Merge pull request #1 from AndreasFMueller/master

update

1 files changed, 120 insertions, 0 deletions

diff --git a/vorlesungen/slides/4/schieberegister.tex b/vorlesungen/slides/4/schieberegister.tex
new file mode 100644
index 0000000..f349337
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+++ b/vorlesungen/slides/4/schieberegister.tex
@@ -0,0 +1,120 @@
+%
+% schieberegister.tex
+%
+% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+%
+\bgroup
+\def\ds{0.7}
+\definecolor{darkgreen}{rgb}{0,0.6,0}
+\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{Implementation der Multiplikation in $\mathbb{F}_2(\alpha)$\uncover<10->{: Schieberegister}}
+Rechnen in $\mathbb{F}_2[X]$\only<5->{ und $\mathbb{F}_2(\alpha)$}
+ist speziell einfach
+\\
+Minimalpolynom von $\alpha$: ${\color{darkgreen}m(X) = X^8 + X^4+X^3+X+1}$
+(aus dem AES Standard)
+
+\begin{center}
+\begin{tikzpicture}[>=latex,thick]
+
+\uncover<4->{
+	\fill[color=blue!20]
+		\punkt{-0.5}{-0.5} rectangle \punkt{7.5}{0.5};
+}
+
+\uncover<2->{
+\begin{scope}
+	\rahmen
+	\node at \punkt{-0.5}{1} [left] {$p(X)=\mathstrut$};
+	\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<4->{
+	\foreach \x in {0,...,7}{
+		\draw[->,color=blue!40]
+			({\x*\ds},{-0.6*\ds}) -- ({(\x-1)*\ds},{-2+0.6*\ds});
+	}
+}
+
+\fill[color=white] (-4.65,0) circle[radius=0.01];
+
+\uncover<3->{
+	\begin{scope}[yshift=-2cm]
+		\uncover<4->{
+			\fill[color=blue!20]
+				\punkt{-1.5}{-0.5} rectangle \punkt{6.5}{0.5};
+			\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]
+				{$\uncover<5->{{\color{darkgreen}\alpha^4+\alpha^3+\alpha+1=\alpha^8}}\only<-4>{X^8}$\strut};
+		\end{scope}
+		\node at \punkt{-1}{0} {$1$\strut};
+	\end{scope}
+}
+
+\uncover<6->{
+	{\color<8->{red}
+		\draw[->] (-2.5,-1.5) to[out=-90,in=180] (-0.5,-2.7);
+	}
+	\begin{scope}[yshift=-2.7cm]
+		\rahmen
+		{\color{darkgreen}
+			\polynom00011011
+		}
+	\end{scope}
+}
+
+\uncover<7->{
+	\node at ({3.5*\ds},-3.45) {$\|$};
+
+	\begin{scope}[yshift=-4.2cm]
+	\rahmen
+	\polynom00110001
+	\node at \punkt{7.6}{0} [right] {$\mathstrut=\alpha\cdot p(\alpha)$};
+	\end{scope}
+}
+
+\uncover<8->{
+	\node[color=red] at (-3.0,-2.5) {Feedback};
+}
+
+\end{tikzpicture}
+\end{center}
+
+\end{frame}
+\egroup