From fcbc9202a51285ff17060f4d330eca0d57b2a3c1 Mon Sep 17 00:00:00 2001 From: couchot Date: Sun, 29 Jan 2017 19:59:04 +0100 Subject: [PATCH 1/1] la veille --- talk/analysevectorielle.tex | 6 +-- talk/asynchrone.tex | 4 +- talk/attracteurs.tex | 13 +++---- talk/bilanacademique.tex | 11 +++--- talk/bittar.tex | 7 ++-- talk/chaosDevaney.tex | 2 +- talk/chaosDevaneyGeneralisees.tex | 18 ++++----- talk/chaosDevaneyUnaire.tex | 15 +++++--- talk/complexity.png | Bin 0 -> 38988 bytes talk/complexity2.png | Bin 0 -> 38988 bytes talk/condunif.tex | 2 +- talk/graphes.tex | 10 +++++ talk/gray.tex | 2 +- talk/hamiltonien1.tex | 4 +- talk/jacobienne.tex | 2 +- talk/kyko.png | Bin 0 -> 53446 bytes talk/main.tex | 61 +++++++++++++++++------------- talk/marquage.tex | 8 ++-- talk/perspectives.tex | 6 +-- talk/plusqu1bit.tex | 8 ++-- talk/preuveconvmotiv.tex | 4 +- talk/prnggeneralise.tex | 28 ++++++++------ talk/prnggeneralise2.tex | 46 ++++++++++++---------- talk/prngunauretheorieok.tex | 58 ++++------------------------ talk/stabylo.tex | 9 +++-- talk/steganalyse.png | Bin 0 -> 9249 bytes talk/synthesescientifique.tex | 6 +-- talk/tipe12.tex | 14 +++---- talk/xplprngyestheorieko.tex | 4 +- talk/xplsddasync.tex | 2 +- 30 files changed, 169 insertions(+), 181 deletions(-) create mode 100644 talk/complexity.png create mode 100644 talk/complexity2.png create mode 100644 talk/kyko.png create mode 100644 talk/steganalyse.png diff --git a/talk/analysevectorielle.tex b/talk/analysevectorielle.tex index 8e2bcde..cb6a66b 100644 --- a/talk/analysevectorielle.tex +++ b/talk/analysevectorielle.tex @@ -12,9 +12,9 @@ hessienne. \end{itemize} \begin{block}{Gradient dans des image~\cite{ccfg16:ip}} -\begin{minipage}{0.60\textwidth} +\begin{minipage}{0.55\textwidth} \begin{itemize} -\item Approches usuelles: convolutions avec des noyaux de type `Sobel'', +\item Approches usuelles: convolutions avec des noyaux de type ``Sobel'', ``Prewitt'',\ldots \item Proposition : noyaux de taille variable \\(entre 3 et 13) \begin{enumerate} @@ -26,7 +26,7 @@ hessienne. \begin{minipage}{0.30\textwidth} %\vspace{-3em} %\begin{center} -\includegraphics[scale=0.3]{steganalyse} +\includegraphics[scale=0.25]{kyko.png} %\end{center} \end{minipage} \end{block} diff --git a/talk/asynchrone.tex b/talk/asynchrone.tex index d408ddf..4fd9857 100644 --- a/talk/asynchrone.tex +++ b/talk/asynchrone.tex @@ -2,9 +2,9 @@ \item Deux modes: \begin{itemize} \item - \emph{Synchrone}: chaque élément attend la valeur des élements dont il dépend. + \emph{Synchrone}: les éléments itèrent simultanément. \item - \emph{Asynchrone}: chaque élément met à jour sa valeur sans attendre. + \emph{Asynchrone}: les éléments peuvent itérer sans attendre. \end{itemize} \item $(D^{t})^{t \in \Nats}$: suite de matrices de taille $\mathsf{N} \times \mathsf{N}$ t.q. diff --git a/talk/attracteurs.tex b/talk/attracteurs.tex index c5ccf6f..e5310e8 100644 --- a/talk/attracteurs.tex +++ b/talk/attracteurs.tex @@ -1,12 +1,9 @@ \begin{itemize} - \item $x$ \emph{point fixe} de $f$ si $x = f (x)$ - \item $A$ \emph{attracteurs} du graphe si -\begin{itemize} - \item pour tout arc $x \rightarrow y$ , si $x \in A$, alors - $y \in A$ et -\item $A$: le plus petit au sens de l'inclusion -\end{itemize} -\end{itemize} + \item \emph{Attracteurs} $A$ du graphe: le plus petit ss ens. (au sens de l'inclusion) t.q.