update to current state of book

7 files changed, 1158 insertions, 1158 deletions

diff --git a/buch/chapters/90-crypto/images/Makefile b/buch/chapters/90-crypto/images/Makefile
index f4bed14..5df9178 100644
--- a/buch/chapters/90-crypto/images/Makefile
+++ b/buch/chapters/90-crypto/images/Makefile
@@ -1,29 +1,29 @@
-#
-# Makefile -- build images for crypto chapter
-#
-# (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
-#
-all:	dh.pdf elliptic.pdf schieberegister.pdf multiplikation.pdf sbox.pdf \
-	shift.pdf keys.pdf
-
-dh.pdf:	dh.tex
-	pdflatex dh.tex
-
-elliptic.pdf:	elliptic.tex
-	pdflatex elliptic.tex
-
-schieberegister.pdf:	schieberegister.tex
-	pdflatex schieberegister.tex
-
-multiplikation.pdf:	multiplikation.tex
-	pdflatex multiplikation.tex
-
-sbox.pdf:	sbox.tex
-	pdflatex sbox.tex
-
-shift.pdf:	shift.tex
-	pdflatex shift.tex
-
-keys.pdf:	keys.tex
-	pdflatex keys.tex
-
+#

+# Makefile -- build images for crypto chapter

+#

+# (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule

+#

+all:	dh.pdf elliptic.pdf schieberegister.pdf multiplikation.pdf sbox.pdf \

+	shift.pdf keys.pdf

+

+dh.pdf:	dh.tex

+	pdflatex dh.tex

+

+elliptic.pdf:	elliptic.tex

+	pdflatex elliptic.tex

+

+schieberegister.pdf:	schieberegister.tex

+	pdflatex schieberegister.tex

+

+multiplikation.pdf:	multiplikation.tex

+	pdflatex multiplikation.tex

+

+sbox.pdf:	sbox.tex

+	pdflatex sbox.tex

+

+shift.pdf:	shift.tex

+	pdflatex shift.tex

+

+keys.pdf:	keys.tex

+	pdflatex keys.tex

+

diff --git a/buch/chapters/90-crypto/images/keys.tex b/buch/chapters/90-crypto/images/keys.tex
index d556b7c..4b1b566 100644
--- a/buch/chapters/90-crypto/images/keys.tex
+++ b/buch/chapters/90-crypto/images/keys.tex
@@ -1,121 +1,121 @@
-%
-% keys.tex -- template for standalon tikz images
-%
-% (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{0.5}
-\def\punkt#1#2{({(#1)*\s},{(#2)*\s})}
-\def\wort#1#2#3{
-	\fill[color=#3] \punkt{#1}{#2} rectangle \punkt{(#1+1)}{(#2+4)};
-	\draw \punkt{#1}{#2} rectangle \punkt{(#1+1)}{(#2+4)};
-}
-
-\def\summe{
-	\foreach \x in {0,3,...,21}{
-		\draw[->] \punkt{(\x+0.5)}{-0.1} -- \punkt{(\x+0.5)}{-2.1};
-		\draw \punkt{(\x+0.5)}{-2.5} circle[radius={0.3*\s}];
-		\draw \punkt{(\x+0.5-0.2)}{-2.5} 
-			--
-			\punkt{(\x+0.5+0.2)}{-2.5};
-		\draw \punkt{(\x+0.5)}{-2.5+0.2} 
-			--
-			\punkt{(\x+0.5)}{-2.5-0.2};
-		\draw[->] \punkt{(\x+0.5)}{-2.9} -- \punkt{(\x+0.5)}{-4.9};
-	}
-	\foreach \x in {0,3,...,18}{
-		\draw[->] \punkt{(\x+1.1)}{-7} -- \punkt{(\x+2)}{-7}
-			-- \punkt{(\x+2)}{-2.5} -- \punkt{(\x+3.1)}{-2.5};
-	}
-	\fill[color=white]
-		\punkt{(9+1.25)}{-5.5}
-		rectangle
-		\punkt{(9+2.75)}{-4.00};
-	\draw
-		\punkt{(9+1.25)}{-5.5}
-		rectangle
-		\punkt{(9+2.75)}{-4.00};
-	\node at \punkt{(9+2)}{-4.75} {$S$};
-}
-
-\def\blocks#1{
-	\foreach \x in {0,3,...,21}{
-		\wort{\x}{0}{#1}
-	}
-}
-
-\def\schlange#1{
-	\draw[->] \punkt{22.1}{2} -- \punkt{23}{2}
-		-- \punkt{23}{-1.0} -- \punkt{-3}{-1.0}
-		-- \punkt{-3}{-8} -- \punkt{-1}{-8} -- \punkt{-1}{-2.5}
-		-- \punkt{0.1}{-2.5};
-	;
-	\fill[color=white] \punkt{-3.75}{-1.75} rectangle \punkt{-2.25}{-3.25};
-	\draw \punkt{-3.75}{-1.75} rectangle \punkt{-2.25}{-3.25};
-	\node at \punkt{-3}{-2.5} {$\pi$};
-
-	\fill[color=white] \punkt{-3.75}{-3.75} rectangle \punkt{-2.25}{-5.25};
-	\draw \punkt{-3.75}{-3.75} rectangle \punkt{-2.25}{-5.25};
-	\node at \punkt{-3}{-4.5} {$S$};
-
-	\fill[color=white] \punkt{-3.75}{-5.75} rectangle \punkt{-2.25}{-7.25};
-	\draw \punkt{-3.75}{-5.75} rectangle \punkt{-2.25}{-7.25};
-	\node at \punkt{-3}{-6.5} {$r_{#1}$};
-}
-
-\begin{scope}
-	\blocks{blue!20}
-	\foreach \x in {0,...,7}{
-		\node at \punkt{(3*\x+0.5)}{2} {$K_\x$};
-	}
-	\schlange{1}
-	\summe
-\end{scope}
-
-\begin{scope}[yshift=-4.5cm]
-	\blocks{darkgreen!20}
-	\foreach \x in {8,...,15}{
-		\node at \punkt{(3*(\x-8)+0.5)}{2} {$K_{\x}$};
-	}
-	\schlange{2}
-	\summe
-\end{scope}
-
-\begin{scope}[yshift=-9cm]
-	\blocks{darkgreen!20}
-	\foreach \x in {16,...,23}{
-		\node at \punkt{(3*(\x-16)+0.5)}{2} {$K_{\x}$};
-	}
-	\schlange{3}
-	\summe
-\end{scope}
-
-\begin{scope}[yshift=-13.5cm]
-	\blocks{darkgreen!20}
-	\foreach \x in {24,...,31}{
-		\node at \punkt{(3*(\x-24)+0.5)}{2} {$K_{\x}$};
-	}
-	\foreach \x in {0,3,...,21}{
-		\draw[->,color=gray]
-			\punkt{(\x+0.5)}{-0.1} -- \punkt{(\x+0.5)}{-2.1};
-		\node[color=gray] at \punkt{(\x+0.5)}{-2.1} [below] {$\vdots$};
-	}
-	\draw[color=gray] \punkt{22.1}{2} -- \punkt{23}{2}
-		-- \punkt{23}{-1.0} -- \punkt{-3}{-1.0}
-		-- \punkt{-3}{-2.1};
-	\node[color=gray] at \punkt{-3}{-2.1} [below] {$\vdots$};
-\end{scope}
-
-\end{tikzpicture}
-\end{document}
-
+%

+% keys.tex -- template for standalon tikz images

+%

+% (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{0.5}

+\def\punkt#1#2{({(#1)*\s},{(#2)*\s})}

+\def\wort#1#2#3{

+	\fill[color=#3] \punkt{#1}{#2} rectangle \punkt{(#1+1)}{(#2+4)};

