\chapter*{List of Symbols}
\addcontentsline{toc}{chapter}{List of Symbols}
\addcontentsline{tof}{chapter}{Liste des symboles et abréviations}

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