From 02fd942d6a30fe7197b732c94450ca466b7a49f5 Mon Sep 17 00:00:00 2001 From: couchot Date: Mon, 29 Aug 2016 20:54:07 +0200 Subject: [PATCH] -> prng inclus --- 11FCT.tex | 1 - 14Secrypt.tex | 51 ++- chaosANN.tex | 35 +- demandeInscription/avis_jef_hdr.pdf | Bin 438585 -> 438682 bytes main.tex | 49 ++- modelchecking.tex | 29 +- sdd.tex | 10 - stegoyousra.tex | 635 ++++++++++------------------ 8 files changed, 329 insertions(+), 481 deletions(-) diff --git a/11FCT.tex b/11FCT.tex index 0e9c64f..45d91c9 100644 --- a/11FCT.tex +++ b/11FCT.tex @@ -90,4 +90,3 @@ Deux fonctions sont équivalentes si leurs \textsc{giu} sont isomorphes \end{center} \caption{Exemple de graphe d'interactions vérifiant le théorème~\ref{th:Adrien}} \label{fig:Adrien:G} \end{figure} - diff --git a/14Secrypt.tex b/14Secrypt.tex index f1fae6f..bc59ba1 100644 --- a/14Secrypt.tex +++ b/14Secrypt.tex @@ -1,16 +1,29 @@ On a vu dans le chapitre précédent que pour avoir un générateur à sortie uniforme, il est nécessaire que la matrice d'adjacence du graphe d'itération du -système soit doublement stochastique. Nous présentons dans cette partie une -méthode permettant de générer de telles matrices. - -Les approches théoriques basées sur la programmation logique par contraintes sur -domaines finis ne sont pas envisageables en pratique dès que la taille des -matrices considérées devient suffisamment grande. - +système soit doublement stochastique. Nous présentons dans cette partie +des méthodes effectives permettant de générer de telles matrices. +La première est basée sur la programmation logique par contraintes +(Section~\ref{sec:plc}). +Cependant celle-ci souffre de ne pas passer à l'échelle et ne fournit pas +une solution en un temps raisonnable dès que la fonction à engendrer +porte sur un grand nombre de bits. Une approche plus pragmatique consiste à supprimer un cycle hamiltonien dans le -graphe d'itérations, ce qui revient à supprimer en chaque n{\oe}ud de ce graphe une -arête sortante et une arête entrante. +graphe d'itérations $\textsc{giu}(\neg)$ (section~\ref{sec:hamiltonian}). +Pour obtenir plus rapidement une distribution uniforme, l'idéal serait +de supprimer un cycle hamiltonien qui nierait autant de fois chaque bit. +Cette forme de cycle est dit équilibré. La section~\ref{sub:gray} établit le +lien avec les codes de Gray équilibrés, étudiés dans la litérature. +La section suivante présente une démarche de génération automatique de code de Gray équilibré (section~\ref{sec:induction}). +La vitesse avec laquelle l'algorithme de PRNG converge en interne vers +une distribution unifiorme est étduiée théoriquement et pratiquement à la +section~\ref{sec:mixing}. +L'extension du travail aux itérations généralisées est présenté à la +section~\ref{sec:prng:gray:general}. +Finalement, des instances de PRNGS engendrés selon les méthodes détaillées dans +ce chapitre sont présentés en section~\ref{sec:prng;gray:tests}. +Les sections~\ref{sec:plc} à~\ref{sub:gray} ont été publiées +à~\ref{chgw+14:oip}. % This aim of this section is to show @@ -442,7 +455,7 @@ Ces fonctions étant générées, on s'intéresse à étudier à quelle vitesse un générateur les embarquant converge vers la distribution uniforme. C'est l'objectif de la section suivante. -\section{Quantifier l'écart par rapport à la distribution uniforme} +\section{Quantifier l'écart par rapport à la distribution uniforme}\label{sec:mixing} On considère ici une fonction construite comme à la section précédente. On s'intéresse ici à étudier de manière théorique les itérations définies à l'équation~(\ref{eq:asyn}) pour une @@ -651,7 +664,7 @@ $\textit{fair}\leftarrow\emptyset$\; -\section{Et les itérations généralisées?} +\section{Et les itérations généralisées?