From 91284841f585ad2e5bf5002ce10ee4f3baa93b95 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Andreas=20M=C3=BCller?= <andreas.mueller@ost.ch>
Date: Thu, 15 Apr 2021 16:43:09 +0200
Subject: add oakley groups

---
 vorlesungen/slides/a/ecc/quadrieren.tex | 59 +++++++++++++++++++++++++++++++++
 1 file changed, 59 insertions(+)
 create mode 100644 vorlesungen/slides/a/ecc/quadrieren.tex

(limited to 'vorlesungen/slides/a/ecc/quadrieren.tex')

diff --git a/vorlesungen/slides/a/ecc/quadrieren.tex b/vorlesungen/slides/a/ecc/quadrieren.tex
new file mode 100644
index 0000000..942c73b
--- /dev/null
+++ b/vorlesungen/slides/a/ecc/quadrieren.tex
@@ -0,0 +1,59 @@
+%
+% quadrieren.tex -- Quadrieren 
+%
+% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+%
+\bgroup
+\begin{frame}[t]
+\setlength{\abovedisplayskip}{5pt}
+\setlength{\belowdisplayskip}{5pt}
+\frametitle{Quadrieren}
+\vspace{-20pt}
+\begin{columns}[t,onlytextwidth]
+\begin{column}{0.40\textwidth}
+\begin{block}{Problem}
+\( g = g_1 = g_2 \)
+$\Rightarrow$
+Tangente
+\\
+\uncover<2->{{\color{red}ohne Analysis!}}
+\end{block}
+\begin{center}
+\includegraphics[width=\textwidth]{../../buch/chapters/90-crypto/images/elliptic.pdf}
+\end{center}
+\end{column}
+\begin{column}{0.56\textwidth}
+\uncover<3->{%
+\begin{block}{Lösung}
+Finde $h\in G$ derart, dass 
+\begin{align*}
+g(t)
+&=
+tg + (1-t)h
+\\
+\uncover<4->{%
+\begin{pmatrix}X(t)\\Y(t)\end{pmatrix}
+&=
+t\begin{pmatrix}x_g\\y_g\end{pmatrix}
++(1-t) \begin{pmatrix}x_h\\y_h\end{pmatrix}
+}
+\end{align*}
+\uncover<5->{eingesetzt
+\[
+p(t)
+=
+Y(t)^2+X(t)Y(t)-X(t)^3-aX(t)-b
+=
+0
+\]}%
+\uncover<6->{%
+Nullstellen $0$ (doppelt) und $1$ hat:}
+\[
+\uncover<7->{p(t) = c(t^3-t)}
+\]
+\uncover<8->{Koeffizientenvergleich: einfachere Gleichungen für $x_h$ und $y_h$}
+\end{block}}
+\end{column}
+\end{columns}
+\end{frame}
+\egroup
-- 
cgit v1.2.1

