From 2db90bfe4b174570424c408f04000902411d8755 Mon Sep 17 00:00:00 2001
From: Joshua Baer <the.baer.joshua@gmail.ch>
Date: Mon, 12 Apr 2021 21:51:55 +0200
Subject: update to current state of book

---
 buch/chapters/90-crypto/images/multiplikation.tex | 928 +++++++++++-----------
 1 file changed, 464 insertions(+), 464 deletions(-)

(limited to 'buch/chapters/90-crypto/images/multiplikation.tex')

diff --git a/buch/chapters/90-crypto/images/multiplikation.tex b/buch/chapters/90-crypto/images/multiplikation.tex
index 27c4329..dd59097 100644
--- a/buch/chapters/90-crypto/images/multiplikation.tex
+++ b/buch/chapters/90-crypto/images/multiplikation.tex
@@ -1,464 +1,464 @@
-%
-% multiplikation.tex -- 
-%
-% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
-%
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-\begin{scope}[yshift=-5.9cm]
-	\summation{1}{1}{1}{1}{0}{1}{1}{1}
-\end{scope}
-
-\begin{scope}[yshift=-7.9cm]
-	\summation{0}{1}{1}{0}{0}{1}{0}{0}
-\end{scope}
-
-\begin{scope}[yshift=-9.9cm]
-	\summation{0}{1}{0}{1}{1}{0}{0}{1}
-\end{scope}
-
-\begin{scope}[yshift=-11.9cm]
-	\summation{0}{1}{0}{1}{1}{0}{0}{1}
-\end{scope}
-
-\begin{scope}[yshift=-13.9cm]
-	\summation{0}{0}{1}{1}{0}{1}{1}{0}
-	\node at \punkt{0}{-1.5} [left] {$p(X)\cdot q(X)=\mathstrut$};
-\end{scope}
-
-\end{scope}
-
-\begin{scope}[xshift=5cm]
-
-\begin{scope}[yshift=2cm]
-	\node at \punkt{0}{0.5} [left] {$q(X)=\mathstrut$};
-	\draw \punkt{0}{0} rectangle \punkt{8}{1};
-	\foreach \x in {1,...,7}{
-		\draw \punkt{\x}{0} -- \punkt{\x}{1};
-	}
-	\node at \punkt{0.5}{0.5} {\texttt{1}};
-	\node at \punkt{1.5}{0.5} {\texttt{0}};
-	\node at \punkt{2.5}{0.5} {\texttt{1}};
-	\node at \punkt{3.5}{0.5} {\texttt{1}};
-	\node at \punkt{4.5}{0.5} {\texttt{0}};
-	\node at \punkt{5.5}{0.5} {\texttt{1}};
-	\node at \punkt{6.5}{0.5} {\texttt{0}};
-	\node at \punkt{7.5}{0.5} {\texttt{1}};
-
-	\draw[->] \punkt{7.5}{-0.1} -- ({7.5*\s},{-1.3});
-	\node at ({7.5*\s},{-1.2}) [below] {$\mathstrut\cdot\texttt{1}$};
-
-	\def\y{1.2}
-
-	\draw[->] \punkt{6.5}{-0.1} -- ({6.5*\s},{-1*2-\y-0.1});
-	\node at ({6.5*\s},{-1*2-\y}) [below] {$\mathstrut\cdot\texttt{0}$};
-
-	\draw[->] \punkt{5.5}{-0.1} -- ({5.5*\s},{-2*2-\y-0.1});
-	\node at ({5.5*\s},{-2*2-\y}) [below] {$\mathstrut\cdot\texttt{1}$};
-
-	\draw[->] \punkt{4.5}{-0.1} -- ({4.5*\s},{-3*2-\y-0.1});
-	\node at ({4.5*\s},{-3*2-\y}) [below] {$\mathstrut\cdot\texttt{0}$};
