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\def\ppa{-- ++(10pt,0pt) -- ++(0pt,10pt) ++(5pt,-10pt)}
\def\ppb{-- ++(10pt,0pt) -- ++(0pt,10pt) ++(-10pt,0pt) -- ++(0pt,-10pt) ++(15pt,0pt)}
\def\ppc{-- ++(10pt,0pt) ++(-10pt,0pt) -- ++(0pt,10pt) ++(15pt,-10pt)}
\def\ppd{-- ++(10pt,0pt) -- ++(0pt,10pt) -- ++(-10pt,0pt) ++(15pt,-10pt)}
\def\ppe{-- ++(10pt,0pt) -- ++(0pt,10pt) -- ++(-10pt,0pt) -- ++(0pt,-10pt) ++(15pt,0pt)}
\def\ppf{-- ++(10pt,0pt) ++(0pt,10pt) -- ++(-10pt,0pt) -- ++(0pt,-10pt) ++(15pt,0pt)}
\def\ppg{ ++(10pt,0pt) -- ++(0pt,10pt) -- ++(-10pt,0pt) ++(15pt,-10pt)}
\def\pph{ ++(10pt,0pt) -- ++(0pt,10pt) -- ++(-10pt,0pt) -- ++(0pt,-10pt) ++(15pt,0pt)}
\def\ppi{ ++(10pt,0pt) ++(0pt,10pt) -- ++(-10pt,0pt) -- ++(0pt,-10pt) ++(15pt,0pt)}
\def\ppj{-- ++(10pt,0pt) -- ++(0pt,10pt) ++(-5pt,-5pt) node {$\cdot$} ++(10pt,-5pt)}
\def\ppk{-- ++(10pt,0pt) -- ++(0pt,10pt) ++(-10pt,0pt) -- ++(0pt,-10pt) ++(5pt,5pt) node {$\cdot$} ++(10pt,-5pt)}
\def\ppl{-- ++(10pt,0pt) ++(-10pt,0pt) -- ++(0pt,10pt) ++(5pt,-5pt) node {$\cdot$} ++(10pt,-5pt)}
\def\ppm{-- ++(10pt,0pt) -- ++(0pt,10pt) -- ++(-10pt,0pt) ++(5pt,-5pt) node {$\cdot$} ++(10pt,-5pt)}
\def\ppn{-- ++(10pt,0pt) -- ++(0pt,10pt) -- ++(-10pt,0pt) -- ++(0pt,-10pt) ++(5pt,5pt) node {$\cdot$} ++(10pt,-5pt)}
\def\ppo{-- ++(10pt,0pt) ++(0pt,10pt) -- ++(-10pt,0pt) -- ++(0pt,-10pt) ++(5pt,5pt) node {$\cdot$} ++(10pt,-5pt)}
\def\ppp{ ++(10pt,0pt) -- ++(0pt,10pt) -- ++(-10pt,0pt) ++(5pt,-5pt) node {$\cdot$} ++(10pt,-5pt)}
\def\ppq{ ++(10pt,0pt) -- ++(0pt,10pt) -- ++(-10pt,0pt) -- ++(0pt,-10pt) ++(5pt,5pt) node {$\cdot$} ++(10pt,-5pt)}
\def\ppr{ ++(10pt,0pt) ++(0pt,10pt) -- ++(-10pt,0pt) -- ++(0pt,-10pt) ++(5pt,5pt) node {$\cdot$} ++(10pt,-5pt)}
\def\pps{ ++(0pt,10pt) -- ++(5pt,-10pt) -- ++(5pt,10pt) ++(5pt,-10pt)}
\def\ppt{ ++(0pt,10pt) -- ++(10pt,-5pt) -- ++(-10pt,-5pt) ++(15pt,0pt)}
\def\ppu{ ++(10pt,10pt) -- ++(-10pt,-5pt) -- ++(10pt,-5pt) ++(5pt,0pt)}
\def\ppv{-- ++(5pt,10pt) -- ++(5pt,-10pt) ++(5pt,0pt)}
\def\ppw{ ++(0pt,10pt) -- ++(5pt,-10pt) -- ++(5pt,10pt) ++(-5pt,-5pt) node {$\cdot$} ++(10pt,-5pt)}
\def\ppx{ ++(0pt,10pt) -- ++(10pt,-5pt) -- ++(-10pt,-5pt) ++(5pt,5pt) node {$\cdot$} ++(10pt,-5pt)}
\def\ppy{ ++(10pt,10pt) -- ++(-10pt,-5pt) -- ++(10pt,-5pt) ++(-5pt,5pt) node {$\cdot$} ++(10pt,-5pt)}
\def\ppz{-- ++(5pt,10pt) -- ++(5pt,-10pt) ++(-5pt,5pt) node {$\cdot$} ++(10pt,-5pt)}
\newcommand \sboxOne{
\mbox{
$
\begin{array}{|c|c|c|c|c|}\hline
\amp 00 \amp 01 \amp 10 \amp 11 \\ \hline
00 \amp 01 \amp 11 \amp 10 \amp 11 \\ \hline
01 \amp 11 \amp 10 \amp 01 \amp 00 \\ \hline
10 \amp 00 \amp 10 \amp 01 \amp 11 \\ \hline
11 \amp 11 \amp 01 \amp 11 \amp 10 \\ \hline
\end{array}
$
}
}
\newcommand \sboxTwo{
\mbox{
$
\begin{array}{|c|c|c|c|c|}\hline
\amp 00 \amp 01 \amp 10 \amp 11 \\ \hline
00 \amp 00 \amp 01 \amp 10 \amp 11 \\ \hline
01 \amp 10 \amp 00 \amp 01 \amp 11 \\ \hline
10 \amp 11 \amp 00 \amp 01 \amp 00 \\ \hline
11 \amp 10 \amp 01 \amp 10 \amp 11 \\ \hline
\end{array}
$
}
}
\newcommand{\lt}{<}
\newcommand{\gt}{>}
\newcommand{\amp}{&}
\)
Section 8.2 (*)Lattice Ciphers
Objectives
- basic definitions
- mini-example