diff --git a/symbols.tex b/symbols.tex index d7c6023..9890527 100644 --- a/symbols.tex +++ b/symbols.tex @@ -3,59 +3,61 @@ \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 \\ + \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 \\ $\mathbf{I}_n$ & the $n$ dimension identity matrix in $\RR^{n \times n}$ \\ - $\U(S)$ & If $S$ is a finite set, $\U(S)$ denotes the uniform distribution over $S$\\ + $\U(S)$ & If $S$ is a finite set, $\U(S)$ denotes the uniform distribution over $S$ \\ $\Supp(D)$ & If $D$ is a probability distribution, $\Supp(D)$ denotes the support of $D$ \\ $\Pr[E]$ & Probability that an event $E$ occurs \\ - $D \approx_s D'$ & $D$ is statistically close to $D'$ \\ - [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 $\mathbb{S}$ \\ - $\permutations_D$ & The set of all permutations over $\{1,\ldots, D\}$ \\ - [1ex] \multicolumn{2}{l}{\scbf{Protocols}} \\ - $\PKE$ & Public Key Encryption \\ - $\ZK$ & Zero-Knowledge \\ - $\ZKAoK$ & Zero-Knowledge Argument of Knowledge \\ - $\NIZK$ & Non-Interactive Zero-Knowledge \\ - $\QANIZK$ & Quasi-Adaptive Non-Interactive Zero-Knowledge \\ + $D \approx_s D'$ & The distribution $D$ is statistically close to the distribution $D'$ \\ + [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 $\mathbb{S}$ \\ + $\permutations_k$ & The set of all permutations over $\{1,\ldots, k\}$ \\ + [1ex] \multicolumn{2}{l}{\scbf{Protocols}} \\ + $\PKE$ & Public Key Encryption \\ + $\ZK$ & Zero-Knowledge \\ + $\ZKAoK$ & Zero-Knowledge Argument of Knowledge \\ + $\NIZK$ & Non-Interactive Zero-Knowledge \\ + $\QANIZK$ & Quasi-Adaptive Non-Interactive Zero-Knowledge \\ $\textsf{WI}$ & Witness indistinguishable \\ - $\OT$ & Oblivious Transfer \\ - [1ex] \multicolumn{2}{l}{\scbf{Security Notions}} \\ + $\textsf{GS}$ & Group Signature \\ + $\GE$ & Group Encryption \\ + $\OT$ & Oblivious Transfer \\ + [1ex] \multicolumn{2}{l}{\scbf{Security Notions}} \\ $\advantage{\mathrm{E}}{\adv}$ & Advantage of adversary $\adv$ for experiment $\mathrm{E}$ \\ 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 $1$ \\ + [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 (\cref{de:sis}) \\ + $\ISIS$ & Inhomogeneous Short Integer Solution (\cref{de:sis}) \\ + $\LWE$ & Learning-with-Errors (\cref{de:lwe}) \\ + $\SIVP$ & Shortest Independent Vectors Problem (\cref{de:sivp}) \\ + [.5ex] \multicolumn{2}{l}{\quad\textbf{Cyclic groups}} \\ + $\DLP$ & Discrete Logarithm Problem (\cref{de:DLP}) \\ + $\DDH$ & Decisional Diffie-Hellman (\cref{de:DDH}) \\ + [.5ex] \multicolumn{2}{l}{\quad\textbf{Bilinear groups}} \\ + $\SXDH$ & Symmetric eXternal Diffie-Hellman (\cref{de:SXDH}) \\ + $\SDL$ & Symmetric Discrete Logarithm (\cref{de:SDL}) \\ + [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}