-
-	\draw[->] \punkt{3.5}{-0.1} -- ({3.5*\s},{-4*2-\y-0.1});
-	\node at ({3.5*\s},{-4*2-\y}) [below] {$\mathstrut\cdot\texttt{1}$};
-
-	\draw[->] \punkt{2.5}{-0.1} -- ({2.5*\s},{-5*2-\y-0.1});
-	\node at ({2.5*\s},{-5*2-\y}) [below] {$\mathstrut\cdot\texttt{1}$};
-
-	\draw[->] \punkt{1.5}{-0.1} -- ({1.5*\s},{-6*2-\y-0.1});
-	\node at ({1.5*\s},{-6*2-\y}) [below] {$\mathstrut\cdot\texttt{0}$};
-
-	\draw[->] \punkt{0.5}{-0.1} -- ({0.5*\s},{-7*2-\y-0.1});
-	\node at ({0.5*\s},{-7*2-\y}) [below] {$\mathstrut\cdot\texttt{1}$};
-\end{scope}
-
-\end{scope}
-
-\end{tikzpicture}
-\end{document}
-
+%
+% multiplikation.tex -- 
+%
+% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+%
+\documentclass[tikz]{standalone}
+\usepackage{amsmath}
+\usepackage{times}
+\usepackage{txfonts}
+\usepackage{pgfplots}
+\usepackage{csvsimple}
+\usetikzlibrary{arrows,intersections,math}
+\begin{document}
+\def\skala{1}
+\begin{tikzpicture}[>=latex,thick,scale=\skala]
+
+\definecolor{darkgreen}{rgb}{0,0.6,0}
+
+\def\s{0.45}
+
+\def\punkt#1#2{({#1*\s},{#2*\s})}
+
+\def\pfeile{
+	\foreach \x in {0.5,1.5,...,7.5}{
+		\draw[->,color=blue] \punkt{\x}{-2.1} -- \punkt{(\x-1)}{-3.3};
+	}
+}
+
+\begin{scope}[yshift=0.1cm]
+	\node at \punkt{0}{0.5} [left] {$p(X)=\mathstrut$};
+	\draw \punkt{0}{0} rectangle \punkt{8}{1};
+	\foreach \x in {1,...,7}{
+		\draw \punkt{\x}{0} -- \punkt{\x}{1};
+	}
+	\node at \punkt{0.5}{0.5} {\texttt{1}};
+	\node at \punkt{1.5}{0.5} {\texttt{0}};
+	\node at \punkt{2.5}{0.5} {\texttt{0}};
+	\node at \punkt{3.5}{0.5} {\texttt{1}};
+	\node at \punkt{4.5}{0.5} {\texttt{0}};
+	\node at \punkt{5.5}{0.5} {\texttt{1}};
+	\node at \punkt{6.5}{0.5} {\texttt{0}};
+	\node at \punkt{7.5}{0.5} {\texttt{1}};
+	\foreach \x in {0.5,1.5,...,7.5}{
+		\draw[->,color=blue] \punkt{\x}{-0.1} -- \punkt{(\x-1)}{-1.3};
+	}
+\end{scope}
+
+\begin{scope}[yshift=-1cm]
+	\draw[<-] \punkt{8.2}{-1.3} arc (-30:30:1.8);
+	\node at \punkt{9.3}{0.6} {$\mathstrut\cdot X$};
+	\fill[color=blue!20] \punkt{-1}{0} rectangle \punkt{0}{1};
+	\draw \punkt{0}{0} rectangle \punkt{8}{1};
+	\foreach \x in {1,...,7}{
+		\draw \punkt{\x}{0} -- \punkt{\x}{1};
+	}
+	\node[color=darkgreen] at \punkt{-0.5}{0.5} {\texttt{1}};
+	\node at \punkt{0.5}{0.5} {\texttt{0}};
+	\node at \punkt{1.5}{0.5} {\texttt{0}};
+	\node at \punkt{2.5}{0.5} {\texttt{1}};
+	\node at \punkt{3.5}{0.5} {\texttt{0}};
