From d83ad723f1f7e5fc30f5e0e4f87a77668aac0918 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Andreas=20M=C3=BCller?= <andreas.mueller@ost.ch>
Date: Thu, 15 Apr 2021 12:16:19 +0200
Subject: more ec slides

---
 vorlesungen/slides/a/ecc/kurve.tex | 56 ++++++++++++++++++++++++++++++++++++++
 1 file changed, 56 insertions(+)
 create mode 100644 vorlesungen/slides/a/ecc/kurve.tex

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

diff --git a/vorlesungen/slides/a/ecc/kurve.tex b/vorlesungen/slides/a/ecc/kurve.tex
new file mode 100644
index 0000000..9cf1aa2
--- /dev/null
+++ b/vorlesungen/slides/a/ecc/kurve.tex
@@ -0,0 +1,56 @@
+%
+% kurve.tex -- elliptische Kurven
+%
+% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+%
+\bgroup
+\begin{frame}[t]
+\setlength{\abovedisplayskip}{5pt}
+\setlength{\belowdisplayskip}{5pt}
+\frametitle{Kubische Kurven}
+\vspace{-20pt}
+\begin{columns}[t,onlytextwidth]
+\begin{column}{0.48\textwidth}
+\begin{center}
+\uncover<5->{%
+\includegraphics[width=\textwidth]{../../buch/chapters/90-crypto/images/elliptic.pdf}
+}
+\end{center}
+\end{column}
+\begin{column}{0.48\textwidth}
+\begin{block}{Allgemein}
+mit $a,b\in\Bbbk$
+\[
+Y^2 + XY = X^3 + aX + b
+\]
+\end{block}
+\vspace{-10pt}
+\uncover<2->{%
+\begin{block}{Spezielle Parametrisierung}
+\vspace{-10pt}
+\begin{align*}
+Y^2 + XY + \frac14X^2
+&=
+X^3 + \frac14X^2 + aX + b
+\\
+\uncover<3->{
+(Y+\frac12X)^2
+&=
+X^3 + \frac14X^2 + aX + b
+}\\
+\uncover<4->{
+v^2
+&=
+u^3+Au+B}
+\end{align*}
+\uncover<4->{mit
+\[
+v=Y+{\textstyle\frac12}X,
+\qquad
+u=X+\frac1{12}
+\]}
+\end{block}}
+\end{column}
+\end{columns}
+\end{frame}
+\egroup
-- 
cgit v1.2.1


From 2c498f3b05e5eb9bf438fe1433dd06311f59d3c3 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Andreas=20M=C3=BCller?= <andreas.mueller@ost.ch>
Date: Fri, 16 Apr 2021 13:41:52 +0200
Subject: typos

---
 vorlesungen/slides/a/ecc/kurve.tex | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

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

diff --git a/vorlesungen/slides/a/ecc/kurve.tex b/vorlesungen/slides/a/ecc/kurve.tex
index 9cf1aa2..04d15f8 100644
--- a/vorlesungen/slides/a/ecc/kurve.tex
+++ b/vorlesungen/slides/a/ecc/kurve.tex
@@ -7,7 +7,7 @@
 \begin{frame}[t]
 \setlength{\abovedisplayskip}{5pt}
 \setlength{\belowdisplayskip}{5pt}
-\frametitle{Kubische Kurven}
+\frametitle{Elliptische Kurven}
 \vspace{-20pt}
 \begin{columns}[t,onlytextwidth]
 \begin{column}{0.48\textwidth}
@@ -47,7 +47,7 @@ u^3+Au+B}
 \[
 v=Y+{\textstyle\frac12}X,
 \qquad
-u=X+\frac1{12}
+u=X-\frac1{12}
 \]}
 \end{block}}
 \end{column}
-- 
cgit v1.2.1