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author | Nao Pross <np@0hm.ch> | 2021-04-19 18:02:30 +0200 |
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committer | Nao Pross <np@0hm.ch> | 2021-04-19 18:02:30 +0200 |
commit | 675239e3d44e8d0b2d7bc022c0d0d773c81889c1 (patch) | |
tree | f20ac2db0ae44384a5ee3781466aaec50f7fdee2 /vorlesungen/slides/a/ecc/kurve.tex | |
parent | Fix complex plane animation (diff) | |
parent | Titleseite und Handout. (diff) | |
download | SeminarMatrizen-675239e3d44e8d0b2d7bc022c0d0d773c81889c1.tar.gz SeminarMatrizen-675239e3d44e8d0b2d7bc022c0d0d773c81889c1.zip |
Merge remote-tracking branch 'upstream/master'
Diffstat (limited to '')
-rw-r--r-- | vorlesungen/slides/a/ecc/kurve.tex | 56 |
1 files changed, 56 insertions, 0 deletions
diff --git a/vorlesungen/slides/a/ecc/kurve.tex b/vorlesungen/slides/a/ecc/kurve.tex new file mode 100644 index 0000000..04d15f8 --- /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{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 |