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authorAndreas Müller <andreas.mueller@ost.ch>2021-03-08 10:27:04 +0100
committerAndreas Müller <andreas.mueller@ost.ch>2021-03-08 10:27:04 +0100
commit18c273cb55ea5f54b125d8d6e3032b25cf56f8f3 (patch)
treeb8a96fc519fd5fc29b8ab61b93f8488ff012c72f /vorlesungen
parentfinal preparation (diff)
downloadSeminarMatrizen-18c273cb55ea5f54b125d8d6e3032b25cf56f8f3.tar.gz
SeminarMatrizen-18c273cb55ea5f54b125d8d6e3032b25cf56f8f3.zip
besser strukturierung
Diffstat (limited to '')
-rw-r--r--vorlesungen/slides/4/schieberegister.tex38
1 files changed, 30 insertions, 8 deletions
diff --git a/vorlesungen/slides/4/schieberegister.tex b/vorlesungen/slides/4/schieberegister.tex
index 6914c79..f349337 100644
--- a/vorlesungen/slides/4/schieberegister.tex
+++ b/vorlesungen/slides/4/schieberegister.tex
@@ -5,6 +5,7 @@
%
\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});
@@ -23,17 +24,25 @@
\node at \punkt{7}{0} {$#8$};
}
\begin{frame}[t]
-\frametitle{Schieberegister}
-Rechnen mit Polynomen in $\mathbb{F}_2(\alpha)$ ist speziell einfach
+\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 $\alpha$: $m(X) = X^8 + X^4+X^3+X+1$ (aus dem AES Standard)
+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};
@@ -48,10 +57,20 @@ Minimalpolynom von $\alpha$: $m(X) = X^8 + X^4+X^3+X+1$ (aus dem AES Standard)
\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
}
@@ -62,7 +81,7 @@ Minimalpolynom von $\alpha$: $m(X) = X^8 + X^4+X^3+X+1$ (aus dem AES Standard)
\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};
+ {$\uncover<5->{{\color{darkgreen}\alpha^4+\alpha^3+\alpha+1=\alpha^8}}\only<-4>{X^8}$\strut};
\end{scope}
\node at \punkt{-1}{0} {$1$\strut};
\end{scope}
@@ -70,11 +89,13 @@ Minimalpolynom von $\alpha$: $m(X) = X^8 + X^4+X^3+X+1$ (aus dem AES Standard)
\uncover<6->{
{\color<8->{red}
- \draw[->] (-3,-1.5) to[out=-90,in=180] (-0.5,-2.7);
+ \draw[->] (-2.5,-1.5) to[out=-90,in=180] (-0.5,-2.7);
}
\begin{scope}[yshift=-2.7cm]
\rahmen
- \polynom00011011
+ {\color{darkgreen}
+ \polynom00011011
+ }
\end{scope}
}
@@ -83,12 +104,13 @@ Minimalpolynom von $\alpha$: $m(X) = X^8 + X^4+X^3+X+1$ (aus dem AES Standard)
\begin{scope}[yshift=-4.2cm]
\rahmen
- \polynom00110111
+ \polynom00110001
+ \node at \punkt{7.6}{0} [right] {$\mathstrut=\alpha\cdot p(\alpha)$};
\end{scope}
}
\uncover<8->{
- \node[color=red] at (-3.5,-2.7) {Feedback};
+ \node[color=red] at (-3.0,-2.5) {Feedback};
}
\end{tikzpicture}