\\ + pour tout arc $x \rightarrow y$ , si $x \in A$, alors + $y \in A$. + \item \emph{Point fixe} $x$ de $f$: si $x = f (x)$. + \end{itemize} \vspace{-1em} \begin{block}{Attracteurs de diff --git a/talk/bilanacademique.tex b/talk/bilanacademique.tex index 665079b..f58b11e 100644 --- a/talk/bilanacademique.tex +++ b/talk/bilanacademique.tex @@ -2,12 +2,11 @@ \begin{itemize} \item Encadrement doctoral: \begin{itemize} - \item Soutenue: dec. 16, Bassam Alkindy (40\%). - \item En cours: Youssra Fadil (50\%), Mohamed Bakiri (50\%), Nesrine Khernane (50\%). + \item Soutenue: Bassam Alkindy (dec. 15, 40\%). + \item En cours: Youssra Fadil (mar. 17, 50\%), Mohamed Bakiri (dec. 17, 50\%), Nesrine Khernane (dec. 18, 50\%). \end{itemize} \item 10 Reviews de journaux internationaux référencés. -\item $2\times$ sessionchair, $1\times$ chairman en conférence - internationale. +%\item $2\times$ sessionchair, $1\times$ chairman en conférence internationale. \item 1 projet région (15--18) ``capteurs multimédias collaboratifs: une approche intégrée de la sécurité et de la robustesse''. @@ -35,7 +34,7 @@ % conf inter -\cite{bcg11:ip,bcg11b:ip,acgs13:onp,chgw+14:onp} +\cite{bcg11:ip,bcg11b:ip} \\ %\hline @@ -64,6 +63,6 @@ \end{tabular} \end{center} \item Mandat d'élu: conseil d'institut de l'IUT BM (10--14). -\item Réponsabilité pédagogique: responsable de la LP SIL CAM, TeProw +\item Responsabilité pédagogique: responsable de la LP SIL CAM, TeProw (14--\ldots). \end{itemize} diff --git a/talk/bittar.tex b/talk/bittar.tex index 5391257..87a9aad 100644 --- a/talk/bittar.tex +++ b/talk/bittar.tex @@ -7,12 +7,11 @@ \begin{block}{STDM dans les PDF textuels~\cite{BDCC16}} \begin{itemize} \item Hôte: l'ensemble des abscisses des caractères du document. -\item Application directe de STDM, de quantification $\Delta$. -\item Compromis: +\item Application de STDM avec comme compromis: \begin{itemize} \item Robustesse: possibilité de retrouver la marque face à chaque - attaque qui laissant le document lisible. -\item Imperceptibilité: le document initialement lisible. + attaque laissant le document lisible. +\item Imperceptibilité: difficile de distinguer l'hôte original du document marqué. \end{itemize} \end{itemize} \end{block} diff --git a/talk/chaosDevaney.tex b/talk/chaosDevaney.tex index 1226075..4b48a58 100644 --- a/talk/chaosDevaney.tex +++ b/talk/chaosDevaney.tex @@ -3,7 +3,7 @@ $k$ continue sur $(\mathcal{X},d)$ est chaotique si elle est transitive, régulière et fortement sensible aux conditions initiales. \begin{itemize} -\item \emph{Transitivitivé}: pour chaque point, chacun de ses voisinages +\item \emph{Transitivité}: pour chaque point, chacun de ses voisinages a un futur pouvant contenir tout point de l'espace. \item \emph{Régularité}: l'ensemble de ses points périodiques est dense dans $\mathcal{X}$. diff --git a/talk/chaosDevaneyGeneralisees.tex b/talk/chaosDevaneyGeneralisees.tex index 99fd442..36a7868 100644 --- a/talk/chaosDevaneyGeneralisees.tex +++ b/talk/chaosDevaneyGeneralisees.tex @@ -1,15 +1,19 @@ \begin{itemize} -\item Vers une fonction de -$\mathcal{X}_g =\Bool^{\mathsf{N}} + +\item $\mathcal{X}_g =\Bool^{\mathsf{N}} \times \left(\mathcal{P}([{\mathsf{N}}]\right)^{\Nats}$ -dans lui même: + et $G_{f_g}: \mathcal{X}_g \rightarrow \mathcal{X}_g$ tq. + $ + G_{f_g}(x,s)=(F_{f_g}(x,s_0),\sigma(s)), + $: + \begin{itemize} \item $F_{f_g}: \Bool^{\mathsf{N}} \times \mathcal{P}([{\mathsf{N}}]) \rightarrow \Bool^{\mathsf{N}}$ par $ - F_{f_g}(x,s)_i=\left\{ + F_{f_g}(x,s_0)_i=\left\{ \begin{array}{l} - f_i(x) \textrm{ si $i \in s$;}\\ + f_i(x) \textrm{ si $i \in s_0$;}\\ x_i \textrm{ sinon.