+	\draw \punkt{#1}{#2} rectangle \punkt{(#1+1)}{(#2+4)};

+}

+

+\def\summe{

+	\foreach \x in {0,3,...,21}{

+		\draw[->] \punkt{(\x+0.5)}{-0.1} -- \punkt{(\x+0.5)}{-2.1};

+		\draw \punkt{(\x+0.5)}{-2.5} circle[radius={0.3*\s}];

+		\draw \punkt{(\x+0.5-0.2)}{-2.5} 

+			--

+			\punkt{(\x+0.5+0.2)}{-2.5};

+		\draw \punkt{(\x+0.5)}{-2.5+0.2} 

+			--

+			\punkt{(\x+0.5)}{-2.5-0.2};

+		\draw[->] \punkt{(\x+0.5)}{-2.9} -- \punkt{(\x+0.5)}{-4.9};

+	}

+	\foreach \x in {0,3,...,18}{

+		\draw[->] \punkt{(\x+1.1)}{-7} -- \punkt{(\x+2)}{-7}

+			-- \punkt{(\x+2)}{-2.5} -- \punkt{(\x+3.1)}{-2.5};

+	}

+	\fill[color=white]

+		\punkt{(9+1.25)}{-5.5}

+		rectangle

+		\punkt{(9+2.75)}{-4.00};

+	\draw

+		\punkt{(9+1.25)}{-5.5}

+		rectangle

+		\punkt{(9+2.75)}{-4.00};

+	\node at \punkt{(9+2)}{-4.75} {$S$};

+}

+

+\def\blocks#1{

+	\foreach \x in {0,3,...,21}{

+		\wort{\x}{0}{#1}

+	}

+}

+

+\def\schlange#1{

+	\draw[->] \punkt{22.1}{2} -- \punkt{23}{2}

+		-- \punkt{23}{-1.0} -- \punkt{-3}{-1.0}

+		-- \punkt{-3}{-8} -- \punkt{-1}{-8} -- \punkt{-1}{-2.5}

+		-- \punkt{0.1}{-2.5};

+	;

+	\fill[color=white] \punkt{-3.75}{-1.75} rectangle \punkt{-2.25}{-3.25};

+	\draw \punkt{-3.75}{-1.75} rectangle \punkt{-2.25}{-3.25};

+	\node at \punkt{-3}{-2.5} {$\pi$};

+

+	\fill[color=white] \punkt{-3.75}{-3.75} rectangle \punkt{-2.25}{-5.25};

+	\draw \punkt{-3.75}{-3.75} rectangle \punkt{-2.25}{-5.25};

+	\node at \punkt{-3}{-4.5} {$S$};

+

+	\fill[color=white] \punkt{-3.75}{-5.75} rectangle \punkt{-2.25}{-7.25};

+	\draw \punkt{-3.75}{-5.75} rectangle \punkt{-2.25}{-7.25};

+	\node at \punkt{-3}{-6.5} {$r_{#1}$};

+}

+

+\begin{scope}

+	\blocks{blue!20}

+	\foreach \x in {0,...,7}{

+		\node at \punkt{(3*\x+0.5)}{2} {$K_\x$};

+	}

+	\schlange{1}

+	\summe

+\end{scope}

+

+\begin{scope}[yshift=-4.5cm]

+	\blocks{darkgreen!20}

+	\foreach \x in {8,...,15}{

+		\node at \punkt{(3*(\x-8)+0.5)}{2} {$K_{\x}$};

+	}

+	\schlange{2}

+	\summe

+\end{scope}

+

+\begin{scope}[yshift=-9cm]

+	\blocks{darkgreen!20}

+	\foreach \x in {16,...,23}{

+		\node at \punkt{(3*(\x-16)+0.5)}{2} {$K_{\x}$};

+	}

+	\schlange{3}

+	\summe

+\end{scope}

+

+\begin{scope}[yshift=-13.5cm]

+	\blocks{darkgreen!20}

+	\foreach \x in {24,...,31}{

+		\node at \punkt{(3*(\x-24)+0.5)}{2} {$K_{\x}$};

+	}

+	\foreach \x in {0,3,...,21}{

+		\draw[->,color=gray]

+			\punkt{(\x+0.5)}{-0.1} -- \punkt{(\x+0.5)}{-2.1};

+		\node[color=gray] at \punkt{(\x+0.5)}{-2.1} [below] {$\vdots$};

+	}

+	\draw[color=gray] \punkt{22.1}{2} -- \punkt{23}{2}

+		-- \punkt{23}{-1.0} -- \punkt{-3}{-1.0}

+		-- \punkt{-3}{-2.1};

+	\node[color=gray] at \punkt{-3}{-2.1} [below] {$\vdots$};

+\end{scope}

+

+\end{tikzpicture}

+\end{document}

+

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
-%
-\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}};
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-	\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}
-
+%

+% 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}

+

diff --git a/buch/chapters/90-crypto/images/sbox.m b/buch/chapters/90-crypto/images/sbox.m
index 973ffc9..1f0c2ce 100644
--- a/buch/chapters/90-crypto/images/sbox.m
+++ b/buch/chapters/90-crypto/images/sbox.m
@@ -1,52 +1,52 @@
-#
-# sbox.m
-#
-# (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
-#
-A=[
-1,0,0,0,1,1,1,1;
-1,1,0,0,0,1,1,1;
-1,1,1,0,0,0,1,1;
-1,1,1,1,0,0,0,1;
-1,1,1,1,1,0,0,0;
-0,1,1,1,1,1,0,0;
-0,0,1,1,1,1,1,0;
-0,0,0,1,1,1,1,1;
-]
-
-R = zeros(8,16);
-R(:,1:8) = A;
-R(:,9:16) = eye(8);
-
-for k = (1:5)
-	for i=(k+1:8)
-		pivot = R(i,k);
-		R(i,:) = R(i,:) + pivot * R(k,:);
-	end
-	R = mod(R, 2)
-end
-
-P = [
-1,0,0,0,0,0,0,0;
-0,1,0,0,0,0,0,0;
-0,0,1,0,0,0,0,0;
-0,0,0,1,0,0,0,0;
-0,0,0,0,1,0,0,0;
-0,0,0,0,0,0,0,1;
-0,0,0,0,0,1,0,0;
-0,0,0,0,0,0,1,0;
-]
-
-R = P * R
-
-for k = (8:-1:2)
-	for i = (1:k-1)
-		pivot = R(i,k);
-		R(i,:) = R(i,:) + pivot * R(k,:);
-	end
-	R = mod(R, 2)
-end
-
-B = R(:,9:16)
-
-A * B
+#

+# sbox.m

+#

+# (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule

+#

+A=[

+1,0,0,0,1,1,1,1;

+1,1,0,0,0,1,1,1;

+1,1,1,0,0,0,1,1;

+1,1,1,1,0,0,0,1;

+1,1,1,1,1,0,0,0;

+0,1,1,1,1,1,0,0;

+0,0,1,1,1,1,1,0;

+0,0,0,1,1,1,1,1;

+]

+

+R = zeros(8,16);

+R(:,1:8) = A;

+R(:,9:16) = eye(8);

+

+for k = (1:5)

+	for i=(k+1:8)

+		pivot = R(i,k);

+		R(i,:) = R(i,:) + pivot * R(k,:);

+	end

+	R = mod(R, 2)

+end

+

+P = [

+1,0,0,0,0,0,0,0;

+0,1,0,0,0,0,0,0;

+0,0,1,0,0,0,0,0;

+0,0,0,1,0,0,0,0;

+0,0,0,0,1,0,0,0;

+0,0,0,0,0,0,0,1;

