diff options
Diffstat (limited to '')
| -rw-r--r-- | buch/chapters/90-crypto/images/Makefile | 58 | ||||
| -rw-r--r-- | buch/chapters/90-crypto/images/keys.tex | 242 | ||||
| -rw-r--r-- | buch/chapters/90-crypto/images/multiplikation.tex | 928 | ||||
| -rw-r--r-- | buch/chapters/90-crypto/images/sbox.m | 104 | ||||
| -rw-r--r-- | buch/chapters/90-crypto/images/sbox.tex | 482 | ||||
| -rw-r--r-- | buch/chapters/90-crypto/images/schieberegister.tex | 240 | ||||
| -rw-r--r-- | buch/chapters/90-crypto/images/shift.tex | 262 |
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}}; - \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} - +%
+% 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}}; -\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} - +%
+% 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}
+
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