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author | Andreas Müller <andreas.mueller@ost.ch> | 2021-03-08 09:40:32 +0100 |
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committer | Andreas Müller <andreas.mueller@ost.ch> | 2021-03-08 09:40:32 +0100 |
commit | f2454006fa4e2a0b4093507300fab8a29e3b5901 (patch) | |
tree | 407df3e48376af0962cebaedad6db75fe886ebb0 /vorlesungen/slides/4/schieberegister.tex | |
parent | euklidslide (diff) | |
download | SeminarMatrizen-f2454006fa4e2a0b4093507300fab8a29e3b5901.tar.gz SeminarMatrizen-f2454006fa4e2a0b4093507300fab8a29e3b5901.zip |
final preparation
Diffstat (limited to 'vorlesungen/slides/4/schieberegister.tex')
-rw-r--r-- | vorlesungen/slides/4/schieberegister.tex | 98 |
1 files changed, 98 insertions, 0 deletions
diff --git a/vorlesungen/slides/4/schieberegister.tex b/vorlesungen/slides/4/schieberegister.tex new file mode 100644 index 0000000..6914c79 --- /dev/null +++ b/vorlesungen/slides/4/schieberegister.tex @@ -0,0 +1,98 @@ +% +% schieberegister.tex +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\bgroup +\def\ds{0.7} +\def\punkt#1#2{({(#1)*\ds},{(#2)*\ds})} +\def\rahmen{ + \draw ({-0.5*\ds},{-0.5*\ds}) rectangle ({7.5*\ds},{0.5*\ds}); + \foreach \x in {0.5,1.5,...,6.5}{ + \draw ({\x*\ds},{-0.5*\ds}) rectangle ({\x*\ds},{0.5*\ds}); + } +} +\def\polynom#1#2#3#4#5#6#7#8{ + \node at \punkt{0}{0} {$#1$}; + \node at \punkt{1}{0} {$#2$}; + \node at \punkt{2}{0} {$#3$}; + \node at \punkt{3}{0} {$#4$}; + \node at \punkt{4}{0} {$#5$}; + \node at \punkt{5}{0} {$#6$}; + \node at \punkt{6}{0} {$#7$}; + \node at \punkt{7}{0} {$#8$}; +} +\begin{frame}[t] +\frametitle{Schieberegister} +Rechnen mit Polynomen in $\mathbb{F}_2(\alpha)$ ist speziell einfach +\\ +Minimalpolynom von $\alpha$: $m(X) = X^8 + X^4+X^3+X+1$ (aus dem AES Standard) + +\begin{center} +\begin{tikzpicture}[>=latex,thick] + +\uncover<2->{ +\begin{scope} + \rahmen + \node at \punkt{0}{1} {$X^7$\strut}; + \node at \punkt{2.5}{1}{$+$\strut}; + \node at \punkt{3}{1} {$X^4$\strut}; + \node at \punkt{4.5}{1}{$+$\strut}; + \node at \punkt{5}{1} {$X^2$\strut}; + \node at \punkt{6.5}{1}{$+$\strut}; + \node at \punkt{7}{1} {$1$\strut}; + \polynom10010101 +\end{scope}} + +\uncover<3->{ + \draw[->] ({7.7*\ds},-0.2) to[out=-45,in=45] ({7.7*\ds},-1.8); + \node at ({8*\ds},-1) [right] {$\mathstrut\cdot X = \text{Shift}$}; +} + +\uncover<3->{ + \begin{scope}[yshift=-2cm] + \uncover<4->{ + \rahmen + \polynom00101010 + } + \node at \punkt{2}{1} {$X^5$\strut}; + \node at \punkt{3.5}{1}{$+$\strut}; + \node at \punkt{4}{1} {$X^3$\strut}; + \node at \punkt{5.5}{1}{$+$\strut}; + \node at \punkt{6}{1} {$X$\strut}; + \begin{scope}[xshift=0.4cm] + \node at \punkt{-1}{1} [left] + {$\uncover<5->{X^4+X^3+X+1=}X^8$\strut}; + \end{scope} + \node at \punkt{-1}{0} {$1$\strut}; + \end{scope} +} + +\uncover<6->{ + {\color<8->{red} + \draw[->] (-3,-1.5) to[out=-90,in=180] (-0.5,-2.7); + } + \begin{scope}[yshift=-2.7cm] + \rahmen + \polynom00011011 + \end{scope} +} + +\uncover<7->{ + \node at ({3.5*\ds},-3.45) {$\|$}; + + \begin{scope}[yshift=-4.2cm] + \rahmen + \polynom00110111 + \end{scope} +} + +\uncover<8->{ + \node[color=red] at (-3.5,-2.7) {Feedback}; +} + +\end{tikzpicture} +\end{center} + +\end{frame} +\egroup |