+0,0,0,0,0,1,0,0;

+0,0,0,0,0,0,1,0;

+]

+

+R = P * R

+

+for k = (8:-1:2)

+	for i = (1:k-1)

+		pivot = R(i,k);

+		R(i,:) = R(i,:) + pivot * R(k,:);

+	end

+	R = mod(R, 2)

+end

+

+B = R(:,9:16)

+

+A * B

diff --git a/buch/chapters/90-crypto/images/sbox.tex b/buch/chapters/90-crypto/images/sbox.tex
index 41f8812..fefb823 100644
--- a/buch/chapters/90-crypto/images/sbox.tex
+++ b/buch/chapters/90-crypto/images/sbox.tex
@@ -1,241 +1,241 @@
-%
-% sbox.tex -- template for standalon tikz images
-%
-% (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]
-
-\def\s{0.2}
-\def\punkt#1#2{({#1*\s},{(8-(#2))*\s})}
-
-\definecolor{b}{rgb}{0,0,0}
-\definecolor{w}{rgb}{1,1,1}
-
-\def\feld#1#2#3{
-	\fill[color=#3] \punkt{#1}{#2} rectangle \punkt{(#1+1)}{(#2-1)};
-}
-
-\def\zeile#1#2#3#4#5#6#7#8#9{
-	\feld{0}{#1}{#2}
-	\feld{1}{#1}{#3}
-	\feld{2}{#1}{#4}
-	\feld{3}{#1}{#5}
-	\feld{4}{#1}{#6}
-	\feld{5}{#1}{#7}
-	\feld{6}{#1}{#8}
-	\feld{7}{#1}{#9}
-}
-\def\inverse#1#2#3#4#5#6#7#8#9{
-	\feld{8}{#1}{#2}
-	\feld{9}{#1}{#3}
-	\feld{10}{#1}{#4}
-	\feld{11}{#1}{#5}
-	\feld{12}{#1}{#6}
-	\feld{13}{#1}{#7}
-	\feld{14}{#1}{#8}
-	\feld{15}{#1}{#9}
-}
-\def\rechteck{
-	\draw (0,{1*\s}) rectangle ({16*\s},{(8+1)*\s});
-	\draw ({8*\s},{1*\s}) -- ({8*\s},{(8+1)*\s});
-}
-
-\def\pivot#1#2{
-	\draw[color=red,line width=1.2pt]
-		\punkt{(#1+\inset)}{(#2-\inset)}
-		rectangle
-		\punkt{(#1+1-\inset)}{(#2-1+\inset)};
-}
-\def\inset{0.1}
-\def\cleanup#1#2#3{
-	\pgfmathparse{(#3-#2)/abs(#3-#2)}
-	\xdef\signum{\pgfmathresult}
-	\draw[color=blue!50,line width=1.2pt]
-		\punkt{(#1+\inset)}{#3}
-		--
-		\punkt{(#1+\inset)}{(#2-1+\inset*\signum)}
-		--
-		\punkt{(#1+1-\inset)}{(#2-1+\inset*\signum)}
-		--
-		\punkt{(#1+1-\inset)}{#3}
-	;
-}
-
-\begin{scope}
-	\zeile0bwwwbbbb \inverse0bwwwwwww
-	\zeile1bbwwwbbb \inverse1wbwwwwww
-	\zeile2bbbwwwbb \inverse2wwbwwwww
-	\zeile3bbbbwwwb \inverse3wwwbwwww
-	\zeile4bbbbbwww \inverse4wwwwbwww
-	\zeile5wbbbbbww \inverse5wwwwwbww
-	\zeile6wwbbbbbw \inverse6wwwwwwbw
-	\zeile7wwwbbbbb \inverse7wwwwwwwb
-	\rechteck
-	\pivot{0}{0}
-	\cleanup{0}{1}{7}
-\end{scope}
-
-\begin{scope}[xshift=4cm]
-	\draw[->,shorten >= 0.05cm,shorten <= 0.05cm]
-		\punkt{-4}{3} -- \punkt{0}{3};
-	\zeile0bwwwbbbb \inverse0bwwwwwww
-	\zeile1wbwwbwww \inverse1bbwwwwww
-	\zeile2wbbwbbww \inverse2bwbwwwww
-	\zeile3wbbbbbbw \inverse3bwwbwwww
-	\zeile4wbbbwbbb \inverse4bwwwbwww
-	\zeile5wbbbbbww \inverse5wwwwwbww
-	\zeile6wwbbbbbw \inverse6wwwwwwbw
-	\zeile7wwwbbbbb \inverse7wwwwwwwb
-	\rechteck
-	\pivot{1}{1}
-	\cleanup{1}{2}{7}
-\end{scope}
-
-\begin{scope}[xshift=8cm]
-	\draw[->,shorten >= 0.05cm,shorten <= 0.05cm]
-		\punkt{-4}{3} -- \punkt{0}{3};
-	\zeile0bwwwbbbb \inverse0bwwwwwww
-	\zeile1wbwwbwww \inverse1bbwwwwww
-	\zeile2wwbwwbww \inverse2wbbwwwww
-	\zeile3wwbbwbbw \inverse3wbwbwwww
-	\zeile4wwbbbbbb \inverse4wbwwbwww
-	\zeile5wwbbwbww \inverse5bbwwwbww
-	\zeile6wwbbbbbw \inverse6wwwwwwbw
-	\zeile7wwwbbbbb \inverse7wwwwwwwb
-	\rechteck
-	\pivot{2}{2}
-	\cleanup{2}{3}{7}
-\end{scope}
-
-\begin{scope}[xshift=12cm,yshift=0cm]
-	\draw[->,shorten >= 0.05cm,shorten <= 0.05cm]
-		\punkt{-4}{3} -- \punkt{0}{3};
-	\zeile0bwwwbbbb \inverse0bwwwwwww
-	\zeile1wbwwbwww \inverse1bbwwwwww
-	\zeile2wwbwwbww \inverse2wbbwwwww
-	\zeile3wwwbwwbw \inverse3wwbbwwww
-	\zeile4wwwbbwbb \inverse4wwbwbwww
-	\zeile5wwwbwwww \inverse5bwbwwbww
-	\zeile6wwwbbwbw \inverse6wbbwwwbw
-	\zeile7wwwbbbbb \inverse7wwwwwwwb
-	\rechteck
-	\pivot{3}{3}
-	\cleanup{3}{4}{7}
-	\draw[->,shorten >= 0.05cm,shorten <= 0.05cm]
-		\punkt{8}{7} -- \punkt{8}{11};
-\end{scope}
-
-\begin{scope}[xshift=12cm,yshift=-2.4cm]
-	\draw[<-,shorten >= 0.05cm,shorten <= 0.05cm]
-		\punkt{-4}{3} -- \punkt{0}{3};
-	\zeile0bwwwbbbb \inverse0bwwwwwww
-	\zeile1wbwwbwww \inverse1bbwwwwww
-	\zeile2wwbwwbww \inverse2wbbwwwww
-	\zeile3wwwbwwbw \inverse3wwbbwwww
-	\zeile4wwwwbwwb \inverse4wwwbbwww
-	\zeile5wwwwwwbw \inverse5bwwbwbww
-	\zeile6wwwwbwww \inverse6wbwbwwbw
-	\zeile7wwwwbbwb \inverse7wwbbwwwb
-	\rechteck
-	\pivot{4}{4}
-	\cleanup{4}{5}{7}
-\end{scope}
-
-\begin{scope}[xshift=8cm,yshift=-2.4cm]
-	\draw[<-,shorten >= 0.05cm,shorten <= 0.05cm]
-		\punkt{-4}{3} -- \punkt{0}{3};
-	\zeile0bwwwbbbb \inverse0bwwwwwww
-	\zeile1wbwwbwww \inverse1bbwwwwww
-	\zeile2wwbwwbww \inverse2wbbwwwww
-	\zeile3wwwbwwbw \inverse3wwbbwwww
-	\zeile4wwwwbwwb \inverse4wwwbbwww
-	\zeile5wwwwwwbw \inverse5bwwbwbww
-	\zeile6wwwwwwwb \inverse6wbwwbwbw
-	\zeile7wwwwwbww \inverse7wwbwbwwb
-	\rechteck
-\end{scope}
-
-\begin{scope}[xshift=4cm,yshift=-2.4cm]
-	\draw[<-,shorten >= 0.05cm,shorten <= 0.05cm]
-		\punkt{-4}{3} -- \punkt{0}{3};
-	\zeile0bwwwbbbb \inverse0bwwwwwww
-	\zeile1wbwwbwww \inverse1bbwwwwww
-	\zeile2wwbwwbww \inverse2wbbwwwww
-	\zeile3wwwbwwbw \inverse3wwbbwwww
-	\zeile4wwwwbwwb \inverse4wwwbbwww
-	\zeile5wwwwwbww \inverse5wwbwbwwb
-	\zeile6wwwwwwbw \inverse6bwwbwbww
-	\zeile7wwwwwwwb \inverse7wbwwbwbw
-	\rechteck
-	\cleanup{7}{7}{-1}
-\end{scope}
-
-\begin{scope}[xshift=0cm,yshift=-2.4cm]
-	\zeile0bwwwbbbw \inverse0bbwwbwbw
-	\zeile1wbwwbwww \inverse1bbwwwwww
-	\zeile2wwbwwbww \inverse2wbbwwwww
-	\zeile3wwwbwwbw \inverse3wwbbwwww
-	\zeile4wwwwbwww \inverse4wbwbwwbw
-	\zeile5wwwwwbww \inverse5wwbwbwwb
-	\zeile6wwwwwwbw \inverse6bwwbwbww
-	\zeile7wwwwwwwb \inverse7wbwwbwbw
-	\rechteck
-	\cleanup{6}{6}{-1}
-	\draw[->,shorten >= 0.05cm,shorten <= 0.05cm]
-		\punkt{8}{7} -- \punkt{8}{11};
-\end{scope}
-
-\begin{scope}[xshift=0cm,yshift=-4.8cm]
-	\zeile0bwwwbbww \inverse0wbwbbbbw
-	\zeile1wbwwbwww \inverse1bbwwwwww
-	\zeile2wwbwwbww \inverse2wbbwwwww
-	\zeile3wwwbwwww \inverse3bwbwwbww
-	\zeile4wwwwbwww \inverse4wbwbwwbw
-	\zeile5wwwwwbww \inverse5wwbwbwwb
-	\zeile6wwwwwwbw \inverse6bwwbwbww
-	\zeile7wwwwwwwb \inverse7wbwwbwbw
-	\rechteck
-	\cleanup{5}{5}{-1}
-\end{scope}
-
-\begin{scope}[xshift=4cm,yshift=-4.8cm]
-	\draw[->,shorten >= 0.05cm,shorten <= 0.05cm]
-		\punkt{-4}{3} -- \punkt{0}{3};
-	\zeile0bwwwbwww \inverse0wbbbwbbb
-	\zeile1wbwwbwww \inverse1bbwwwwww
-	\zeile2wwbwwwww \inverse2wbwwbwwb
-	\zeile3wwwbwwww \inverse3bwbwwbww
-	\zeile4wwwwbwww \inverse4wbwbwwbw
-	\zeile5wwwwwbww \inverse5wwbwbwwb
-	\zeile6wwwwwwbw \inverse6bwwbwbww
-	\zeile7wwwwwwwb \inverse7wbwwbwbw
-	\rechteck
-	\cleanup{4}{4}{-1}
-\end{scope}
-
-\begin{scope}[xshift=8cm,yshift=-4.8cm]
-	\draw[->,shorten >= 0.05cm,shorten <= 0.05cm]
-		\punkt{-4}{3} -- \punkt{0}{3};
-	\zeile0bwwwwwww \inverse0wwbwwbwb
-	\zeile1wbwwwwww \inverse1bwwbwwbw
-	\zeile2wwbwwwww \inverse2wbwwbwwb
-	\zeile3wwwbwwww \inverse3bwbwwbww
-	\zeile4wwwwbwww \inverse4wbwbwwbw
-	\zeile5wwwwwbww \inverse5wwbwbwwb
-	\zeile6wwwwwwbw \inverse6bwwbwbww
-	\zeile7wwwwwwwb \inverse7wbwwbwbw
-	\rechteck
-\end{scope}
-
-\end{tikzpicture}
-\end{document}
-
+%