}\label{sec:prng:gray:general} Le chaptire précédent a présenté un algorithme de PRNG construit à partir d'itérations unaires. On pourrait penser que cet algorithme est peu efficace puisqu'il @@ -924,7 +937,7 @@ $$ -\section{Tests statistiques} +\section{Tests statistiques}\label{sec:prng;gray:tests} La qualité des séquences aléatoires produites par le générateur des itérations unaires ainsi que @@ -1072,4 +1085,16 @@ Complexité linaire& 0.005 (0.98)& 0.534 (0.99)& 0.085 (0.97)& 0.996 (1.0)\\ \hl \end{table} -% +\section{Conclusion} +Ce chaptitre a montré comment construire un PRNG chaotique, notamment à partir +de codes de Gray équilibrés. Une méthode completement automatique de +construction de ce type de codes a été présentée étendant les méthodes +existantes. +Dans le cas des itérations unaires, +l'algorithme qui en découle a un temps de mélange qui a +une borne sup quadratique de convergence vers la distribution uniforme. +Pratiquement, ce temps de mélange se rapproche de $N\ln N$. +Les expérimentations au travers de la batterie de test de NIST ont montré +que toutes les propriétés statistiques sont obtenues pour + $\mathsf{N} = 4, 5, 6, 7, 8$. + diff --git a/chaosANN.tex b/chaosANN.tex index b814c12..4ea34b9 100644 --- a/chaosANN.tex +++ b/chaosANN.tex @@ -1,5 +1,3 @@ -% \section{Introduction} -% \label{S1} Les réseaux de neurones chaotiques ont été étudiés à de maintes reprises par le passé en raison notamment de leurs applications potentielles: @@ -28,8 +26,6 @@ fonctions chaotiques. - - Ces réseaux de neurones partagent le fait qu'ils sont qualifiés de ``chaotiques'' sous prétexte qu'ils embarquent une fonction de ce type et ce sans aucune preuve rigoureuse. Ce chapitre caractérise la @@ -37,23 +33,13 @@ classe des réseaux de neurones MLP chaotiques. Il s'intéresse ensuite à l'étude de prévisibilité de systèmes dynamiques discrets chaotiques par cette famille de MLP. -\JFC{revoir plan} - -The remainder of this research work is organized as follows. The next -section is devoted to the basics of Devaney's chaos. Section~\ref{S2} -formally describes how to build a neural network that operates -chaotically. Section~\ref{S3} is devoted to the dual case of checking -whether an existing neural network is chaotic or not. Topological -properties of chaotic neural networks are discussed in Sect.~\ref{S4}. -The Section~\ref{section:translation} shows how to translate such -iterations into an Artificial Neural Network (ANN), in order to -evaluate the capability for this latter to learn chaotic behaviors. -This ability is studied in Sect.~\ref{section:experiments}, where -various ANNs try to learn two sets of data: the first one is obtained -by chaotic iterations while the second one results from a non-chaotic -system. Prediction success rates are given and discussed for the two -sets. The paper ends with a conclusion section where our contribution -is summed up and intended future work is exposed. +La section~\ref{S2} définit la construction d'un réseau de neurones +chaotique selon Devanay. La section~\ref{S3} présente l'approche duale +de vérification si un réseau de neurones est chaotique ou non. +La section~\ref{sec:ann:approx} s'intéresse à étudier pratiquement +si un réseau de +neurones peut approximer des itération unaires chaotiques. Ces itérations +étant obtenues à partir de fonction générées à l'aide du chapitre précédent. \section{Un réseau de neurones chaotique au sens de Devaney} @@ -159,7 +145,7 @@ $\textsc{giu}(f)$ est fortement connexe. \section{Un réseau de neurones peut-il approximer -des itération unaires chaotiques?} +des itération unaires chaotiques?}\label{sec:ann:approx} Cette section s'intéresse à étudier le comportement d'un réseau de neurones face à des itérations unaires chaotiques, comme définies à @@ -424,6 +410,11 @@ Nous avons présenté ensuite comment vérifier si un réseau de neurones Nous avons enfin montré en pratique qu'il est difficile pour un réseau de neurones d'apprendre le comportement global d'itérations chaotiques. +Comme il est difficile (voir impossible) d'apprendre le comportement +de telles fonction, il paraît naturelle de savoir si celles ci peuvent être +utilisées pour générer des nombres pseudo aléatoires. + + % \appendix{} % \begin{Def} \label{def2} diff --git 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