+	\node at \punkt{4.5}{0.5} {\texttt{1}};
+	\node at \punkt{5.5}{0.5} {\texttt{0}};
+	\node at \punkt{6.5}{0.5} {\texttt{1}};
+	\node at \punkt{7.5}{0.5} {\texttt{0}};
+
+	\draw[->,color=darkgreen]
+		\punkt{-0.5}{0.1} -- \punkt{-0.5}{-0.5} -- \punkt{3.1}{-0.5};
+	\node[color=darkgreen] at \punkt{3.5}{-0.5} {\texttt{1}};
+	\node[color=darkgreen] at \punkt{4.5}{-0.5} {\texttt{1}};
+	\node[color=darkgreen] at \punkt{6.5}{-0.5} {\texttt{1}};
+	\node[color=darkgreen] at \punkt{7.5}{-0.5} {\texttt{1}};
+
+	\draw \punkt{0}{-2} rectangle \punkt{8}{-1};
+	\foreach \x in {1,...,7}{
+		\draw \punkt{\x}{-2} -- \punkt{\x}{-1};
+	}
+	\node at \punkt{0.5}{-1.5} {\texttt{0}};
+	\node at \punkt{1.5}{-1.5} {\texttt{0}};
+	\node at \punkt{2.5}{-1.5} {\texttt{1}};
+	\node at \punkt{3.5}{-1.5} {\texttt{1}};
+	\node at \punkt{4.5}{-1.5} {\texttt{0}};
+	\node at \punkt{5.5}{-1.5} {\texttt{0}};
+	\node at \punkt{6.5}{-1.5} {\texttt{0}};
+	\node at \punkt{7.5}{-1.5} {\texttt{1}};
+
+	\pfeile
+\end{scope}
+
+\begin{scope}[yshift=-3cm]
+	\draw[<-] \punkt{8.2}{-1.3} arc (-30:30:1.8);
+	\node at \punkt{9.3}{0.6} {$\mathstrut\cdot X$};
+	\fill[color=blue!20] \punkt{-1}{0} rectangle \punkt{0}{1};
+	\draw \punkt{0}{0} rectangle \punkt{8}{1};
+	\foreach \x in {1,...,7}{
+		\draw \punkt{\x}{0} -- \punkt{\x}{1};
+	}
+	\node[color=darkgreen] at \punkt{-0.5}{0.5} {\texttt{0}};
+	\node at \punkt{0.5}{0.5} {\texttt{0}};
+	\node at \punkt{1.5}{0.5} {\texttt{1}};
+	\node at \punkt{2.5}{0.5} {\texttt{1}};
+	\node at \punkt{3.5}{0.5} {\texttt{0}};
+	\node at \punkt{4.5}{0.5} {\texttt{0}};
+	\node at \punkt{5.5}{0.5} {\texttt{0}};
+	\node at \punkt{6.5}{0.5} {\texttt{1}};
+	\node at \punkt{7.5}{0.5} {\texttt{0}};
+
+%	\draw[->,color=darkgreen]
+%		\punkt{-0.5}{0.1} -- \punkt{-0.5}{-0.5} -- \punkt{3.1}{-0.5};
+%	\node[color=darkgreen] at \punkt{3.5}{-0.5} {\texttt{1}};
+%	\node[color=darkgreen] at \punkt{4.5}{-0.5} {\texttt{1}};
+%	\node[color=darkgreen] at \punkt{6.5}{-0.5} {\texttt{1}};
+%	\node[color=darkgreen] at \punkt{7.5}{-0.5} {\texttt{1}};
+	\node[color=darkgreen] at \punkt{4}{-0.5} {$\|$};
+
+	\draw \punkt{0}{-2} rectangle \punkt{8}{-1};
+	\foreach \x in {1,...,7}{
+		\draw \punkt{\x}{-2} -- \punkt{\x}{-1};
+	}
+	\node at \punkt{0.5}{-1.5} {\texttt{0}};
+	\node at \punkt{1.5}{-1.5} {\texttt{1}};
+	\node at \punkt{2.5}{-1.5} {\texttt{1}};
+	\node at \punkt{3.5}{-1.5} {\texttt{0}};