+% sbox.tex -- template for standalon tikz images

+%

+% (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]

+

+\def\s{0.2}

+\def\punkt#1#2{({#1*\s},{(8-(#2))*\s})}

+

+\definecolor{b}{rgb}{0,0,0}

+\definecolor{w}{rgb}{1,1,1}

+

+\def\feld#1#2#3{

+	\fill[color=#3] \punkt{#1}{#2} rectangle \punkt{(#1+1)}{(#2-1)};

+}

+

+\def\zeile#1#2#3#4#5#6#7#8#9{

+	\feld{0}{#1}{#2}

+	\feld{1}{#1}{#3}

+	\feld{2}{#1}{#4}

+	\feld{3}{#1}{#5}

+	\feld{4}{#1}{#6}

+	\feld{5}{#1}{#7}

+	\feld{6}{#1}{#8}

+	\feld{7}{#1}{#9}

+}

+\def\inverse#1#2#3#4#5#6#7#8#9{

+	\feld{8}{#1}{#2}

+	\feld{9}{#1}{#3}

+	\feld{10}{#1}{#4}

+	\feld{11}{#1}{#5}

+	\feld{12}{#1}{#6}

+	\feld{13}{#1}{#7}

+	\feld{14}{#1}{#8}

+	\feld{15}{#1}{#9}

+}

+\def\rechteck{

+	\draw (0,{1*\s}) rectangle ({16*\s},{(8+1)*\s});

+	\draw ({8*\s},{1*\s}) -- ({8*\s},{(8+1)*\s});

+}

+

+\def\pivot#1#2{

+	\draw[color=red,line width=1.2pt]

+		\punkt{(#1+\inset)}{(#2-\inset)}

+		rectangle

+		\punkt{(#1+1-\inset)}{(#2-1+\inset)};

+}

+\def\inset{0.1}

+\def\cleanup#1#2#3{

+	\pgfmathparse{(#3-#2)/abs(#3-#2)}

+	\xdef\signum{\pgfmathresult}

+	\draw[color=blue!50,line width=1.2pt]

+		\punkt{(#1+\inset)}{#3}

+		--

+		\punkt{(#1+\inset)}{(#2-1+\inset*\signum)}

+		--

+		\punkt{(#1+1-\inset)}{(#2-1+\inset*\signum)}

+		--

+		\punkt{(#1+1-\inset)}{#3}

+	;

+}

+

+\begin{scope}

+	\zeile0bwwwbbbb \inverse0bwwwwwww

+	\zeile1bbwwwbbb \inverse1wbwwwwww

+	\zeile2bbbwwwbb \inverse2wwbwwwww

+	\zeile3bbbbwwwb \inverse3wwwbwwww

+	\zeile4bbbbbwww \inverse4wwwwbwww

+	\zeile5wbbbbbww \inverse5wwwwwbww

+	\zeile6wwbbbbbw \inverse6wwwwwwbw

+	\zeile7wwwbbbbb \inverse7wwwwwwwb

+	\rechteck

+	\pivot{0}{0}

+	\cleanup{0}{1}{7}

+\end{scope}

+

+\begin{scope}[xshift=4cm]

