From a5eaa4838f81fe396b428708702bc392189e7484 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Andreas=20M=C3=BCller?= <andreas.mueller@ost.ch>
Date: Sun, 7 Mar 2021 21:15:31 +0100
Subject: Diffie-Hellmann

---
 vorlesungen/slides/4/Makefile.inc |  1 +
 vorlesungen/slides/4/chapter.tex  |  1 +
 vorlesungen/slides/4/dh.tex       | 62 +++++++++++++++++++++++++++++++++++++++
 vorlesungen/slides/test.tex       |  2 +-
 4 files changed, 65 insertions(+), 1 deletion(-)
 create mode 100644 vorlesungen/slides/4/dh.tex

diff --git a/vorlesungen/slides/4/Makefile.inc b/vorlesungen/slides/4/Makefile.inc
index 91767a9..4eae5b0 100644
--- a/vorlesungen/slides/4/Makefile.inc
+++ b/vorlesungen/slides/4/Makefile.inc
@@ -12,5 +12,6 @@ chapter4 =								\
 	../slides/4/fp.tex						\
 	../slides/4/division.tex					\
 	../slides/4/gauss.tex						\
+	../slides/4/dh.tex						\
 	../slides/4/chapter.tex
 
diff --git a/vorlesungen/slides/4/chapter.tex b/vorlesungen/slides/4/chapter.tex
index 27884a1..38e90eb 100644
--- a/vorlesungen/slides/4/chapter.tex
+++ b/vorlesungen/slides/4/chapter.tex
@@ -10,3 +10,4 @@
 \folie{4/fp.tex}
 \folie{4/division.tex}
 \folie{4/gauss.tex}
+\folie{4/dh.tex}
diff --git a/vorlesungen/slides/4/dh.tex b/vorlesungen/slides/4/dh.tex
new file mode 100644
index 0000000..b0a88e5
--- /dev/null
+++ b/vorlesungen/slides/4/dh.tex
@@ -0,0 +1,62 @@
+%
+% dh.tex
+%
+% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+%
+\begin{frame}[t]
+\frametitle{Diffie-Hellmann Schlüsselaushandlung}
+
+\begin{center}
+\definecolor{darkgreen}{rgb}{0,0.6,0}
+\def\skala{0.95}
+\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,-5.0);
+\coordinate (B) at (\l,-2.5);
+\coordinate (D) at (-\l,-5.0);
+\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) {$B$};
+\uncover<2->{
+	\node at (-\l,-1.5) [left] {$a$ auswählen\strut};
+	\node at (-\l,-2.0) [left] {$x=g^a\in\mathbb{F}_p$\strut};
+	\node at (\l,-1.5) [right] {$b$ auswählen\strut};
+	\node at (\l,-2.0) [right] {$y=g^b\in\mathbb{F}_p$\strut};
+}
+\draw[->] (-\l,-1) -- (-\l,-6);
+\draw[->] (\l,-1) -- (\l,-6);
+\uncover<3->{
+	\draw[->] (A) -- (C);
+	\draw[->] (B) -- (D);
+	\fill (A) circle[radius=0.08];
+	\fill (B) circle[radius=0.08];
+	\node at ($0.8*(A)+0.2*(C)+(-0.4,0)$) [above right] {$x=g^a$};
+	\node at ($0.8*(B)+0.2*(D)+(0.4,0)$) [above left] {$y=g^b$};
+}
+\uncover<4->{
+	\node at (-\l,-5.0) [left] {$s=g^{ab}=y^a\in\mathbb{F}_p$};
+	\node at (-\l,-5.5) [left] {ausrechnen};
+	\node at (\l,-5.0) [right] {$s=g^{ab}=x^b\in\mathbb{F}_p$};
+	\node at (\l,-5.5) [right] {ausrechnen};
+}
+\uncover<5->{
+	\fill[rounded corners=0.3cm,color=darkgreen!20]
+		({-\l-1.7},-7) rectangle ({\l+1.7},-6);
+	\draw[rounded corners=0.3cm] ({-\l-1.7},-7) rectangle ({\l+1.7},-6);
+	\node at (0,-6.5) {$A$ und $B$ haben den gemeinsamen Schlüssel $s$};
+}
+\end{tikzpicture}
+
+\end{center}
+
+\end{frame}
diff --git a/vorlesungen/slides/test.tex b/vorlesungen/slides/test.tex
index 07fb6a8..9d1f6ef 100644
--- a/vorlesungen/slides/test.tex
+++ b/vorlesungen/slides/test.tex
@@ -31,7 +31,7 @@
 %\folie{4/fp.tex}
 %\folie{4/division.tex}
 %\folie{4/gauss.tex}
-% XXX \folie{4/dh.tex}
+\folie{4/dh.tex}
 % XXX ? \folie{4/polynomefp.tex}
 % XXX \folie{4/frobenius.tex}
 
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