+	\node at \punkt{4.5}{-1.5} {\texttt{0}};
+	\node at \punkt{5.5}{-1.5} {\texttt{0}};
+	\node at \punkt{6.5}{-1.5} {\texttt{1}};
+	\node at \punkt{7.5}{-1.5} {\texttt{0}};
+
+	\pfeile
+\end{scope}
+
+\begin{scope}[yshift=-5cm]
+	\draw[<-] \punkt{8.2}{-1.3} arc (-30:30:1.8);
+	\node at \punkt{9.3}{0.6} {$\mathstrut\cdot X$};
+	\fill[color=blue!20] \punkt{-1}{0} rectangle \punkt{0}{1};
+	\draw \punkt{0}{0} rectangle \punkt{8}{1};
+	\foreach \x in {1,...,7}{
+		\draw \punkt{\x}{0} -- \punkt{\x}{1};
+	}
+	\node[color=darkgreen] at \punkt{-0.5}{0.5} {\texttt{0}};
+	\node at \punkt{0.5}{0.5} {\texttt{1}};
+	\node at \punkt{1.5}{0.5} {\texttt{1}};
+	\node at \punkt{2.5}{0.5} {\texttt{0}};
+	\node at \punkt{3.5}{0.5} {\texttt{0}};
+	\node at \punkt{4.5}{0.5} {\texttt{0}};
+	\node at \punkt{5.5}{0.5} {\texttt{1}};
+	\node at \punkt{6.5}{0.5} {\texttt{0}};
+	\node at \punkt{7.5}{0.5} {\texttt{0}};
+
+%	\draw[->,color=darkgreen]
+%		\punkt{-0.5}{0.1} -- \punkt{-0.5}{-0.5} -- \punkt{3.1}{-0.5};
+%	\node[color=darkgreen] at \punkt{3.5}{-0.5} {\texttt{1}};
+%	\node[color=darkgreen] at \punkt{4.5}{-0.5} {\texttt{1}};
+%	\node[color=darkgreen] at \punkt{6.5}{-0.5} {\texttt{1}};
+%	\node[color=darkgreen] at \punkt{7.5}{-0.5} {\texttt{1}};
+	\node[color=darkgreen] at \punkt{4}{-0.5} {$\|$};
+
+	\draw \punkt{0}{-2} rectangle \punkt{8}{-1};
+	\foreach \x in {1,...,7}{
+		\draw \punkt{\x}{-2} -- \punkt{\x}{-1};
+	}
+	\node at \punkt{0.5}{-1.5} {\texttt{1}};
+	\node at \punkt{1.5}{-1.5} {\texttt{1}};
+	\node at \punkt{2.5}{-1.5} {\texttt{0}};
+	\node at \punkt{3.5}{-1.5} {\texttt{0}};
+	\node at \punkt{4.5}{-1.5} {\texttt{0}};
+	\node at \punkt{5.5}{-1.5} {\texttt{1}};
+	\node at \punkt{6.5}{-1.5} {\texttt{0}};
+	\node at \punkt{7.5}{-1.5} {\texttt{0}};
+
+	\pfeile
+\end{scope}
+
+\begin{scope}[yshift=-7cm]
+	\draw[<-] \punkt{8.2}{-1.3} arc (-30:30:1.8);
+	\node at \punkt{9.3}{0.6} {$\mathstrut\cdot X$};
+	\fill[color=blue!20] \punkt{-1}{0} rectangle \punkt{0}{1};
+	\draw \punkt{0}{0} rectangle \punkt{8}{1};
+	\foreach \x in {1,...,7}{
+		\draw \punkt{\x}{0} -- \punkt{\x}{1};
+	}
+	\node[color=darkgreen] at \punkt{-0.5}{0.5} {\texttt{1}};
+	\node at \punkt{0.5}{0.5} {\texttt{1}};
+	\node at \punkt{1.5}{0.5} {\texttt{0}};
+	\node at \punkt{2.5}{0.5} {\texttt{0}};
+	\node at \punkt{3.5}{0.5} {\texttt{0}};
+	\node at \punkt{4.5}{0.5} {\texttt{1}};
+	\node at \punkt{5.5}{0.5} {\texttt{0}};