+	\draw[->,shorten >= 0.05cm,shorten <= 0.05cm]

+		\punkt{-4}{3} -- \punkt{0}{3};

+	\zeile0bwwwbbbb \inverse0bwwwwwww

+	\zeile1wbwwbwww \inverse1bbwwwwww

+	\zeile2wbbwbbww \inverse2bwbwwwww

+	\zeile3wbbbbbbw \inverse3bwwbwwww

+	\zeile4wbbbwbbb \inverse4bwwwbwww

+	\zeile5wbbbbbww \inverse5wwwwwbww

+	\zeile6wwbbbbbw \inverse6wwwwwwbw

+	\zeile7wwwbbbbb \inverse7wwwwwwwb

+	\rechteck

+	\pivot{1}{1}

+	\cleanup{1}{2}{7}

+\end{scope}

+

+\begin{scope}[xshift=8cm]

+	\draw[->,shorten >= 0.05cm,shorten <= 0.05cm]

+		\punkt{-4}{3} -- \punkt{0}{3};

+	\zeile0bwwwbbbb \inverse0bwwwwwww

+	\zeile1wbwwbwww \inverse1bbwwwwww

+	\zeile2wwbwwbww \inverse2wbbwwwww

+	\zeile3wwbbwbbw \inverse3wbwbwwww

+	\zeile4wwbbbbbb \inverse4wbwwbwww

+	\zeile5wwbbwbww \inverse5bbwwwbww

+	\zeile6wwbbbbbw \inverse6wwwwwwbw

+	\zeile7wwwbbbbb \inverse7wwwwwwwb

+	\rechteck

+	\pivot{2}{2}

+	\cleanup{2}{3}{7}

+\end{scope}

+

+\begin{scope}[xshift=12cm,yshift=0cm]

+	\draw[->,shorten >= 0.05cm,shorten <= 0.05cm]

+		\punkt{-4}{3} -- \punkt{0}{3};

+	\zeile0bwwwbbbb \inverse0bwwwwwww

+	\zeile1wbwwbwww \inverse1bbwwwwww

+	\zeile2wwbwwbww \inverse2wbbwwwww

+	\zeile3wwwbwwbw \inverse3wwbbwwww

+	\zeile4wwwbbwbb \inverse4wwbwbwww

+	\zeile5wwwbwwww \inverse5bwbwwbww

+	\zeile6wwwbbwbw \inverse6wbbwwwbw

+	\zeile7wwwbbbbb \inverse7wwwwwwwb

+	\rechteck

+	\pivot{3}{3}

+	\cleanup{3}{4}{7}

+	\draw[->,shorten >= 0.05cm,shorten <= 0.05cm]

+		\punkt{8}{7} -- \punkt{8}{11};

+\end{scope}

+

+\begin{scope}[xshift=12cm,yshift=-2.4cm]

+	\draw[<-,shorten >= 0.05cm,shorten <= 0.05cm]

+		\punkt{-4}{3} -- \punkt{0}{3};

+	\zeile0bwwwbbbb \inverse0bwwwwwww

+	\zeile1wbwwbwww \inverse1bbwwwwww

+	\zeile2wwbwwbww \inverse2wbbwwwww

+	\zeile3wwwbwwbw \inverse3wwbbwwww

+	\zeile4wwwwbwwb \inverse4wwwbbwww

+	\zeile5wwwwwwbw \inverse5bwwbwbww

+	\zeile6wwwwbwww \inverse6wbwbwwbw

+	\zeile7wwwwbbwb \inverse7wwbbwwwb

+	\rechteck

+	\pivot{4}{4}

+	\cleanup{4}{5}{7}

+\end{scope}

+

+\begin{scope}[xshift=8cm,yshift=-2.4cm]

+	\draw[<-,shorten >= 0.05cm,shorten <= 0.05cm]

+		\punkt{-4}{3} -- \punkt{0}{3};

+	\zeile0bwwwbbbb \inverse0bwwwwwww

+	\zeile1wbwwbwww \inverse1bbwwwwww

+	\zeile2wwbwwbww \inverse2wbbwwwww

+	\zeile3wwwbwwbw \inverse3wwbbwwww

+	\zeile4wwwwbwwb \inverse4wwwbbwww

+	\zeile5wwwwwwbw \inverse5bwwbwbww

+	\zeile6wwwwwwwb \inverse6wbwwbwbw

+	\zeile7wwwwwbww \inverse7wwbwbwwb

+	\rechteck

+\end{scope}

+

+\begin{scope}[xshift=4cm,yshift=-2.4cm]

+	\draw[<-,shorten >= 0.05cm,shorten <= 0.05cm]

+		\punkt{-4}{3} -- \punkt{0}{3};

+	\zeile0bwwwbbbb \inverse0bwwwwwww

+	\zeile1wbwwbwww \inverse1bbwwwwww

+	\zeile2wwbwwbww \inverse2wbbwwwww

+	\zeile3wwwbwwbw \inverse3wwbbwwww

+	\zeile4wwwwbwwb \inverse4wwwbbwww

+	\zeile5wwwwwbww \inverse5wwbwbwwb

+	\zeile6wwwwwwbw \inverse6bwwbwbww

+	\zeile7wwwwwwwb \inverse7wbwwbwbw

+	\rechteck

+	\cleanup{7}{7}{-1}

+\end{scope}

+

+\begin{scope}[xshift=0cm,yshift=-2.4cm]

+	\zeile0bwwwbbbw \inverse0bbwwbwbw

+	\zeile1wbwwbwww \inverse1bbwwwwww

+	\zeile2wwbwwbww \inverse2wbbwwwww

+	\zeile3wwwbwwbw \inverse3wwbbwwww

+	\zeile4wwwwbwww \inverse4wbwbwwbw

+	\zeile5wwwwwbww \inverse5wwbwbwwb

+	\zeile6wwwwwwbw \inverse6bwwbwbww

+	\zeile7wwwwwwwb \inverse7wbwwbwbw

+	\rechteck

+	\cleanup{6}{6}{-1}

+	\draw[->,shorten >= 0.05cm,shorten <= 0.05cm]

+		\punkt{8}{7} -- \punkt{8}{11};

+\end{scope}

+

+\begin{scope}[xshift=0cm,yshift=-4.8cm]

+	\zeile0bwwwbbww \inverse0wbwbbbbw

+	\zeile1wbwwbwww \inverse1bbwwwwww

+	\zeile2wwbwwbww \inverse2wbbwwwww

+	\zeile3wwwbwwww \inverse3bwbwwbww

+	\zeile4wwwwbwww \inverse4wbwbwwbw

+	\zeile5wwwwwbww \inverse5wwbwbwwb

+	\zeile6wwwwwwbw \inverse6bwwbwbww

+	\zeile7wwwwwwwb \inverse7wbwwbwbw

+	\rechteck

+	\cleanup{5}{5}{-1}

+\end{scope}

+

+\begin{scope}[xshift=4cm,yshift=-4.8cm]

+	\draw[->,shorten >= 0.05cm,shorten <= 0.05cm]

+		\punkt{-4}{3} -- \punkt{0}{3};

+	\zeile0bwwwbwww \inverse0wbbbwbbb

+	\zeile1wbwwbwww \inverse1bbwwwwww

+	\zeile2wwbwwwww \inverse2wbwwbwwb

+	\zeile3wwwbwwww \inverse3bwbwwbww

+	\zeile4wwwwbwww \inverse4wbwbwwbw

+	\zeile5wwwwwbww \inverse5wwbwbwwb

+	\zeile6wwwwwwbw \inverse6bwwbwbww

+	\zeile7wwwwwwwb \inverse7wbwwbwbw

+	\rechteck

+	\cleanup{4}{4}{-1}

+\end{scope}

+

+\begin{scope}[xshift=8cm,yshift=-4.8cm]

