2018-01-27 20:27:06 +00:00
|
|
|
\chapter*{List of Symbols}
|
|
|
|
|
\addcontentsline{toc}{chapter}{List of Symbols}
|
2018-04-04 16:46:37 +00:00
|
|
|
\addcontentsline{tof}{chapter}{Liste des symboles et abréviations}
|
2018-01-27 20:27:06 +00:00
|
|
|
|
2018-04-06 13:46:55 +00:00
|
|
|
\begin{longtable}{ll}
|
2018-02-09 11:53:52 +00:00
|
|
|
\multicolumn{2}{l}{\scbf{General Notations}} \\
|
|
|
|
|
TM & Turing Machine \\
|
|
|
|
|
$\ppt$ & Probabilistic Polynomial Time \\
|
|
|
|
|
$\epsilon$ & empty word \\
|
2018-04-04 16:46:37 +00:00
|
|
|
$\mathbf A$ & bold uppercase letters represent matrices\\
|
|
|
|
|
$\mathbf b$ & bold lowercase letters represent vectors\\
|
|
|
|
|
$\widetilde{\mathbf A}$ & Gram-Schmidt orthogonalization of matrix $\mathbf A$\\
|
2018-04-06 13:46:55 +00:00
|
|
|
[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 $\ZZ_{/2\ZZ}$ \\
|
2018-02-09 11:53:52 +00:00
|
|
|
[1ex] \multicolumn{2}{l}{\scbf{Protocols}} \\
|
2018-02-09 12:16:05 +00:00
|
|
|
$\PKE$ & Public Key Encryption \\
|
|
|
|
|
$\ZK$ & Zero-Knowledge \\
|
2018-02-09 11:53:52 +00:00
|
|
|
$\NIZK$ & Non-Interactive Zero-Knowledge \\
|
2018-02-10 14:32:00 +00:00
|
|
|
$\OT$ & Oblivious Transfer \\
|
2018-02-09 11:53:52 +00:00
|
|
|
[1ex] \multicolumn{2}{l}{\scbf{Security Models}} \\
|
|
|
|
|
$\ROM$ & Random-Oracle Model \\
|
|
|
|
|
$\UC$ & Universal Composability \\
|
|
|
|
|
[1ex] \multicolumn{2}{l}{\scbf{Security Assumptions}} \\
|
2018-04-06 13:46:55 +00:00
|
|
|
[.5ex] \multicolumn{2}{l}{\quad\textbf{Lattice-based}} \\
|
2018-02-09 11:53:52 +00:00
|
|
|
$\SIS$ & Short Integer Solution \\
|
2018-04-06 13:46:55 +00:00
|
|
|
$\ISIS$ & Inhomogeneous Short Integer Solution \\
|
2018-02-09 11:53:52 +00:00
|
|
|
$\LWE$ & Learning with Errors \\
|
|
|
|
|
$\SIVP$ & Shortest Independent Vectors Problem \\
|
2018-04-06 13:46:55 +00:00
|
|
|
[.5ex] \multicolumn{2}{l}{\quad\textbf{Cyclic groups}} \\
|
2018-02-09 11:53:52 +00:00
|
|
|
$\DLP$ & Discrete Logarithm Problem \\
|
|
|
|
|
$\DDH$ & Decisional Diffie-Hellman \\
|
2018-04-06 13:46:55 +00:00
|
|
|
[.5ex] \multicolumn{2}{l}{\quad\textbf{Bilinear groups}} \\
|
2018-03-20 10:06:46 +00:00
|
|
|
$\SXDH$ & Symmetric eXternal Diffie-Hellman \\
|
|
|
|
|
$\SDL$ & Symmetric Discrete Logarithm
|
2018-04-06 13:46:55 +00:00
|
|
|
\end{longtable}
|