} \end{array}\right. $ @@ -18,10 +22,6 @@ dans lui même: \rightarrow \mathcal{P}([{\mathsf{N}}])^{\Nats}$ t.q. $\forall t\in\Nats,\sigma(s)_t=s_{t+1}$ -\item $G_{f_g}$ définie par - $ - G_{f_g}(x,S)=(F_{f_g}(x,s_0),\sigma(S)), - $ \end{itemize} diff --git a/talk/chaosDevaneyUnaire.tex b/talk/chaosDevaneyUnaire.tex index f3efc5e..9b80fbd 100644 --- a/talk/chaosDevaneyUnaire.tex +++ b/talk/chaosDevaneyUnaire.tex @@ -1,13 +1,11 @@ \begin{itemize} -\item Vers une fonction de -$\mathcal{X}_u =\Bool^{\mathsf{N}} \times [{\mathsf{N}}]^\Nats$ -dans lui même~\cite{guyeuxphd}: +\item $\mathcal{X}_u =\Bool^{\mathsf{N}} \times [{\mathsf{N}}]^\Nats$ et +$G_{f_u}:\mathcal{X}_u \rightarrow \mathcal{X}_u$ tq. + $G_{f_u}(x,s)=(F_{f_u}(x,s_0),\sigma(s))$~\cite{guyeuxphd}: \begin{itemize} \item $F_{f_u}: \Bool^{\mathsf{N}} \times [{\mathsf{N}}] \rightarrow \Bool^{\mathsf{N}}$, $(x,i) \mapsto (x_1,\dots,x_{i-1},f_i(x),x_{i+1},\dots,x_{\mathsf{N}})$ \item $\sigma: [{\mathsf{N}}]^\Nats \rightarrow [{\mathsf{N}}]^\Nats$ t.q. $\forall t\in\Nats,\sigma(s)_t=s_{t+1}$ -\item $G_{f_u}$ définie par - $G_{f_u}(x,s)=(F_{f_u}(x,s_0),\sigma(s))$ \end{itemize} \item Distance $d$: $d((x,s),(x',s'))= d_H(x,x')+d_S(s,s')$ @@ -19,3 +17,10 @@ Soit $f:\Bool^{\mathsf{N}}\to\Bool^{\mathsf{N}}$. 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a/talk/condunif.tex +++ b/talk/condunif.tex @@ -48,7 +48,7 @@ \end{array} \right) $ - \item $\pi_h=(\frac{1}{2}, \frac{1}{2},\frac{1}{2},\frac{1}{2})$ + \item $\pi_h=(\frac{1}{4}, \frac{1}{4},\frac{1}{4},\frac{1}{4})$ \end{itemize} \end{minipage} \end{block} diff --git a/talk/graphes.tex b/talk/graphes.tex index bf29c3e..957331c 100644 --- a/talk/graphes.tex +++ b/talk/graphes.tex @@ -34,5 +34,15 @@ x_1 + x_2 + x_3)$.} %\caption{} \end{figure} \end{block} + +\begin{itemize} +\item Etude du comportement / schéma: +\begin{itemize} +\item Convergence vers des points fixes. +\item Divergence: entrée dans des cycles. +\end{itemize} +\end{itemize} + + % On remarque le cycle $((101,111),(111,011),(011,101))$ % à la \textsc{Figure}~(\ref{fig:fsig}). \ No newline at end of file diff --git a/talk/gray.tex b/talk/gray.tex index 6888dad..6571035 100644 --- a/talk/gray.tex +++ b/talk/gray.tex @@ -6,7 +6,7 @@ preuve de l'existence (sans construction) de cycle hamiltonien équilibré. \begin{theorem}[Constr. de cycle hamiltonien équilibré~\cite{ccgh16}] -Il existe une séquence (et construction de celle-ci) dans de l'extension +Il existe une séquence (et construction de celle-ci) dans l'extension de l'algorithme de \emph{Robinson-Cohn} telle que le cycle est équilibré. \end{theorem} diff --git a/talk/hamiltonien1.tex b/talk/hamiltonien1.tex index b532822..8343765 100644 --- a/talk/hamiltonien1.tex +++ b/talk/hamiltonien1.tex @@ -12,7 +12,7 @@ $000,100,101,001,011,111,110,010,000$. \begin{minipage}{0.49\textwidth} %\includegraphics[scale=0.5]{iter_f0c} \includegraphics<1>[scale=0.4]{../images/iter_f0c} - \includegraphics<2>[scale=0.4]{../images/iter_f0d} + \includegraphics<2>[scale=0.4]{./iter_f0d2} \end{minipage} \begin{minipage}{0.49\textwidth} \vspace{-1em} @@ -36,7 +36,7 @@ M=\dfrac{1}{3} \left( \begin{theorem}[ $\mathsf{N}$-cube privé d'un cycle hamiltonien ~\cite{chgw+14:oip}] - Dans un $\mathsf{N}$-cube, dans lequel un cycle hamiltonien a été enelvé: + Dans un $\mathsf{N}$-cube, dans lequel un cycle hamiltonien a été enlevé: \begin{itemize} \item La matrice de Markov engendrée est doublement stochastique. \item Le graphe $\textsc{giu}$ correspondant est fortement connexe. diff --git a/talk/jacobienne.tex b/talk/jacobienne.tex index 144bfdc..e29bd94 100644 --- a/talk/jacobienne.tex +++ b/talk/jacobienne.tex @@ -10,7 +10,7 @@ $f'_{ij}=\dfrac{f_i(\overline{x}^j){-}f_i(x)}{\overline{x_j}{-}x_j}$. \end{itemize} \end{itemize} -\begin{block}{Graphes des interractions de +\begin{block}{Graphes des interactions de $(x_1, x_2, x_3) \mapsto ((\overline{x_1} + \overline{x_2}).x_3, x_1.x_3, diff --git a/talk/kyko.png b/talk/kyko.png new file mode 100644 index 0000000000000000000000000000000000000000..c9f653c817b19a0adaf9c6f4152aec71783f1a15 GIT binary patch literal 53446 zcmeFYWmJ@3_%=F2Hww}z5>f&VDJjxONF!ZCNP~1LN;lFWk`j{AF@k{N5Q>sRmnaO~ zb@ups|L-~Ltn=x7IbY7K#TtcY=Gpsx?tSm;y6$U7YilZ#644VuAP`bj6$Kp#1e+BC 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+%\pgfpagesuselayout{2 on 1 with notes}[a4paper,border shrink=5mm] % \theoremstyle{plain} % \theoremsymbol{\ensuremath{\clubsuit}} @@ -110,51 +115,53 @@ %\frame{\frametitle{Plan}\tableofcontents[hideallsubsections]} -\section{Introduction: iterations de réseaux booléens} +\section{Introduction: itérations de réseaux booléens (07--09)} \inputFrameb{Réseau booléen (définition)}{rb} -\inputFrameb{3 schémas $\leadsto$ 3 graphes d'itérations}{graphes} -\inputFrameb{Attracteurs}{attracteurs} +\inputFrameb{Graphes d'itérations et convergence}{graphes} +%\inputFrameb{Comportement / attracteurs}{attracteurs} \inputFrameb{Dépendance entre éléments}{jacobienne} -\inputFrameb{Mode asynchrone}{asynchrone} -\inputFrameb{Un exemple motivant}{xplsddasync} +%\inputFrameb{Mode asynchrone}{asynchrone} +%\inputFrameb{Un exemple motivant}{xplsddasync} %\inputFrameb{Problématique}{sddproblematique} \frame{\frametitle{Plan}\tableofcontents[hideallsubsections]} -\section{Réseaux booléens: des preuves de convergences}\label{sec:sdd} -\frame{\frametitle{Plan}\tableofcontents[currentsection]} -\inputFrameb{Suffisamment de synchronisme}{synchronisons} -\inputFrameb{Mode mixte avec $g$}{mixteexample} -\inputFrameb{Convergence par la pratique}{preuveconvmotiv} -\inputFrameb{Du système booléen au modèle PROMELA}{sdd2promela} +% \section{Réseaux booléens: des preuves de convergences}\label{sec:sdd} +% \frame{\frametitle{Plan}\tableofcontents[currentsection]} +% \inputFrameb{Suffisamment de synchronisme}{synchronisons} +% \inputFrameb{Mode mixte avec $g$}{mixteexample} +% \inputFrameb{Convergence par la pratique}{preuveconvmotiv} +% \inputFrameb{Du système booléen au modèle PROMELA}{sdd2promela} -\section{Des systèmes dynamiques discrets au chaos}\label{sec:sddchaos} -\frame{\frametitle{Plan}\tableofcontents[currentsection]} -\inputFrameb{Rappels sur les itérations chaotiques}{chaosDevaney} -\inputFrameb{Espace pour itérations chaotiques (unaires)}{chaosDevaneyUnaire} -\inputFrameb{Espace pour itérations chaotiques (généralisées)}{chaosDevaneyGeneralisees} +\section{Des systèmes dynamiques discrets au chaos (09--12)}\label{sec:sddchaos} +\subsection{Bahi, Guyeux, Richard} +\frame{\frametitle{Plan}\tableofcontents[currentsection,hideothersubsections]} +\inputFrameb{Contexte: chaos selon Devaney}{chaosDevaney} +\inputFrameb{``Chaoticité'' des itérations unaires/généralisées}{chaosDevaneyUnaire} +%\inputFrameb{``Chaoticité'' des itérations généralisées}{chaosDevaneyGeneralisees} \inputFrameb{Générer un graphe ${\textsc{giu}}$ fortement connexe}{tipe12} -\section{Applications à la génération de nombres pseudo-aléatoires}\label{sec:prng} -\frame{\frametitle{Plan}\tableofcontents[currentsection]} +\section{Application à la génération de nombres pseudo-aléatoires (11--\ldots)}\label{sec:prng} +\subsection{Bahi, Bakiri, Contassot-Vivier, Guyeux, Heam, Richard, Wang} +\frame{\frametitle{Plan}\tableofcontents[currentsection,hideothersubsections]} \inputFrameb{PRNG par itérations unaires}{prngualgo} \inputFrameb{Condition néc. suff. pour l'uniformité}{condunif} \inputFrameb{Succès pratiques et limites théoriques}{xplprngyestheorieko} - -\inputFrameb{Espace pour itérations chaotiques ($b$)}{prngunauretheorieok} +\inputFrameb{Formalisation de $b$ itérations unaires}{prngunauretheorieok} \inputFrameb{$\textsc{giu}$ fortement connexe par construction}{hamiltonien1} \inputFrameb{Cycle hamiltonien équilibré}{gray} -\inputFrameb{Evaluation de l'écart / ditribution uniforme}{heam} +\inputFrameb{Évaluation de l'écart / distribution uniforme}{heam} \inputFrameb{Et les itérations généralisées?