+	\node at \punkt{6.5}{0.5} {\texttt{0}};
+	\node at \punkt{7.5}{0.5} {\texttt{0}};
+
+	\draw[->,color=darkgreen]
+		\punkt{-0.5}{0.1} -- \punkt{-0.5}{-0.5} -- \punkt{3.1}{-0.5};
+	\node[color=darkgreen] at \punkt{3.5}{-0.5} {\texttt{1}};
+	\node[color=darkgreen] at \punkt{4.5}{-0.5} {\texttt{1}};
+	\node[color=darkgreen] at \punkt{6.5}{-0.5} {\texttt{1}};
+	\node[color=darkgreen] at \punkt{7.5}{-0.5} {\texttt{1}};
+%	\node[color=darkgreen] at \punkt{4}{-0.5} {$\|$};
+
+	\draw \punkt{0}{-2} rectangle \punkt{8}{-1};
+	\foreach \x in {1,...,7}{
+		\draw \punkt{\x}{-2} -- \punkt{\x}{-1};
+	}
+	\node at \punkt{0.5}{-1.5} {\texttt{1}};
+	\node at \punkt{1.5}{-1.5} {\texttt{0}};
+	\node at \punkt{2.5}{-1.5} {\texttt{0}};
+	\node at \punkt{3.5}{-1.5} {\texttt{1}};
+	\node at \punkt{4.5}{-1.5} {\texttt{0}};
+	\node at \punkt{5.5}{-1.5} {\texttt{0}};
+	\node at \punkt{6.5}{-1.5} {\texttt{1}};
+	\node at \punkt{7.5}{-1.5} {\texttt{1}};
+
+	\pfeile
+\end{scope}
+
+\begin{scope}[yshift=-9cm]
+	\draw[<-] \punkt{8.2}{-1.3} arc (-30:30:1.8);
+	\node at \punkt{9.3}{0.6} {$\mathstrut\cdot X$};
+	\fill[color=blue!20] \punkt{-1}{0} rectangle \punkt{0}{1};
+	\draw \punkt{0}{0} rectangle \punkt{8}{1};
+	\foreach \x in {1,...,7}{
+		\draw \punkt{\x}{0} -- \punkt{\x}{1};
+	}
+	\node[color=darkgreen] at \punkt{-0.5}{0.5} {\texttt{1}};
+	\node at \punkt{0.5}{0.5} {\texttt{0}};
+	\node at \punkt{1.5}{0.5} {\texttt{0}};
+	\node at \punkt{2.5}{0.5} {\texttt{1}};
+	\node at \punkt{3.5}{0.5} {\texttt{0}};
+	\node at \punkt{4.5}{0.5} {\texttt{0}};
+	\node at \punkt{5.5}{0.5} {\texttt{1}};
+	\node at \punkt{6.5}{0.5} {\texttt{1}};
+	\node at \punkt{7.5}{0.5} {\texttt{0}};
+
+	\draw[->,color=darkgreen]
+		\punkt{-0.5}{0.1} -- \punkt{-0.5}{-0.5} -- \punkt{3.1}{-0.5};
+	\node[color=darkgreen] at \punkt{3.5}{-0.5} {\texttt{1}};
+	\node[color=darkgreen] at \punkt{4.5}{-0.5} {\texttt{1}};
+	\node[color=darkgreen] at \punkt{6.5}{-0.5} {\texttt{1}};
+	\node[color=darkgreen] at \punkt{7.5}{-0.5} {\texttt{1}};
+%	\node[color=darkgreen] at \punkt{4}{-0.5} {$\|$};
+
+	\draw \punkt{0}{-2} rectangle \punkt{8}{-1};
+	\foreach \x in {1,...,7}{
+		\draw \punkt{\x}{-2} -- \punkt{\x}{-1};
+	}
+	\node at \punkt{0.5}{-1.5} {\texttt{0}};
+	\node at \punkt{1.5}{-1.5} {\texttt{0}};
+	\node at \punkt{2.5}{-1.5} {\texttt{1}};
+	\node at \punkt{3.5}{-1.5} {\texttt{1}};
+	\node at \punkt{4.5}{-1.5} {\texttt{1}};