+	\draw[->,shorten >= 0.05cm,shorten <= 0.05cm]

+		\punkt{-4}{3} -- \punkt{0}{3};

+	\zeile0bwwwwwww \inverse0wwbwwbwb

+	\zeile1wbwwwwww \inverse1bwwbwwbw

+	\zeile2wwbwwwww \inverse2wbwwbwwb

+	\zeile3wwwbwwww \inverse3bwbwwbww

+	\zeile4wwwwbwww \inverse4wbwbwwbw

+	\zeile5wwwwwbww \inverse5wwbwbwwb

+	\zeile6wwwwwwbw \inverse6bwwbwbww

+	\zeile7wwwwwwwb \inverse7wbwwbwbw

+	\rechteck

+\end{scope}

+

+\end{tikzpicture}

+\end{document}

+

diff --git a/buch/chapters/90-crypto/images/schieberegister.tex b/buch/chapters/90-crypto/images/schieberegister.tex
index 7c24e52..49302ac 100644
--- a/buch/chapters/90-crypto/images/schieberegister.tex
+++ b/buch/chapters/90-crypto/images/schieberegister.tex
@@ -1,120 +1,120 @@
-%
-% schieberegister.tex -- template for standalon tikz images
-%
-% (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{0.8}
-
-\def\punkt#1#2{({#1*\s},{#2*\s})}
-
-\fill[color=blue!20] \punkt{0}{0} rectangle \punkt{8}{1};
-
-\node at \punkt{0.5}{1} [above] {$X^7\mathstrut$};
-\node at \punkt{3}{1}   [above] {$+\mathstrut$};
-\node at \punkt{3.5}{1} [above] {$X^4\mathstrut$};
-\node at \punkt{5}{1}   [above] {$+\mathstrut$};
-\node at \punkt{5.5}{1} [above] {$X^2\mathstrut$};
-\node at \punkt{7}{1}   [above] {$+\mathstrut$};
-\node at \punkt{7.5}{1} [above] {$1\mathstrut$};
-
-\node at \punkt{0}{1} [above left] {\llap{$p(X)=\mathstrut$}};
-
-\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}};
-
-\draw \punkt{0}{0} rectangle \punkt{8}{1};
-\foreach \x in {1,...,7}{
-	\draw \punkt{\x}{0} -- \punkt{\x}{1};
-}
-
-\fill[color=blue!20] \punkt{-1}{-3} rectangle \punkt{7}{-2};
-\fill[color=darkgreen!20] \punkt{0}{-4} rectangle \punkt{8}{-3};
-
-\node[color=darkgreen] at \punkt{-1}{-1.5} [left] 
-	{$m(X) = X^8+X^4+X^3+X+1$};
-
-\node[color=darkgreen] at \punkt{-1}{-2.7} [left]
-	{$\underbrace{X^4+X^3+X+1}_{}= X^8=\mathstrut$};
-
-\coordinate (A) at ({-4.15*\s},{-3*\s});
-\coordinate (B) at ({0*\s},{-3.5*\s});
-
-\draw[->,color=red,shorten >= 0.1cm] (A) to[out=-90,in=180] (B);
-\node[color=red] at \punkt{-3.1}{-3.8} [below] {Feedback};
-
-\node at \punkt{-0.5}{-2.5} {\texttt{1}};
-\node at \punkt{0.5}{-2.5} {\texttt{0}};
-\node at \punkt{1.5}{-2.5} {\texttt{0}};
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-\node at \punkt{3.5}{-2.5} {\texttt{0}};
-\node at \punkt{4.5}{-2.5} {\texttt{1}};
-\node at \punkt{5.5}{-2.5} {\texttt{0}};
-\node at \punkt{6.5}{-2.5} {\texttt{1}};
-\node at \punkt{7.5}{-2.5} {\texttt{0}};
-
-\node[color=darkgreen] at \punkt{0.5}{-3.5} {\texttt{0}};
-\node[color=darkgreen] at \punkt{1.5}{-3.5} {\texttt{0}};
-\node[color=darkgreen] at \punkt{2.5}{-3.5} {\texttt{0}};
-\node[color=darkgreen] at \punkt{3.5}{-3.5} {\texttt{1}};
-\node[color=darkgreen] at \punkt{4.5}{-3.5} {\texttt{1}};
-\node[color=darkgreen] at \punkt{5.5}{-3.5} {\texttt{0}};
-\node[color=darkgreen] at \punkt{6.5}{-3.5} {\texttt{1}};
-\node[color=darkgreen] at \punkt{7.5}{-3.5} {\texttt{1}};
-
-\draw \punkt{0}{-4} rectangle \punkt{8}{-2};
-\draw \punkt{0}{-3} -- \punkt{8}{-3};
-\foreach \x in {1,...,7}{
-	\draw \punkt{\x}{-4} -- \punkt{\x}{-2};
-}
-
-\foreach \x in {0.5,1.5,...,7.5}{
-	\draw[->,color=blue] \punkt{\x}{-0.1} -- \punkt{(\x-1)}{-1.9};
-}
-
-\draw \punkt{0}{-6} rectangle \punkt{8}{-5};
-\foreach \x in {1,...,7}{
-	\draw \punkt{\x}{-6} -- \punkt{\x}{-5};
-}
-
-\node at \punkt{0.5}{-5.5} {\texttt{0}};
-\node at \punkt{1.5}{-5.5} {\texttt{0}};
-\node at \punkt{2.5}{-5.5} {\texttt{1}};
-\node at \punkt{3.5}{-5.5} {\texttt{1}};
-\node at \punkt{4.5}{-5.5} {\texttt{0}};
-\node at \punkt{5.5}{-5.5} {\texttt{0}};
-\node at \punkt{6.5}{-5.5} {\texttt{0}};
-\node at \punkt{7.5}{-5.5} {\texttt{1}};
-
-\node at \punkt{4}{-4.5} {$\|$};
-
-\node at \punkt{10.3}{-3} [left]
-	{$\left.\begin{matrix}\\ \\ \\ \end{matrix}\right\} + = \text{XOR}$};
-
-\draw[<-,shorten >= 0.1cm, shorten <= 0.1cm]
-	\punkt{8.0}{-2.0} arc (-30:30:{2.0*\s});
-\node at \punkt{8.3}{-1} [right] {$\mathstrut \cdot X$};
-
-\node at \punkt{8.1}{-5.5} [right] {$=X\cdot p(X)\mathstrut$};
-
-\end{tikzpicture}
-\end{document}
-
+%

+% schieberegister.tex -- template for standalon tikz images

+%

+% (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{0.8}

+

+\def\punkt#1#2{({#1*\s},{#2*\s})}

+

+\fill[color=blue!20] \punkt{0}{0} rectangle \punkt{8}{1};

+

+\node at \punkt{0.5}{1} [above] {$X^7\mathstrut$};

+\node at \punkt{3}{1}   [above] {$+\mathstrut$};

+\node at \punkt{3.5}{1} [above] {$X^4\mathstrut$};

+\node at \punkt{5}{1}   [above] {$+\mathstrut$};

+\node at \punkt{5.5}{1} [above] {$X^2\mathstrut$};

+\node at \punkt{7}{1}   [above] {$+\mathstrut$};

+\node at \punkt{7.5}{1} [above] {$1\mathstrut$};

+

+\node at \punkt{0}{1} [above left] {\llap{$p(X)=\mathstrut$}};