}{prnggeneralise} -\inputFrameb{Analyse pratique des deux classes de PRNGS}{prnggeneralise2} +\inputFrameb{Plateforme d'implantation FPGA~\cite{DBLP:conf/secrypt/MohammedCG16}}{prnggeneralise2} -\section{Application au masquage d'information}\label{sec:ih} -\frame{\frametitle{Plan}\tableofcontents[currentsection]} -\inputFrameb{Marquage de média: un processsus iteratif}{marquage} +\section{Application au masquage d'information (11--\ldots)}\label{sec:ih} +\subsection{Bahi, Bittar, Couturier, Darazi, Fadil, Friot, Guyeux} +\frame{\frametitle{Plan}\tableofcontents[currentsection,hideothersubsections]} +\inputFrameb{Marquage de média: un processus itératif}{marquage} \inputFrameb{Embarquons plus qu'un bit}{plusqu1bit} \inputFrameb{Tatouage (flottant) de PDF }{bittar} \inputFrameb{Stéganographie: introduction avec STABYLO }{stabylo} @@ -162,7 +169,7 @@ \section{Conclusion} -\frame{\frametitle{Plan}\tableofcontents[currentsection]} +\frame{\frametitle{Plan}\tableofcontents[currentsection,hideothersubsections]} \inputFrameb{Synthèse scientifique}{synthesescientifique} \inputFrameb{Perspectives}{perspectives} \inputFrameb{Bilan académique}{bilanacademique} diff --git a/talk/marquage.tex b/talk/marquage.tex index 4367be9..5618744 100644 --- a/talk/marquage.tex +++ b/talk/marquage.tex @@ -3,7 +3,7 @@ \label{def:dhCI:ext} Soit un hôte $x$, $u_m$ les indices de ses bits modifiables, $\phi_{m}$ leur valeur, - $y$ un message, $q$ un nombre d'itération. + $y$ un message, $q$ un nombre d'itérations. L'algorithme d'embarquement retourne le résultat de l'embarquement de $\hat{y}$ dans $x$, t. q.: \begin{itemize} @@ -21,11 +21,11 @@ si $f_l$ est tq. $\textsc{giu}(f_l)$ fortement connexe et a une matrice de Markov doublement stochastique. \begin{itemize} -\item Le marquage est $\epsilon$-stégo sécure. -\item Le marquage est chaos sécure. +\item Le marquage est $\epsilon$-stégo sécurisé. +\item Le marquage est chaos sécurisé. \end{itemize} \end{theorem} \begin{itemize} \item Particularisation dans différents domaines (spatial, fréquentiel). -\item Robustesse evaluée. +\item Robustesse évaluée. \end{itemize} diff --git a/talk/perspectives.tex b/talk/perspectives.tex index afd14ae..27d5b5b 100644 --- a/talk/perspectives.tex +++ b/talk/perspectives.tex @@ -3,12 +3,10 @@ \begin{itemize} \item S'affranchir de l'algorithme \emph{Robinson-Cohn}: trop restrictif. \item Génération exhaustive de cycles non isomorphes: une forme canonique. - \item Equilibre local, global: conséquences dans un PRNG. + \item Équilibre local, global: conséquences dans un PRNG. \end{itemize} \item Générateurs de nombres pseudo-aléatoires: \begin{itemize} - \item Implantation sur FPGA ou ASIC: - comparaison pratique avec l'état de l'art. \item S'affranchir du générateur interne. \item Majorer finement le délai d'obtention de la distribution uniforme. \item Exploiter le $\textsc{gig}$ à la place du $\textsc{giu}$. @@ -16,7 +14,7 @@ \item Masquage d'information: \begin{itemize} \item Creuser la piste \og Analyse vectorielle\fg{}. - \item Steganalyse par Deep Learning: comprendre pourquoi cela marche. + \item Stéganalyse par Deep Learning: comprendre pourquoi cela marche. \item Tatouage STDM dans un PDF: comment contrer les attaques? \end{itemize} \end{itemize} diff --git a/talk/plusqu1bit.tex