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Fabrice Mouhartem
2018-04-12 18:42:39 +02:00
parent 324565e63c
commit b87c4a9de1
15 changed files with 605 additions and 128 deletions
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10
fig-lwe-sis.tex
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@ -11,9 +11,9 @@
\draw[matA, xshift=-2cm, yshift=.5cm] (0,0) rectangle node {$\mathbf{A}$} (1.5,1);
\node at (-.2, .75) {$,$};
\draw[matA] (0,0) rectangle node {$\mathbf{A}^T_{}$} (1,1.5);
\draw[|-|, vecS] (1.2, 1.5) -- node[right] {$\mathbf s$} ++(0, -1);
\draw[|-|, vecS] (1.2, 1.5) -- node[right] {$\mathbf{s}$} ++(0, -1);
\node at (1.8, .75) {$+$};
\draw[|-|, vecE] (2.1, 1.5) -- node[right] {$\mathbf e$} ++ (0, -1.5);
\draw[|-|, vecE] (2.1, 1.5) -- node[right] {$\mathbf{e}$} ++ (0, -1.5);
\end{tikzpicture}
\right)$\\[.5em]
$\in \Zq^{n \times m} \times \Zq^{m}$,
@ -22,15 +22,15 @@
\begin{minipage}[t]{.4\textwidth}
\textbf{$\SIS_{n,m,q,\beta}$ problem:}\\Given\\[.5em]
$\tikz[baseline=.3cm]{ \draw[fill=blue!10] (0,0) rectangle node {$\mathbf{A}$} (1.5,1); } \in \Zq^{n \times m},$
find $\textcolor{red!70!black}{\mathbf x} \in \ZZ^m_{}$ such that\\[.5em]
find $\textcolor{red!70!black}{\mathbf{x}} \in \ZZ^m_{}$ such that\\[.5em]
$\begin{tikzpicture}[baseline=.25cm]
\tikzstyle{matA}=[fill=blue!10]
\tikzstyle{vecX}=[color=red!70!black]
\draw[matA] (0,0) rectangle node {$\mathbf{A}$} (1.5,1);
\draw[|-|, vecX] (1.7, 1) -- node[right] {$\mathbf x$} ++ (0, -1.5);
\draw[|-|, vecX] (1.7, 1) -- node[right] {$\mathbf{x}$} ++ (0, -1.5);
\node at (2.4, .25) {$=$};
\draw[|-|] (2.8, 1) -- node[right] {$\mathbf 0^n$} ++ (0, -1);
\end{tikzpicture},$ and\\$0< \|\textcolor{red!70!black}{\mathbf x}\| \leq \beta$.
\end{tikzpicture},$ and\\$0< \|\textcolor{red!70!black}{\mathbf{x}}\| \leq \beta$.
\end{minipage}
\hfill
\medskip