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+%
+% kurve.tex -- elliptische Kurven
+%
+% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+%
+\bgroup
+\begin{frame}[t]
+\setlength{\abovedisplayskip}{5pt}
+\setlength{\belowdisplayskip}{5pt}
+\frametitle{Elliptische 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