+	\node at \punkt{5.5}{-1.5} {\texttt{1}};
+	\node at \punkt{6.5}{-1.5} {\texttt{0}};
+	\node at \punkt{7.5}{-1.5} {\texttt{1}};
+
+	\pfeile
+\end{scope}
+
+\begin{scope}[yshift=-11cm]
+	\draw[<-] \punkt{8.2}{-1.3} arc (-30:30:1.8);
+	\node at \punkt{9.3}{0.6} {$\mathstrut\cdot X$};
+	\fill[color=blue!20] \punkt{-1}{0} rectangle \punkt{0}{1};
+	\draw \punkt{0}{0} rectangle \punkt{8}{1};
+	\foreach \x in {1,...,7}{
+		\draw \punkt{\x}{0} -- \punkt{\x}{1};
+	}
+	\node[color=darkgreen] at \punkt{-0.5}{0.5} {\texttt{0}};
+	\node at \punkt{0.5}{0.5} {\texttt{0}};
+	\node at \punkt{1.5}{0.5} {\texttt{0}};
+	\node at \punkt{2.5}{0.5} {\texttt{1}};
+	\node at \punkt{3.5}{0.5} {\texttt{1}};
+	\node at \punkt{4.5}{0.5} {\texttt{1}};
+	\node at \punkt{5.5}{0.5} {\texttt{0}};
+	\node at \punkt{6.5}{0.5} {\texttt{1}};
+	\node at \punkt{7.5}{0.5} {\texttt{0}};
+
+%	\draw[->,color=darkgreen]
+%		\punkt{-0.5}{0.1} -- \punkt{-0.5}{-0.5} -- \punkt{3.1}{-0.5};
+%	\node[color=darkgreen] at \punkt{3.5}{-0.5} {\texttt{1}};
+%	\node[color=darkgreen] at \punkt{4.5}{-0.5} {\texttt{1}};
+%	\node[color=darkgreen] at \punkt{6.5}{-0.5} {\texttt{1}};
+%	\node[color=darkgreen] at \punkt{7.5}{-0.5} {\texttt{1}};
+	\node[color=darkgreen] at \punkt{4}{-0.5} {$\|$};
+
+	\draw \punkt{0}{-2} rectangle \punkt{8}{-1};
+	\foreach \x in {1,...,7}{
+		\draw \punkt{\x}{-2} -- \punkt{\x}{-1};
+	}
+	\node at \punkt{0.5}{-1.5} {\texttt{0}};
+	\node at \punkt{1.5}{-1.5} {\texttt{0}};
+	\node at \punkt{2.5}{-1.5} {\texttt{1}};
+	\node at \punkt{3.5}{-1.5} {\texttt{1}};
+	\node at \punkt{4.5}{-1.5} {\texttt{1}};
+	\node at \punkt{5.5}{-1.5} {\texttt{0}};
+	\node at \punkt{6.5}{-1.5} {\texttt{1}};
+	\node at \punkt{7.5}{-1.5} {\texttt{0}};
+
+	\pfeile
+\end{scope}
+
+\begin{scope}[yshift=-13cm]
+	\draw[<-] \punkt{8.2}{-1.3} arc (-30:30:1.8);
+	\node at \punkt{9.3}{0.6} {$\mathstrut\cdot X$};
+	\fill[color=blue!20] \punkt{-1}{0} rectangle \punkt{0}{1};
+	\draw \punkt{0}{0} rectangle \punkt{8}{1};
+	\foreach \x in {1,...,7}{
+		\draw \punkt{\x}{0} -- \punkt{\x}{1};
+	}
+	\node[color=darkgreen] at \punkt{-0.5}{0.5} {\texttt{0}};
+	\node at \punkt{0.5}{0.5} {\texttt{0}};
+	\node at \punkt{1.5}{0.5} {\texttt{1}};
+	\node at \punkt{2.5}{0.5} {\texttt{1}};
+	\node at \punkt{3.5}{0.5} {\texttt{1}};
+	\node at \punkt{4.5}{0.5} {\texttt{0}};
+	\node at \punkt{5.5}{0.5} {\texttt{1}};