+

+\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}};

+

+\draw \punkt{0}{0} rectangle \punkt{8}{1};

+\foreach \x in {1,...,7}{

+	\draw \punkt{\x}{0} -- \punkt{\x}{1};

+}

+

+\fill[color=blue!20] \punkt{-1}{-3} rectangle \punkt{7}{-2};

+\fill[color=darkgreen!20] \punkt{0}{-4} rectangle \punkt{8}{-3};

+

+\node[color=darkgreen] at \punkt{-1}{-1.5} [left] 

+	{$m(X) = X^8+X^4+X^3+X+1$};

+

+\node[color=darkgreen] at \punkt{-1}{-2.7} [left]

+	{$\underbrace{X^4+X^3+X+1}_{}= X^8=\mathstrut$};

+

+\coordinate (A) at ({-4.15*\s},{-3*\s});

+\coordinate (B) at ({0*\s},{-3.5*\s});

+

+\draw[->,color=red,shorten >= 0.1cm] (A) to[out=-90,in=180] (B);

+\node[color=red] at \punkt{-3.1}{-3.8} [below] {Feedback};

+

+\node at \punkt{-0.5}{-2.5} {\texttt{1}};

+\node at \punkt{0.5}{-2.5} {\texttt{0}};

+\node at \punkt{1.5}{-2.5} {\texttt{0}};

+\node at \punkt{2.5}{-2.5} {\texttt{1}};

+\node at \punkt{3.5}{-2.5} {\texttt{0}};

+\node at \punkt{4.5}{-2.5} {\texttt{1}};

+\node at \punkt{5.5}{-2.5} {\texttt{0}};

+\node at \punkt{6.5}{-2.5} {\texttt{1}};

+\node at \punkt{7.5}{-2.5} {\texttt{0}};

+

+\node[color=darkgreen] at \punkt{0.5}{-3.5} {\texttt{0}};

+\node[color=darkgreen] at \punkt{1.5}{-3.5} {\texttt{0}};

+\node[color=darkgreen] at \punkt{2.5}{-3.5} {\texttt{0}};

+\node[color=darkgreen] at \punkt{3.5}{-3.5} {\texttt{1}};

+\node[color=darkgreen] at \punkt{4.5}{-3.5} {\texttt{1}};

+\node[color=darkgreen] at \punkt{5.5}{-3.5} {\texttt{0}};

+\node[color=darkgreen] at \punkt{6.5}{-3.5} {\texttt{1}};

+\node[color=darkgreen] at \punkt{7.5}{-3.5} {\texttt{1}};

+

+\draw \punkt{0}{-4} rectangle \punkt{8}{-2};

+\draw \punkt{0}{-3} -- \punkt{8}{-3};

+\foreach \x in {1,...,7}{

+	\draw \punkt{\x}{-4} -- \punkt{\x}{-2};

+}

+

+\foreach \x in {0.5,1.5,...,7.5}{

+	\draw[->,color=blue] \punkt{\x}{-0.1} -- \punkt{(\x-1)}{-1.9};

+}

+

+\draw \punkt{0}{-6} rectangle \punkt{8}{-5};

+\foreach \x in {1,...,7}{

+	\draw \punkt{\x}{-6} -- \punkt{\x}{-5};

+}

+

+\node at \punkt{0.5}{-5.5} {\texttt{0}};

+\node at \punkt{1.5}{-5.5} {\texttt{0}};

+\node at \punkt{2.5}{-5.5} {\texttt{1}};

+\node at \punkt{3.5}{-5.5} {\texttt{1}};

+\node at \punkt{4.5}{-5.5} {\texttt{0}};

+\node at \punkt{5.5}{-5.5} {\texttt{0}};

+\node at \punkt{6.5}{-5.5} {\texttt{0}};

+\node at \punkt{7.5}{-5.5} {\texttt{1}};

+

+\node at \punkt{4}{-4.5} {$\|$};

+

+\node at \punkt{10.3}{-3} [left]

+	{$\left.\begin{matrix}\\ \\ \\ \end{matrix}\right\} + = \text{XOR}$};

+

+\draw[<-,shorten >= 0.1cm, shorten <= 0.1cm]

+	\punkt{8.0}{-2.0} arc (-30:30:{2.0*\s});

+\node at \punkt{8.3}{-1} [right] {$\mathstrut \cdot X$};

+

+\node at \punkt{8.1}{-5.5} [right] {$=X\cdot p(X)\mathstrut$};

+

+\end{tikzpicture}

+\end{document}

+

diff --git a/buch/chapters/90-crypto/images/shift.tex b/buch/chapters/90-crypto/images/shift.tex
index bcdf819..af225a7 100644
--- a/buch/chapters/90-crypto/images/shift.tex
+++ b/buch/chapters/90-crypto/images/shift.tex
@@ -1,131 +1,131 @@
-%
-% shift.tex -- template for standalon tikz images
-%
-% (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{0.8}
-\def\punkt#1#2{({#1*\s},{#2*\s})}
-
-\def\feld#1#2#3#4{
-	\fill[color=#3] \punkt{#1}{#2} rectangle \punkt{(#1+1)}{(#2+1)};
-	\node at \punkt{(#1+0.5)}{(#2+0.5)} {$\mathstrut #4$};
-}
-\def\gitter{
-	\draw \punkt{0}{0} rectangle \punkt{8}{4};
-	\foreach \x in {1,...,7}{
-		\draw \punkt{\x}{0} -- \punkt{\x}{4};
-	}
-	\foreach \y in {1,...,3}{
-		\draw \punkt{0}{\y} -- \punkt{8}{\y};
-	}
-}
-
-\begin{scope}
-	\feld{0}{3}{red!20}{b_{0}}
-	\feld{0}{2}{red!20}{b_{1}}
-	\feld{0}{1}{red!20}{b_{2}}
-	\feld{0}{0}{red!20}{b_{3}}
-
-	\feld{1}{3}{red!10}{b_{4}}
-	\feld{1}{2}{red!10}{b_{5}}
-	\feld{1}{1}{red!10}{b_{6}}
-	\feld{1}{0}{red!10}{b_{7}}
-
-	\feld{2}{3}{yellow!20}{b_{8}}
-	\feld{2}{2}{yellow!20}{b_{9}}
-	\feld{2}{1}{yellow!20}{b_{10}}
-	\feld{2}{0}{yellow!20}{b_{11}}
-
-	\feld{3}{3}{yellow!10}{b_{12}}
-	\feld{3}{2}{yellow!10}{b_{13}}
-	\feld{3}{1}{yellow!10}{b_{14}}
-	\feld{3}{0}{yellow!10}{b_{15}}
-
-	\feld{4}{3}{darkgreen!20}{b_{16}}
-	\feld{4}{2}{darkgreen!20}{b_{17}}
-	\feld{4}{1}{darkgreen!20}{b_{18}}
-	\feld{4}{0}{darkgreen!20}{b_{19}}
-
-	\feld{5}{3}{darkgreen!10}{b_{20}}
-	\feld{5}{2}{darkgreen!10}{b_{21}}
-	\feld{5}{1}{darkgreen!10}{b_{22}}
-	\feld{5}{0}{darkgreen!10}{b_{23}}
-
-	\feld{6}{3}{blue!20}{b_{24}}
-	\feld{6}{2}{blue!20}{b_{25}}
-	\feld{6}{1}{blue!20}{b_{26}}
-	\feld{6}{0}{blue!20}{b_{27}}
-
-	\feld{7}{3}{blue!10}{b_{28}}
-	\feld{7}{2}{blue!10}{b_{29}}
-	\feld{7}{1}{blue!10}{b_{30}}
-	\feld{7}{0}{blue!10}{b_{31}}
-
-	\gitter
-
-	\draw[->] \punkt{8.1}{2} -- \punkt{9.3}{2};
-\end{scope}
-
-
-\begin{scope}[xshift=7.5cm]
-
-	\feld{0}{3}{red!20}{b_{0}}
-	\feld{1}{2}{red!20}{b_{1}}
-	\feld{2}{1}{red!20}{b_{2}}
-	\feld{3}{0}{red!20}{b_{3}}
-
-	\feld{1}{3}{red!10}{b_{4}}
-	\feld{2}{2}{red!10}{b_{5}}
-	\feld{3}{1}{red!10}{b_{6}}
-	\feld{4}{0}{red!10}{b_{7}}
-
-	\feld{2}{3}{yellow!20}{b_{8}}
-	\feld{3}{2}{yellow!20}{b_{9}}
-	\feld{4}{1}{yellow!20}{b_{10}}
-	\feld{5}{0}{yellow!20}{b_{11}}
-
-	\feld{3}{3}{yellow!10}{b_{12}}
-	\feld{4}{2}{yellow!10}{b_{13}}
-	\feld{5}{1}{yellow!10}{b_{14}}
-	\feld{6}{0}{yellow!10}{b_{15}}
-
-	\feld{4}{3}{darkgreen!20}{b_{16}}
-	\feld{5}{2}{darkgreen!20}{b_{17}}
-	\feld{6}{1}{darkgreen!20}{b_{18}}
-	\feld{7}{0}{darkgreen!20}{b_{19}}
-
-	\feld{5}{3}{darkgreen!10}{b_{20}}
-	\feld{6}{2}{darkgreen!10}{b_{21}}
-	\feld{7}{1}{darkgreen!10}{b_{22}}
-	\feld{0}{0}{darkgreen!10}{b_{23}}
-
-	\feld{6}{3}{blue!20}{b_{24}}
-	\feld{7}{2}{blue!20}{b_{25}}
-	\feld{0}{1}{blue!20}{b_{26}}
-	\feld{1}{0}{blue!20}{b_{27}}
-
-	\feld{7}{3}{blue!10}{b_{28}}
-	\feld{0}{2}{blue!10}{b_{29}}
-	\feld{1}{1}{blue!10}{b_{30}}
-	\feld{2}{0}{blue!10}{b_{31}}
-
-	\gitter
-
-\end{scope}
-
-\end{tikzpicture}
-\end{document}
-
+%

