64 lines
3.6 KiB
TeX
64 lines
3.6 KiB
TeX
\chapter*[List of Symbols]{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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$\mathbf{I}_n$ & the $n$ dimension identity matrix in $\RR^{n \times n}$ \\
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$\U(S)$ & If $S$ is a finite set, $\U(S)$ denotes the uniform distribution over $S$ \\
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$\Supp(D)$ & If $D$ is a probability distribution, $\Supp(D)$ denotes the support of $D$ \\
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$\Pr[E]$ & Probability that an event $E$ occurs \\
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$D \approx_s D'$ & The distribution $D$ is statistically close to the distribution $D'$ \\
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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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$\mathbb{S}^d$ & the set of vectors of dimension $d$ in the set $\mathbb{S}$ \\
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$\mathbb{S}^{n \times m}$ & the set of matrices with $n$ rows and $m$ columns in the set $\mathbb{S}$ \\
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$\permutations_k$ & The set of all permutations over $\{1,\ldots, k\}$ \\
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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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$\ZKAoK$ & Zero-Knowledge Argument of Knowledge \\
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$\NIZK$ & Non-Interactive Zero-Knowledge \\
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$\QANIZK$ & Quasi-Adaptive Non-Interactive Zero-Knowledge \\
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$\textsf{WI}$ & Witness Indistinguishable \\
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$\textsf{GS}$ & Group Signature \\
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$\GE$ & Group Encryption \\
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$\OT$ & Oblivious Transfer \\
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[1ex] \multicolumn{2}{l}{\scbf{Security Notions}} \\
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$\advantage{\mathrm{E}}{\adv}$ & Advantage of adversary $\adv$ for experiment $\mathrm{E}$ \\
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EU-CMA & Existentially Unforgeable under chosen-message attacks \\
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EU-RMA & Existentially Unforgeable under random-message attacks \\
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IND-CPA & Indistinguishable under chosen-plaintext attacks (passive adversary) \\
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IND-CCA1 & Indistinguishable under non-adaptive active adversary\\
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IND-CCA2 & Indistinguishable under adaptive active adversary\\
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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{Lattices}} \\
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$\SIS$ & Short Integer Solution (\cref{de:sis}) \\
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$\ISIS$ & Inhomogeneous Short Integer Solution (\cref{de:sis}) \\
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$\LWE$ & Learning-with-Errors (\cref{de:lwe}) \\
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$\SIVP$ & Shortest Independent Vectors Problem (\cref{de:sivp}) \\
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[.5ex] \multicolumn{2}{l}{\quad\textbf{Cyclic groups}} \\
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$\DLP$ & Discrete Logarithm Problem (\cref{de:DLP}) \\
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$\DDH$ & Decisional Diffie-Hellman (\cref{de:DDH}) \\
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[.5ex] \multicolumn{2}{l}{\quad\textbf{Bilinear groups}} \\
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$\SXDH$ & Symmetric eXternal Diffie-Hellman (\cref{de:SXDH}) \\
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$\SDL$ & Symmetric Discrete Logarithm (\cref{de:SDL}) \\
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[1ex] \multicolumn{2}{l}{\scbf{Stern-like protocol}} \\
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$\mathsf{B}^2_{\mathfrak m}$ & The set of $\bit$ vector of hamming weight $\mathfrak m$ \\
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$\mathsf{B}^3_{\mathfrak m}$ & The set of $\nbit$ vectors with $\mathfrak m$ elements in $-1$, $0$ and $1$ \\
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\end{longtable}
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