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\chapter*{Résumé}
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\addcontentsline{toc}{chapter}{Résumé}
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\begin{comment}
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\begin{otherlanguage}{french}
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Dans cette thèse, nous étudions les constructions cryptographiques prouvées pour la protection de la vie privée.
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Pour cela nous nous sommes intéressés aux preuves et arguments à divulgation nulles de connaissances et leurs applications.
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Finalement, ces travaux nous ont amené à la construction d'un schéma de transfert inconscient adaptatif avec contrôle d'accès à base de réseaux euclidiens.
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Ces constructions à base de réseaux ont été rendues possibles par l'amélioration graduelle de l'expressivité du protocole de Stern.
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\end{otherlanguage}
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\end{comment}
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\clearpage
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\flushright
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1
chap-GE-LWE.tex
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1
chap-GE-LWE.tex
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\chapter{Lattice-Based Group Encryption}
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1
chap-GS-LWE.tex
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chap-GS-LWE.tex
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\chapter{Lattice-Based Dynamic Group Signatures}
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1
chap-OT-LWE.tex
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chap-OT-LWE.tex
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\chapter{Lattice-Based Oblivious Transfer with Access Control}
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chap-ZK.tex
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chap-ZK.tex
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\chapter{Zero-Knowledge Arguments}
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\section{Schnorr Proofs}
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\section{Stern-like Proofs}
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\chapter{Introduction}
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\chapter{Pairing-based cryptography}
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chap-proofs.tex
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chap-proofs.tex
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\chapter{Security Proofs in Cryptography}
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\section{Security Reductions}
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\section{Random-Oracle Model and Standard Model}
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1
chap-sigmasig.tex
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chap-sigmasig.tex
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\chapter{Pairing-Based Dynamic Group Signatures}
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7
chap-structures.tex
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chap-structures.tex
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\chapter{Underlying Structures}
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\section{Pairing-Based Cryptography}
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\section{Lattice-Based Cryptography}
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\input sec-lattices.tex
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@ -57,7 +57,7 @@ Soutenue publiquement le jj/mm/aaaa, par :\\
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\rule[20pt]{\textwidth}{0.5pt}
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\fontsize{25pt}{28pt}\selectfont
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\textbf{Protocoles cryptographiques pour la protection de la vie privée à base de couplages et de réseaux euclidiens}
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\textbf{Privacy-preserving cryptography from pairings and lattices}
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\rule{\textwidth}{0.5pt}
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30
main.tex
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main.tex
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\renewcommand*{\backref}[1]{}
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\renewcommand*{\backrefalt}[4]{\small Citations: \S{} #4}
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\hypersetup{colorlinks=true, linkcolor=black!50!blue, citecolor=black!50!green, breaklinks=true}
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% numbering
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\setsecnumdepth{subsection}
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\maxtocdepth {subsection}
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\usepackage{amsmath, amssymb, mathrsfs}
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\usepackage{amsthm}
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\usepackage{comment}
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\newtheorem{theorem}{Theorem}
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\newtheorem{lemma}{Lemma}
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\end{flushright}
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\vspace*{\stretch{2}}
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\input acknowledgements
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\input abstract
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\input acknowledgements
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\cleardoublepage
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\tableofcontents
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\mainmatter
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\input chap-introduction
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\part{Background and Definitions}
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\input chap-lattices
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\part{Background}
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\input chap-proofs
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\input chap-pairings
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\input chap-structures
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\input chap-ZK
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\part{Group Signatures and Anonymous Credentials}
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\input chap-sigmasig
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\input chap-GS-LWE
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\part{Group Encryption and Adaptive Oblivious Transfer}
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\input chap-GE-LWE
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\input chap-OT-LWE
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\part*{Conclusion}
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\bibliographystyle{alpha}
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\bibliography{these.bib}
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\chapter{Lattices}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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% \section{Lattice-Based Cryptography} %
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\subsection{Lattices and Hard Lattice Problems}
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A (full-rank) lattice~$L$ is defined as the set of all integer linear
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combinations of some linearly independent basis
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\leq \sqrt{n} \sigma] \geq 1-2^{-\Omega(n)}.$
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\end{lemma}
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\noindent As shown by Gentry {\em et al.}~\cite{GePeVa08}, Gaussian
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\subsection{Lattice Trapdoors}
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\noindent As shown by Gentry {\em et al.}~\cite{GPV08}, Gaussian
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distributions with lattice support can be sampled efficiently
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given a sufficiently short basis of the lattice.
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lattice $\Lambda^\mathbf{u}_q \left( \left[ \begin{array}{c|c} \mathbf A ~&~ \mathbf A \cdot \mathbf R + \mathbf C \end{array} \right] \right)$.
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%$\{ \mathbf x \in \ZZ^{2 m} : \left[ \begin{array}{c|c} \mathbf A ~&~ \mathbf A \cdot \mathbf R + \mathbf C \end{array} \right] \cdot \mathbf x = \mathbf u \bmod q \}$.
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\end{lemma}
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