intro to elliptic curve crypto

5 files changed, 163 insertions, 0 deletions

diff --git a/buch/chapters/90-crypto/images/Makefile b/buch/chapters/90-crypto/images/Makefile
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+++ b/buch/chapters/90-crypto/images/Makefile
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+#
+# Makefile -- build images for crypto chapter
+#
+# (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+#
+all:	dh.pdf elliptic.pdf
+
+dh.pdf:	dh.tex
+	pdflatex dh.tex
+
+elliptic.pdf:	elliptic.tex
+	pdflatex elliptic.tex
+
diff --git a/buch/chapters/90-crypto/images/dh.pdf b/buch/chapters/90-crypto/images/dh.pdf
new file mode 100644
index 0000000..67b95a5
--- /dev/null
+++ b/buch/chapters/90-crypto/images/dh.pdf
diff --git a/buch/chapters/90-crypto/images/dh.tex b/buch/chapters/90-crypto/images/dh.tex
new file mode 100644
index 0000000..1faa830
--- /dev/null
+++ b/buch/chapters/90-crypto/images/dh.tex
@@ -0,0 +1,53 @@
+%
+% dh.tex -- diffie hellmann key exchange
+%
+% (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,calc,hobby}
+\begin{document}
+\definecolor{darkgreen}{rgb}{0,0.6,0}
+\def\skala{1}
+\begin{tikzpicture}[>=latex,thick,scale=\skala]
+\def\l{2.5}
+\fill[color=blue!20] (-7,-6.5) rectangle (7,0.5);
+\fill[color=red!20] (-\l,-6.5) rectangle (\l,0.501);
+\node[color=red] at (0,-1.5) {öffentliches Netzwerk};
+\node[color=blue] at (-7,0.2) [right] {privat};
+\node[color=blue] at (7,0.2) [left] {privat};
+\coordinate (A) at (-\l,-2.5);
+\coordinate (C) at (\l,-5.5);
+\coordinate (B) at (\l,-2.5);
+\coordinate (D) at (-\l,-5.5);
+\node at (0,0) {$p\in\mathbb{N},g\in\mathbb{F}_p$ aushandeln};
+\fill[color=white] (-\l,-0.7) circle[radius=0.3];
+\draw (-\l,-0.7) circle[radius=0.3];
+\fill[color=white] (\l,-0.7) circle[radius=0.3];
+\draw (\l,-0.7) circle[radius=0.3];
+\node at (-\l,-0.7) {$A$};
+\node at (\l,-0.7) {$B$};
+\node at (-\l,-1.5) [left] {$a$ auswählen};
+\node at (-\l,-2.0) [left] {$x=g^a\in\mathbb{F}_p$ auswählen};
+\node at (\l,-1.5) [right] {$b$ auswählen};
+\node at (\l,-2.0) [right] {$y=g^b\in\mathbb{F}_p$ auswählen};
+\draw[->] (-\l,-1) -- (-\l,-6);
+\draw[->] (\l,-1) -- (\l,-6);
+\draw[->] (A) -- (C);
+\draw[->] (B) -- (D);
+\fill (A) circle[radius=0.08];
+\fill (B) circle[radius=0.08];
+\node at ($0.8*(A)+0.2*(C)$) [above right] {$x=g^a$};
+\node at ($0.8*(B)+0.2*(D)$) [above left] {$y=g^b$};
+\node at (-\l,-5.5) [left] {$s=g^{ab}=y^a\in\mathbb{F}_p$ ausrechnen};
+\node at (\l,-5.5) [right] {$s=g^{ab}=x^b\in\mathbb{F}_p$ ausrechnen};
+\fill[rounded corners=0.3cm,color=darkgreen!20] ({-\l-1},-7) rectangle ({\l+1},-6);
+\draw[rounded corners=0.3cm] ({-\l-1},-7) rectangle ({\l+1},-6);
+\node at (0,-6.5) {$A$ und $B$ haben den gemeinsamen Schlüssel $s$};
+\end{tikzpicture}
+\end{document}
+
diff --git a/buch/chapters/90-crypto/images/elliptic.pdf b/buch/chapters/90-crypto/images/elliptic.pdf
new file mode 100644
index 0000000..d408f1e
--- /dev/null
+++ b/buch/chapters/90-crypto/images/elliptic.pdf
