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\chapter*{List of Symbols}
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\addcontentsline{toc}{chapter}{List of Symbols}
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\addcontentsline{tof}{chapter}{Liste des symboles et abréviations}
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\begin{longtable}{ll}
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\multicolumn{2}{l}{\scbf{General Notations}} \\
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TM & Turing Machine \\
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$\ppt$ & Probabilistic Polynomial Time \\
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$\epsilon$ & empty word \\
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$\mathbf A$ & bold uppercase letters represent matrices\\
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$\mathbf b$ & bold lowercase letters represent column vectors\\
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$\widetilde{\mathbf A}$ & Gram-Schmidt orthogonalization of matrix $\mathbf A$\\
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$\mathbf{A}^T_{}, \mathbf{u}^T_{}$ & the transpose of a matrix or a vector respectively\\
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2018-04-10 14:48:01 +00:00
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$\U(S)$ & If $S$ is a finite set, $\U(S)$ denotes the uniform distribution over $S$ \\
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[1ex] \multicolumn{2}{l}{\scbf{Usual sets}} \\
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$\QQ$ & the set of rational numbers \\
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$\RR$ & the set of real numbers \\
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$\ZZ$ & the set of relative integers \\
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$\ZZ_q$ & the field $\ZZ_{/q\ZZ}$, with $q$ prime \\
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$\FF_2$ & the field $\ZZ_{/2\ZZ}$ \\
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[1ex] \multicolumn{2}{l}{\scbf{Protocols}} \\
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$\PKE$ & Public Key Encryption \\
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$\ZK$ & Zero-Knowledge \\
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$\NIZK$ & Non-Interactive Zero-Knowledge \\
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$\OT$ & Oblivious Transfer \\
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[1ex] \multicolumn{2}{l}{\scbf{Security Models}} \\
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$\ROM$ & Random-Oracle Model \\
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$\UC$ & Universal Composability \\
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[1ex] \multicolumn{2}{l}{\scbf{Security Assumptions}} \\
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[.5ex] \multicolumn{2}{l}{\quad\textbf{Lattice-based}} \\
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$\SIS$ & Short Integer Solution \\
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$\ISIS$ & Inhomogeneous Short Integer Solution \\
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$\LWE$ & Learning with Errors \\
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$\SIVP$ & Shortest Independent Vectors Problem \\
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[.5ex] \multicolumn{2}{l}{\quad\textbf{Cyclic groups}} \\
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$\DLP$ & Discrete Logarithm Problem \\
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$\DDH$ & Decisional Diffie-Hellman \\
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[.5ex] \multicolumn{2}{l}{\quad\textbf{Bilinear groups}} \\
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2018-03-20 10:06:46 +00:00
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$\SXDH$ & Symmetric eXternal Diffie-Hellman \\
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$\SDL$ & Symmetric Discrete Logarithm
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\end{longtable}
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