From 07fc9a29ed26c33dfe987821fc94b3afa4cdd3a5 Mon Sep 17 00:00:00 2001
From: Christophe Guyeux <christophe.guyeux@univ-fcomte.fr>
Date: Sat, 14 Mar 2015 09:01:03 +0100
Subject: [PATCH 1/1] =?utf8?q?fin=20de=20la=20relecture=20de=20la=20premi?=
=?utf8?q?=C3=A8re=20version=20de=20l'intro?=
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---
biblio.bib | 17 +++++++++++++++++
intro.tex | 18 +++++++++---------
2 files changed, 26 insertions(+), 9 deletions(-)
diff --git a/biblio.bib b/biblio.bib
index 30bdba6..7faa670 100644
--- a/biblio.bib
+++ b/biblio.bib
@@ -17,6 +17,23 @@
OPTmonth = {},
}
+@inproceedings{chgw14oip,
+inhal = {no},
+domainehal = {INFO:INFO_DC, INFO:INFO_CR, INFO:INFO_MO, INFO:INFO_SE},
+equipe = {ie},
+classement = {COM},
+author = {Couchot, Jean-Fran\c{c}ois and H\'eam, Pierre-Cyrille and Guyeux, Christophe and Wang, Qianxue and Bahi, Jacques},
+title = {Pseudorandom Number Generators with Balanced Gray Codes},
+booktitle = {Secrypt 2014, 11th Int. Conf. on Security and Cryptography},
+pages = {469--475},
+address = {Vienna, Austria},
+month = aug,
+date = {28-30 aout},
+year = 2014,
+note = {Position short paper},
+
+}
+
@Misc{GridComp,
OPTkey = {},
OPTauthor = {},
diff --git a/intro.tex b/intro.tex
index dafa1cf..569c493 100644
--- a/intro.tex
+++ b/intro.tex
@@ -4,20 +4,20 @@ chosen due to their unpredictable character and their sensitiveness to initial c
In most cases, these generators simply consist in iterating a chaotic function like
the logistic map~\cite{915396,915385} or the Arnold's one~\cite{5376454}\ldots
It thus remains to find optimal parameters in such functions so that attractors are
-avoided, guaranteeing by doing so that generated numbers follow a uniform distribution.
+avoided, hoping by doing so that the generated numbers follow a uniform distribution.
In order to check the quality of the produced outputs, it is usual to test the
PRNGs (Pseudo-Random Number Generators) with statistical batteries like
-the so-called DieHARD~\cite{Marsaglia1996}, NIST~\cite{Nist10}, or TestU01~\cite{LEcuyerS07}.
+the so-called DieHARD~\cite{Marsaglia1996}, NIST~\cite{Nist10}, or TestU01~\cite{LEcuyerS07} ones.
-In its general understanding, the chaos notion is often reduced to the strong
+In its general understanding, chaos notion is often reduced to the strong
sensitiveness to the initial conditions (the well known ``butterfly effect''):
a continuous function $k$ defined on a metrical space is said
-\emph{strongly sensitive to the initial conditions} if for all point
-$x$ and all positive value $\epsilon$, it is possible to find another
-point $y$, as close as possible to $x$, and an integer $t$ such that the distance
+\emph{strongly sensitive to the initial conditions} if for each point
+$x$ and each positive value $\epsilon$, it is possible to find another
+point $y$ as close as possible to $x$, and an integer $t$ such that the distance
between the $t$-th iterates of $x$ and $y$, denoted by $k^t(x)$ and $k^t(y)$,
are larger than $\epsilon$. However, in his definition of chaos, Devaney~\cite{Devaney}
-impose to the chaotic function two other properties called
+imposes to the chaotic function two other properties called
\emph{transitivity} and \emph{regularity}. Functions evoked above have
been studied according to these properties, and they have been proven as chaotic on $\R$.
But nothing guarantees that such properties are preserved when iterating the functions
@@ -38,7 +38,7 @@ asynchronous iterations are strongly connected. We then have proven that it is n
and sufficient that the Markov matrix associated to this graph is doubly stochastic,
in order to have a uniform distribution of the outputs. We have finally established
sufficient conditions to guarantee the first property of connectivity. Among the
-generated functions, we thus considered for further investigations only the one that
+generated functions, we thus have considered for further investigations only the one that
satisfy the second property too. In~\cite{chgw14oip}, we have proposed an algorithmic
method allowing to directly obtain a strongly connected iteration graph having a doubly
stochastic Markov matrix. The research work presented here generalizes this latter article
@@ -219,7 +219,7 @@ The remainder of this article is organized as follows. The next section is devot
preliminaries, basic notations, and terminologies regarding asynchronous iterations.
Then, in Section~\ref{sec:proofOfChaos}, Devaney's definition of chaos is recalled
while the proofs of chaos of our most general PRNGs is provided. Section~\ref{sec:SCCfunc} shows how to generate functions and a number of iterations such that the iteration graph is strongly connected, making the
-PRNG chaotic. The next section focus on examples of such graphs obtained by modifying the
+PRNG chaotic. The next section focuses on examples of such graphs obtained by modifying the
hypercube, while Section~\ref{sec:prng} establishes the link between the theoretical study and
pseudorandom number generation.
This research work ends by a conclusion section, where the contribution is summarized and
--
2.39.5