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Fabrice Mouhartem
2018-04-12 18:42:39 +02:00
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symbols.tex
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\chapter*{List of Symbols}
\chapter*[List of Symbols]{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
\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 $S$\\
$\Pr[E]$ & Probability that an event $E$ occurs \\
[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 $\ZZ_{/2\ZZ}$ \\
$\mathbb{S}^d$ & the set of vectors of dimension $d$ in the set $\mathbb{S}$ \\
$\mathbb{S}^{n \times m}$ & the set of matrices with $n$ rows and $m$ columns in the set $\mathbb{S}$ \\
[1ex] \multicolumn{2}{l}{\scbf{Protocols}} \\
$\PKE$ & Public Key Encryption \\
$\ZK$ & Zero-Knowledge \\
$\ZKAoK$ & Zero-Knowledge Argument of Knowledge \\
$\NIZK$ & Non-Interactive Zero-Knowledge \\
$\OT$ & Oblivious Transfer \\
[1ex] \multicolumn{2}{l}{\scbf{Security Notions}} \\
EU-CMA & Existentially Unforgeable under chosen-message attacks \\
EU-RMA & Existentially Unforgeable under random-message attacks \\
IND-CPA & Indistinguishable under chosen-plaintext attacks (passive adversary) \\
IND-CCA1 & Indistinguishable under non-adaptive active adversary\\
IND-CCA2 & Indistinguishable under adaptive active adversary\\
[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{Lattices}} \\
$\SIS$ & 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 \\
[1ex] \multicolumn{2}{l}{\scbf{Stern-like protocol}} \\
$\mathsf{B}^2_{\mathfrak m}$ & The set of $\bit$ vector of hamming weight $\mathfrak m$ \\
$\mathsf{B}^3_{\mathfrak m}$ & The set of $\nbit$ vectors with $\mathfrak m$ elements in $-1$, $0$ and $1$ \\
\end{longtable}