ if }i \in \mathcal{S}^n.
- \end{array}\right.
- \label{general CIs}
- \end{equation}
+  The general chaotic iterations defined in Equation~\ref{eq:generalIC}
 satisfy
  the Devaney's property of chaos.
  \end{theorem}
@@ -998,10 +989,10 @@ satisfy
 %%RAF : mis en supplementary
 
 
-\section{Statistical Improvements Using Chaotic Iterations}
-\label{The generation of pseudorandom sequence}
-The content is this section is given in Section~\ref{A-The generation of pseudorandom sequence} of the annex document.
-
+%\section{Statistical Improvements Using Chaotic Iterations}
+%\label{The generation of pseudorandom sequence}
+%The content is this section is given in Section~\ref{A-The generation of pseudorandom sequence} of the annex document.
+The reasons to desire chaos to achieve randomness are given in Annex~\ref{A-The generation of pseudorandom sequence}.
 
 %% \label{The generation of pseudorandom sequence}
 
@@ -1325,7 +1316,7 @@ The content is this section is given in Section~\ref{A-The generation of pseudor
 %% raise ambiguity.
 
 
-\subsection{First Efficient Implementation of a PRNG based on Chaotic Iterations}
+\section{First Efficient Implementation of a PRNG based on Chaotic Iterations}
 \label{sec:efficient PRNG}
 %
 %Based on the proof presented in the previous section, it is now possible to 
@@ -1647,13 +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
@@ -1662,7 +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 $uv$.
@@ -1775,9 +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
 
 
@@ -2019,7 +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.