b/talk/plusqu1bit.tex index 21a9fb9..78abf7e 100644 --- a/talk/plusqu1bit.tex +++ b/talk/plusqu1bit.tex @@ -8,7 +8,7 @@ \item Stratégie de choix $s_c \in [\mathsf{P}]^{\Nats} $: indice de l'élément de $m$ embarqué à l'itération $t$. \item Stratégie de mélange $s_m \in [\mathsf{P}]^{\Nats}$: - élément de $m$ inversé à l'titération $t$. + élément de $m$ inversé à l'itération $t$. \end{itemize} On remplace $x $ par $x^l \in \mathbb{B}^{\mathsf{N}}$ avec $ @@ -39,8 +39,8 @@ est une condition nécessaire et suffisante pour l'extraction du message du média marqué. \end{theorem} -\begin{itemize} -\item Pratique: mesure de Fermi-Dirac utilisée pour la classification. -\end{itemize} +% \begin{itemize} +% \item Pratique: mesure de Fermi-Dirac utilisée pour la classification. +% \end{itemize} diff --git a/talk/preuveconvmotiv.tex b/talk/preuveconvmotiv.tex index f6540e9..0e8c621 100644 --- a/talk/preuveconvmotiv.tex +++ b/talk/preuveconvmotiv.tex @@ -2,10 +2,10 @@ \begin{itemize} \item Conditions suffisantes de convergence: facile à appliquer, domaine restreint. -\item Recherche d'une métrique decroissante minorée: difficile. +%\item Recherche d'une métrique decroissante minorée: difficile. \item Simulations: \begin{itemize} -\item Non exhaustives pour les schémas généralisés et asynchrones. +\item Non exhaustives pour les schémas unaires, généralisés, asynchrones\ldots \item Verdict $\leftrightarrow$ vérité ssi divergence (contre-exemple). \end{itemize} \item Souhait: exploiter un outil qui traiterait toutes les transitions. diff --git a/talk/prnggeneralise.tex b/talk/prnggeneralise.tex index 49152b8..a42b9df 100644 --- a/talk/prnggeneralise.tex +++ b/talk/prnggeneralise.tex @@ -1,26 +1,30 @@ \begin{block}{} \begin{algorithm}[H] -\KwIn{une fonction $f$, un nombre d'itérations $b$, -une configuration initiale $x^0$ (${\mathsf{N}}$ bits)} -\KwOut{une configuration $x$ (${\mathsf{N}}$ bits)} -$x\leftarrow x^0$\; -$k\leftarrow b $\; -\For{$i=1,\dots,k$} +\ldots\For{$i=1,\dots,k$} { $s\leftarrow{\textit{Set}(\textit{Random}(2^{\mathsf{N}}))}$\; $x\leftarrow{F_{f_g}(x,s)}$\; -} -return $x$\; +}\ldots \end{algorithm} \end{block} \begin{theorem}[Uniformité de la sortie ds le cas généralisé] - Soit $f: \Bool^{{\mathsf{N}}} \rightarrow \Bool^{{\mathsf{N}}}$ et - $\check{M}$ sa matrice d'adjacence. + % Soit $f: \Bool^{{\mathsf{N}}} \rightarrow \Bool^{{\mathsf{N}}}$ et + % $\check{M}$ sa matrice d'adjacence. Si $\textsc{gig}(f)$ est fortement connexe, alors la sortie du PRNG suit une loi qui - tend vers la distribution uniforme si - et ssi $\dfrac{1}{2^{\mathsf{N}}} \check{M} + tend vers la distribution uniforme + ssi $\dfrac{1}{2^{\mathsf{N}}} \check{M} $ est une matrice doublement stochastique. \end{theorem} +\begin{block}{Nombre moyen d'appels à un générateur binaire par bit généré} +\begin{itemize} +\item Unaires:$\nearrow$ +\item Généralisées: $\searrow$ +\end{itemize} + + + + +\end{block} diff --git a/talk/prnggeneralise2.tex b/talk/prnggeneralise2.tex index 9a900d9..229376d 100644 --- a/talk/prnggeneralise2.tex +++ b/talk/prnggeneralise2.tex @@ -1,25 +1,33 @@ -\begin{block}{Nombre moyen d'appels à un générateur binaire par bit généré} -$$ -\begin{array}{|l|l|l|l|l|l|} -\hline -\textrm{Itérations} & 4 & 5 & 6 & 7 & 8 \\ -\hline -\textrm{Unaires} & 19.0 & 22.3 & 23.7 & 25.3 & 27.0\\ + +\begin{block}{Bilan d'implantation de PRNGs sur FPGA} +\begin{center} + +\begin{tabular}{|l|l|l|} + \cline{2-3} +\multicolumn{1}{c|}{} & \multicolumn{2}{c|}{Test U01}\\ + \cline{2-3} +\multicolumn{1}{c|}{}& \multicolumn{1}{c|}{KO} & \multicolumn{1}{c|}{OK} \\ \hline -\textrm{Généralisées} & 17 & 13 & 11 & 10 & 