+	\node at \punkt{6.5}{0.5} {\texttt{0}};
+	\node at \punkt{7.5}{0.5} {\texttt{0}};
+
+%	\draw[->,color=darkgreen]
+%		\punkt{-0.5}{0.1} -- \punkt{-0.5}{-0.5} -- \punkt{3.1}{-0.5};
+%	\node[color=darkgreen] at \punkt{3.5}{-0.5} {\texttt{1}};
+%	\node[color=darkgreen] at \punkt{4.5}{-0.5} {\texttt{1}};
+%	\node[color=darkgreen] at \punkt{6.5}{-0.5} {\texttt{1}};
+%	\node[color=darkgreen] at \punkt{7.5}{-0.5} {\texttt{1}};
+	\node[color=darkgreen] at \punkt{4}{-0.5} {$\|$};
+
+	\draw \punkt{0}{-2} rectangle \punkt{8}{-1};
+	\foreach \x in {1,...,7}{
+		\draw \punkt{\x}{-2} -- \punkt{\x}{-1};
+	}
+	\node at \punkt{0.5}{-1.5} {\texttt{0}};
+	\node at \punkt{1.5}{-1.5} {\texttt{1}};
+	\node at \punkt{2.5}{-1.5} {\texttt{1}};
+	\node at \punkt{3.5}{-1.5} {\texttt{0}};
+	\node at \punkt{4.5}{-1.5} {\texttt{1}};
+	\node at \punkt{5.5}{-1.5} {\texttt{1}};
+	\node at \punkt{6.5}{-1.5} {\texttt{1}};
+	\node at \punkt{7.5}{-1.5} {\texttt{1}};
+
+%	\pfeile
+\end{scope}
+
+\begin{scope}[xshift=9cm]
+
+\begin{scope}[yshift=0.1cm]
+	\draw[->] \punkt{-11.8}{0.5} -- \punkt{-0.1}{0.5};
+	\draw \punkt{0}{0} rectangle \punkt{8}{1};
+	\foreach \x in {1,...,7}{
+		\draw \punkt{\x}{0} -- \punkt{\x}{1};
+	}
+	\draw \punkt{4}{-0.1} -- \punkt{4}{-3};
+	\node at \punkt{0.5}{0.5} {\texttt{1}};
+	\node at \punkt{1.5}{0.5} {\texttt{0}};
+	\node at \punkt{2.5}{0.5} {\texttt{0}};
+	\node at \punkt{3.5}{0.5} {\texttt{1}};
+	\node at \punkt{4.5}{0.5} {\texttt{0}};
+	\node at \punkt{5.5}{0.5} {\texttt{1}};
+	\node at \punkt{6.5}{0.5} {\texttt{0}};
+	\node at \punkt{7.5}{0.5} {\texttt{1}};
+\end{scope}
+
+\def\summation#1#2#3#4#5#6#7#8{
+	\draw[->] \punkt{4}{2.3} -- \punkt{4}{1};
+
+	\draw[->] \punkt{-11.8}{0.5} -- \punkt{3.5}{0.5};
+
+	\draw \punkt{4}{0.5} circle[radius=0.2];
+	\draw \punkt{4}{0.20} -- \punkt{4}{0.80};
+	\draw \punkt{3.7}{0.5} -- \punkt{4.3}{0.5};
+
+	\draw[->] \punkt{4}{-0.05} -- \punkt{4}{-0.95};
+	\draw \punkt{0}{-2} rectangle \punkt{8}{-1};
+	\foreach \x in {1,...,7}{
+		\draw \punkt{\x}{-2} -- \punkt{\x}{-1};
+	}
+
+	\node at \punkt{0.5}{-1.5} {\texttt{#1}};
+	\node at \punkt{1.5}{-1.5} {\texttt{#2}};
+	\node at \punkt{2.5}{-1.5} {\texttt{#3}};
+	\node at \punkt{3.5}{-1.5} {\texttt{#4}};
+	\node at \punkt{4.5}{-1.5} {\texttt{#5}};
+	\node at \punkt{5.5}{-1.5} {\texttt{#6}};
+	\node at \punkt{6.5}{-1.5} {\texttt{#7}};
+	\node at \punkt{7.5}{-1.5} {\texttt{#8}};
+}
+