diff --git a/buch/chapters/90-crypto/images/elliptic.tex b/buch/chapters/90-crypto/images/elliptic.tex
new file mode 100644
index 0000000..f0843cd
--- /dev/null
+++ b/buch/chapters/90-crypto/images/elliptic.tex
@@ -0,0 +1,97 @@
+%
+% elliptic.tex -- elliptic curve
+%
+% (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{4}
+\begin{tikzpicture}[>=latex,thick,scale=\skala]
+
+\def\uone{-1.1}
+\def\utwo{0.3}
+\pgfmathparse{-(\uone+\utwo)}
+\xdef\uthree{\pgfmathresult}
+\xdef\r{0.017}
+
+\def\gone{-1.05}
+\def\gtwo{0.2}
+\def\gthree{1.105}
+
+\pgfmathparse{-sqrt((\gone-\uone)*(\gone-\utwo)*(\gone-\uthree))}
+\xdef\yone{\pgfmathresult}
+\pgfmathparse{sqrt((\gtwo-\uone)*(\gtwo-\utwo)*(\gtwo-\uthree))}
+\xdef\ytwo{\pgfmathresult}
+\pgfmathparse{sqrt((\gthree-\uone)*(\gthree-\utwo)*(\gthree-\uthree))}
+\xdef\ythree{\pgfmathresult}
+
+\begin{scope}
+\clip (-1.5,-1.5) rectangle (1.5,1.5);
+\draw[color=blue]
+	({\gone-(\gtwo-\gone)},{\yone-(\ytwo-\yone)})
+	--
+	({\gone+2*(\gtwo-\gone)},{\yone+2*(\ytwo-\yone)});
+\draw[color=blue] (\gthree,-2) -- (\gthree,2);
+\end{scope}
+
+\draw[line width=1.4pt,color=red]
+	(\uone,0) --
+	plot[domain={\uone+0.001}:{\utwo-0.001},samples=100]
+		(\x,{sqrt((\x-\uone)*(\x-\utwo)*(\x-\uthree))})
+	-- (\utwo,0);
+\draw[line width=1.4pt,color=red]
+	(\uone,0) --
+	plot[domain={\uone+0.001}:{\utwo-0.001},samples=100]
+		(\x,{-sqrt((\x-\uone)*(\x-\utwo)*(\x-\uthree))})
+	-- (\utwo,0);
+
+\draw[line width=1.4pt,color=red]
+	(\uthree,0) --
+	plot[domain={\uthree}:1.5,samples=100]
+		(\x,{sqrt((\x-\uone)*(\x-\utwo)*(\x-\uthree))}) ;
+\draw[line width=1.4pt,color=red]
+	(\uthree,0) --
+	plot[domain={\uthree}:1.5,samples=100]
+		(\x,{-sqrt((\x-\uone)*(\x-\utwo)*(\x-\uthree))}) ;
+
+\draw[->] (-1.5,0) -- (1.5,0) coordinate[label={$u$}];
+\draw[->] (0,-1.5) -- (0,1.5) coordinate[label={right:$v$}];
+\node at (0,0) [below left] {$O$};
+
+\fill[color=white] (\uone,0) circle[radius=\r];
+\draw (\uone,0) circle[radius=\r];
+\node at ({\uone+0.01},-0.01) [above left] {$u_1$};
+
+\fill[color=white] (\utwo,0) circle[radius=\r];
+\draw (\utwo,0) circle[radius=\r];
+\node at ({\utwo-0.01},-0.01) [above right] {$u_2$};
+
+\fill[color=white] (\uthree,0) circle[radius=\r];
+\draw (\uthree,0) circle[radius=\r];
+\node at ({\uthree+0.01},-0.01) [above left] {$u_3$};
+
+\fill[color=white] (\gone,\yone) circle[radius=\r];
+\draw[color=blue] (\gone,\yone) circle[radius=\r];
+
+\fill[color=white] (\gtwo,\ytwo) circle[radius=\r];
+\draw[color=blue] (\gtwo,\ytwo) circle[radius=\r];
+
+\fill[color=white] (\gthree,\ythree) circle[radius=\r];
+\draw[color=blue] (\gthree,\ythree) circle[radius=\r];
+\fill[color=white] (\gthree,-\ythree) circle[radius=\r];
+\draw[color=blue] (\gthree,-\ythree) circle[radius=\r];
+
+\node[color=blue] at (\gone,{\yone-0.03}) [above left] {$g_1$};
+\node[color=blue] at ({\gtwo+0.03},{\ytwo+0.01}) [above] {$g_2$};
+\node[color=blue] at (\gthree,{\ythree+0.02}) [below right] {$g_3$};
+\node[color=blue] at (\gthree,{-\ythree+0.03}) [below left] {$g_1g_2=g_3^{-1}$};
+
+\end{tikzpicture}
+\end{document}
+