+% shift.tex -- template for standalon tikz images

+%

+% (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{0.8}

+\def\punkt#1#2{({#1*\s},{#2*\s})}

+

+\def\feld#1#2#3#4{

+	\fill[color=#3] \punkt{#1}{#2} rectangle \punkt{(#1+1)}{(#2+1)};

+	\node at \punkt{(#1+0.5)}{(#2+0.5)} {$\mathstrut #4$};

+}

+\def\gitter{

+	\draw \punkt{0}{0} rectangle \punkt{8}{4};

+	\foreach \x in {1,...,7}{

+		\draw \punkt{\x}{0} -- \punkt{\x}{4};

+	}

+	\foreach \y in {1,...,3}{

+		\draw \punkt{0}{\y} -- \punkt{8}{\y};

+	}

+}

+

+\begin{scope}

+	\feld{0}{3}{red!20}{b_{0}}

+	\feld{0}{2}{red!20}{b_{1}}

+	\feld{0}{1}{red!20}{b_{2}}

+	\feld{0}{0}{red!20}{b_{3}}

+

+	\feld{1}{3}{red!10}{b_{4}}

+	\feld{1}{2}{red!10}{b_{5}}

+	\feld{1}{1}{red!10}{b_{6}}

+	\feld{1}{0}{red!10}{b_{7}}

+

+	\feld{2}{3}{yellow!20}{b_{8}}

+	\feld{2}{2}{yellow!20}{b_{9}}

+	\feld{2}{1}{yellow!20}{b_{10}}

+	\feld{2}{0}{yellow!20}{b_{11}}

+

+	\feld{3}{3}{yellow!10}{b_{12}}

+	\feld{3}{2}{yellow!10}{b_{13}}

+	\feld{3}{1}{yellow!10}{b_{14}}

+	\feld{3}{0}{yellow!10}{b_{15}}

+

+	\feld{4}{3}{darkgreen!20}{b_{16}}

+	\feld{4}{2}{darkgreen!20}{b_{17}}

+	\feld{4}{1}{darkgreen!20}{b_{18}}

+	\feld{4}{0}{darkgreen!20}{b_{19}}

+

+	\feld{5}{3}{darkgreen!10}{b_{20}}

+	\feld{5}{2}{darkgreen!10}{b_{21}}

+	\feld{5}{1}{darkgreen!10}{b_{22}}

+	\feld{5}{0}{darkgreen!10}{b_{23}}

+

+	\feld{6}{3}{blue!20}{b_{24}}

+	\feld{6}{2}{blue!20}{b_{25}}

+	\feld{6}{1}{blue!20}{b_{26}}

+	\feld{6}{0}{blue!20}{b_{27}}

+

+	\feld{7}{3}{blue!10}{b_{28}}

+	\feld{7}{2}{blue!10}{b_{29}}

+	\feld{7}{1}{blue!10}{b_{30}}

+	\feld{7}{0}{blue!10}{b_{31}}

+

+	\gitter

+

+	\draw[->] \punkt{8.1}{2} -- \punkt{9.3}{2};

+\end{scope}

+

+

+\begin{scope}[xshift=7.5cm]

+

+	\feld{0}{3}{red!20}{b_{0}}

+	\feld{1}{2}{red!20}{b_{1}}

+	\feld{2}{1}{red!20}{b_{2}}

+	\feld{3}{0}{red!20}{b_{3}}

+

+	\feld{1}{3}{red!10}{b_{4}}

+	\feld{2}{2}{red!10}{b_{5}}

+	\feld{3}{1}{red!10}{b_{6}}

+	\feld{4}{0}{red!10}{b_{7}}

+

+	\feld{2}{3}{yellow!20}{b_{8}}

+	\feld{3}{2}{yellow!20}{b_{9}}

+	\feld{4}{1}{yellow!20}{b_{10}}

+	\feld{5}{0}{yellow!20}{b_{11}}

+

+	\feld{3}{3}{yellow!10}{b_{12}}

+	\feld{4}{2}{yellow!10}{b_{13}}

+	\feld{5}{1}{yellow!10}{b_{14}}

+	\feld{6}{0}{yellow!10}{b_{15}}

+

+	\feld{4}{3}{darkgreen!20}{b_{16}}

+	\feld{5}{2}{darkgreen!20}{b_{17}}

+	\feld{6}{1}{darkgreen!20}{b_{18}}

+	\feld{7}{0}{darkgreen!20}{b_{19}}

+

+	\feld{5}{3}{darkgreen!10}{b_{20}}

+	\feld{6}{2}{darkgreen!10}{b_{21}}

+	\feld{7}{1}{darkgreen!10}{b_{22}}

+	\feld{0}{0}{darkgreen!10}{b_{23}}

+

+	\feld{6}{3}{blue!20}{b_{24}}

+	\feld{7}{2}{blue!20}{b_{25}}

+	\feld{0}{1}{blue!20}{b_{26}}

+	\feld{1}{0}{blue!20}{b_{27}}

+

+	\feld{7}{3}{blue!10}{b_{28}}

+	\feld{0}{2}{blue!10}{b_{29}}

+	\feld{1}{1}{blue!10}{b_{30}}

+	\feld{2}{0}{blue!10}{b_{31}}

+

+	\gitter

+

+\end{scope}

+

+\end{tikzpicture}

+\end{document}

+