9\\ +\multirow{7}{0.3cm}{\begin{turn}{90}Débits (Gb/s)\end{turn}} & Xorshift (8--16) & \\ +& LFSR (6--10) & \onslide<4->{Xor avec 3 PRNGs~\cite{Fang:2014:FAP:2643744.2643848} (8)}\\ +& & \onslide<3->{Hamiltonien, généralisé (2)} \\ +& TGFSR (0.7--1.3) & \\ +& LCG (0.02--0.3) & PCG32 (0.3), MRG32 (0.4) \\ +& & \onslide<2->{Négation, unaire (0.031--3.5)} \\ +& & \onslide<2->{Hamiltonien, unaire (0.05)}\\ \hline -\end{array} -$$ -\end{block} - +\end{tabular} +\end{center} +\onslide<2->{ +Détails d'implantation: \begin{itemize} -\item Fréqence des configurations non accessibles en 1 itération: - \begin{itemize} -\item Unaire: $1-\dfrac{n-1}{2^n}$ (croissant). -\item généralisée: $1/2$ (constant), mais décroissance de la fréquence des - bits constants. -\end{itemize} -\item Test de NIST: succès dans tous les cas. +\item Stratégie: extraite de XorShift128+. +\item $\mathsf{N}$: négation (32), unaire (16), \onslide<3->{ généralisé (4$\times$4).} +\item Mélange: négation (variable), unaire (190), \onslide<3->{ généralisé (4).} \end{itemize} +} +\end{block} + + diff --git a/talk/prngunauretheorieok.tex b/talk/prngunauretheorieok.tex index 38ec70d..e525591 100644 --- a/talk/prngunauretheorieok.tex +++ b/talk/prngunauretheorieok.tex @@ -1,14 +1,9 @@ +\vspace{1em} \begin{itemize} -\item Vers une fonction de -$\mathcal{X}_u =\Bool^{\mathsf{N}} \times \llbracket1;{\mathsf{N}}\rrbracket^\Nats$ -dans lui même~\cite{ccgh16}: -\begin{itemize} -\item $F_{f_u}: \Bool^{\mathsf{N}} \times \llbracket1;{\mathsf{N}}\rrbracket \rightarrow \Bool^{\mathsf{N}}$, -$(x,i) \mapsto (x_1,\dots,x_{i-1},f_i(x),x_{i+1},\dots,x_{\mathsf{N}})$ -\item $\sigma: \llbracket1;{\mathsf{N}}\rrbracket^\Nats \rightarrow \llbracket1;{\mathsf{N}}\rrbracket^\Nats$ t.q. $\forall t\in\Nats,\sigma(s)_t=s_{t+1}$ -\item $G_{{f_u},b}$ définie par - $G_{{f_u},b}(x,s)=(F_{f_u}( \dots(F_{f_u}(x,s_0),\dots),s_{b-1}),\sigma^b(s))$ -\end{itemize} +\item $\mathcal{X}_u =\Bool^{\mathsf{N}} \times [{\mathsf{N}}]^\Nats$ et +$G_{{f_u},b}:\mathcal{X}_u \rightarrow \mathcal{X}_u$ tq. +$$ +G_{{f_u},b}(x,s) = (F_{f_u}( \dots(F_{f_u}(x,s_0),\dots),s_{b-1}),\sigma^b(s))$$ \item Distance $d((x,s),(x',s'))= d_H(x,x')+d''_S(s,s')$ \end{itemize} @@ -20,55 +15,18 @@ le graphe d'itérations $\textsc{giu}_{b}(f)$ est fortement connexe. \end{theorem} - -\vspace{-4.5em} +\vspace{-3em} \begin{center} \begin{minipage}{0.30\textwidth} \begin{center} - \includegraphics[scale=0.35]{../images/h2prng} + \includegraphics[scale=0.31]{../images/h2prng} \end{center} \end{minipage} \begin{minipage}{0.40\textwidth} \begin{center} - \includegraphics[scale=0.35]{../images/h3prng} + \includegraphics[scale=0.31]{../images/h3prng} \end{center} \end{minipage} \end{center} - -% \begin{itemize} -% \item Vers une fonction de -% $\mathcal{X}_u$ dans lui même: -% \begin{itemize} -% \item -% $F_{{f_u},b} : \mathds{B}^\mathsf{N} \times [\mathsf{N}]^{b} -% \rightarrow \mathds{B}^\mathsf{N}$ définie par -% $ -% F_{f_u,b} (x,(u^1, \hdots, u^{b})) = -% F_{f_u}(\hdots (F_{f_u}(x,u^1), \hdots), u^{b}). -% $ - - - -% \item $\sigma: -% \left(\mathcal{P}(\llbracket 1;{\mathsf{N}}\rrbracket)\right)^{\Nats} -% \rightarrow -% \left(\mathcal{P}(\llbracket 1;{\mathsf{N}}\rrbracket)\right)^{\Nats}$ -% t.q. $\forall t\in\Nats,\sigma(s)_t=s_{t+1}$ -% \item $G_{f_g}$ définie par -% \[ -% G_{f_g}(x,S)=(F_{f_g}(x,s_0),\sigma(S)), -% \] - -% \end{itemize} - -% \item Distance $d$: $d((x,s),(x',s'))= d_H(x,x')+d'_S(s,s')$ -% \end{itemize} - -% \begin{theorem}[Fonctions t.q. $G_{f_g}$ est chaotique] -% \label{Th:CaracIC} -% Soit $f:\Bool^{\mathsf{N}}\to\Bool^{\mathsf{N}}$. -% Les itérations de la fonction $G_{f_g}$ sont chaotiques -% si et seulement si $\textsc{gig}(f)$ est fortement connexe. -% \end{theorem} diff --git a/talk/stabylo.tex b/talk/stabylo.tex index a7e5f45..b5fb306 100644 --- a/talk/stabylo.tex +++ b/talk/stabylo.tex @@ -3,7 +3,7 @@ \begin{itemize} \item Objectif: embarquer un message de manière imperceptible. \item Méthode: construction d'une carte de distorsion des éléments modifiables. -\item Evaluation de la sécurité: étude de la détectabilité par steganalyse. +\item Évaluation de la sécurité: étude de la détectabilité par stéganalyse. \end{itemize} \end{itemize} \vspace{-0.5em} @@ -14,7 +14,10 @@ fenêtres. \end{itemize} -\vspace{-3em}\begin{center} -\includegraphics[scale=0.3]{../images/error} +\vspace{-3em} +\begin{center} +\includegraphics[width=0.45\textwidth]{../images/error} +\qquad +\includegraphics[width=0.45\textwidth]{complexity.png} \end{center} \end{block} diff --git a/talk/steganalyse.png b/talk/steganalyse.png new file mode 100644 index 0000000000000000000000000000000000000000..1bf198bd54d0e348a042f265e00a4347dbabd4ba GIT binary patch literal 9249 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d'interaction, par suppression d'1 cycle hamiltonien équilibré. + d'interactions, par suppression d'1 cycle hamiltonien équilibré. \item Application aux PRNG: étude théorique et pratique de la sortie en fonction du nombre d'itérations. \item Masquage d'information: de la propriété de transitivité du chaos diff --git a/talk/tipe12.tex b/talk/tipe12.tex index afd862c..c98676f 100644 --- a/talk/tipe12.tex +++ b/talk/tipe12.tex @@ -35,10 +35,10 @@ Alors, $\textsc{giu}(f)$ est fortement connexe. \end{minipage} \end{center} -\vspace{-3em} -\begin{block}{Apprendre un comportement chaotique par MLP~\cite{bcgs12:ij}} -\begin{itemize} -\item Il est possible de construire un MLP ayant un comportement chaotique. -\item Il est difficile pour un MLP d'apprendre des itérations chaotiques. -\end{itemize} -\end{block} +% \vspace{-3em} +% \begin{block}{Apprendre un comportement chaotique par MLP~\cite{bcgs12:ij}} +% \begin{itemize} +% \item Il est possible de construire un MLP ayant un comportement chaotique. +% \item Il est difficile pour un MLP d'apprendre des itérations chaotiques. +% \end{itemize} +% \end{block} diff --git a/talk/xplprngyestheorieko.tex b/talk/xplprngyestheorieko.tex index 64ca989..446a036 100644 --- a/talk/xplprngyestheorieko.tex +++ b/talk/xplprngyestheorieko.tex @@ -5,7 +5,7 @@ \begin{minipage}{0.8\textwidth} \begin{itemize} \item Seules 16 vérifient les hypothèses du théorème précédent. -\item $b$: nombre d'itérations suffisant pour une déviation p.r. la distribution uniforme inf. à $10^{-4}$. +\item $b$: nombre d'itérations suffisant pour une déviation p.r. la distribution uniforme inf. à $10^{-4}$ (temps de mélange). \begin{center} \begin{tiny} @@ -39,6 +39,6 @@ aux tests du \emph{National Institute of Standards and Technology} (NIST). \item Générateur prouvé chaotique seulement pour $b=1$. \item Pas compatible avec la pratique: $b \geq 42$ nécessaire pour suivre une loi uniforme (à $10^{-4}$ près). -\item $\leadsto$ Etendre la théorie. +\item $\leadsto$ Étendre la théorie. \end{itemize} \end{itemize} diff --git a/talk/xplsddasync.tex b/talk/xplsddasync.tex index 610a1af..ce0075f 100644 --- a/talk/xplsddasync.tex +++ b/talk/xplsddasync.tex @@ -5,7 +5,7 @@ \subfloat[$\textsc{gis}(g)$]{ \includegraphics[scale=0.30]{../images/para_iterate_dec} }\qquad - \subfloat[$\textsc{giu}(g)$ (extrait)]{ + \subfloat[$\textsc{gig}(g)$ (extrait)]{ \includegraphics[scale=0.30]{../images/chao_iterate_excerpt} } \caption{Graphes des itérations synchrones} -- 2.39.5