+\begin{scope}[yshift=-1.9cm]
+	\summation{1}{0}{0}{1}{0}{1}{0}{1}
+\end{scope}
+
+\begin{scope}[yshift=-3.9cm]
+	\summation{1}{1}{1}{1}{0}{1}{1}{1}
+\end{scope}
+
+\begin{scope}[yshift=-5.9cm]
+	\summation{1}{1}{1}{1}{0}{1}{1}{1}
+\end{scope}
+
+\begin{scope}[yshift=-7.9cm]
+	\summation{0}{1}{1}{0}{0}{1}{0}{0}
+\end{scope}
+
+\begin{scope}[yshift=-9.9cm]
+	\summation{0}{1}{0}{1}{1}{0}{0}{1}
+\end{scope}
+
+\begin{scope}[yshift=-11.9cm]
+	\summation{0}{1}{0}{1}{1}{0}{0}{1}
+\end{scope}
+
+\begin{scope}[yshift=-13.9cm]
+	\summation{0}{0}{1}{1}{0}{1}{1}{0}
+	\node at \punkt{0}{-1.5} [left] {$p(X)\cdot q(X)=\mathstrut$};
+\end{scope}
+
+\end{scope}
+
+\begin{scope}[xshift=5cm]
+
+\begin{scope}[yshift=2cm]
+	\node at \punkt{0}{0.5} [left] {$q(X)=\mathstrut$};
+	\draw \punkt{0}{0} rectangle \punkt{8}{1};
+	\foreach \x in {1,...,7}{
+		\draw \punkt{\x}{0} -- \punkt{\x}{1};
+	}
+	\node at \punkt{0.5}{0.5} {\texttt{1}};
+	\node at \punkt{1.5}{0.5} {\texttt{0}};
+	\node at \punkt{2.5}{0.5} {\texttt{1}};
+	\node at \punkt{3.5}{0.5} {\texttt{1}};
+	\node at \punkt{4.5}{0.5} {\texttt{0}};
+	\node at \punkt{5.5}{0.5} {\texttt{1}};
+	\node at \punkt{6.5}{0.5} {\texttt{0}};
+	\node at \punkt{7.5}{0.5} {\texttt{1}};
+
+	\draw[->] \punkt{7.5}{-0.1} -- ({7.5*\s},{-1.3});
+	\node at ({7.5*\s},{-1.2}) [below] {$\mathstrut\cdot\texttt{1}$};
+
+	\def\y{1.2}
+
+	\draw[->] \punkt{6.5}{-0.1} -- ({6.5*\s},{-1*2-\y-0.1});
+	\node at ({6.5*\s},{-1*2-\y}) [below] {$\mathstrut\cdot\texttt{0}$};
+
+	\draw[->] \punkt{5.5}{-0.1} -- ({5.5*\s},{-2*2-\y-0.1});
+	\node at ({5.5*\s},{-2*2-\y}) [below] {$\mathstrut\cdot\texttt{1}$};
+
+	\draw[->] \punkt{4.5}{-0.1} -- ({4.5*\s},{-3*2-\y-0.1});
+	\node at ({4.5*\s},{-3*2-\y}) [below] {$\mathstrut\cdot\texttt{0}$};
+
+	\draw[->] \punkt{3.5}{-0.1} -- ({3.5*\s},{-4*2-\y-0.1});
+	\node at ({3.5*\s},{-4*2-\y}) [below] {$\mathstrut\cdot\texttt{1}$};
+
+	\draw[->] \punkt{2.5}{-0.1} -- ({2.5*\s},{-5*2-\y-0.1});
+	\node at ({2.5*\s},{-5*2-\y}) [below] {$\mathstrut\cdot\texttt{1}$};
+
+	\draw[->] \punkt{1.5}{-0.1} -- ({1.5*\s},{-6*2-\y-0.1});
+	\node at ({1.5*\s},{-6*2-\y}) [below] {$\mathstrut\cdot\texttt{0}$};
+
+	\draw[->] \punkt{0.5}{-0.1} -- ({0.5*\s},{-7*2-\y-0.1});
+	\node at ({0.5*\s},{-7*2-\y}) [below] {$\mathstrut\cdot\texttt{1}$};
+\end{scope}
+
+\end{scope}
+
+\end{tikzpicture}
+\end{document}
+
-- 
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