\chapter*{List of Symbols} \addcontentsline{toc}{chapter}{List of Symbols} \addcontentsline{tof}{chapter}{Liste des symboles et abréviations} \begin{tabular}{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 vectors\\ $\widetilde{\mathbf A}$ & Gram-Schmidt orthogonalization of matrix $\mathbf A$\\ [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}} \\ $\SIS$ & Short Integer Solution \\ $\LWE$ & Learning with Errors \\ $\SIVP$ & Shortest Independent Vectors Problem \\ $\DLP$ & Discrete Logarithm Problem \\ $\DDH$ & Decisional Diffie-Hellman \\ $\SXDH$ & Symmetric eXternal Diffie-Hellman \\ $\SDL$ & Symmetric Discrete Logarithm \end{tabular}