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author | Roy Seitz <roy.seitz@ost.ch> | 2021-04-15 17:46:16 +0200 |
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committer | Roy Seitz <roy.seitz@ost.ch> | 2021-04-15 17:46:16 +0200 |
commit | a0efb46dd0415f3131021cc825ae4f6bf7172b12 (patch) | |
tree | 68e0bdbc652f89d765498495b4615c926b45ec85 /vorlesungen/slides/a/ecc/inverse.tex | |
parent | Skalar-zu-Matrix DGL Folie. (diff) | |
parent | add oakley groups (diff) | |
download | SeminarMatrizen-a0efb46dd0415f3131021cc825ae4f6bf7172b12.tar.gz SeminarMatrizen-a0efb46dd0415f3131021cc825ae4f6bf7172b12.zip |
Merge branch 'master' of github.com:AndreasFMueller/SeminarMatrizen
Diffstat (limited to 'vorlesungen/slides/a/ecc/inverse.tex')
-rw-r--r-- | vorlesungen/slides/a/ecc/inverse.tex | 48 |
1 files changed, 48 insertions, 0 deletions
diff --git a/vorlesungen/slides/a/ecc/inverse.tex b/vorlesungen/slides/a/ecc/inverse.tex new file mode 100644 index 0000000..c50f698 --- /dev/null +++ b/vorlesungen/slides/a/ecc/inverse.tex @@ -0,0 +1,48 @@ +% +% inverse.tex -- slide template +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\bgroup +\begin{frame}[t] +\setlength{\abovedisplayskip}{5pt} +\setlength{\belowdisplayskip}{5pt} +\frametitle{Involution/Inverse} +\vspace{-20pt} +\begin{columns}[t,onlytextwidth] +\begin{column}{0.48\textwidth} +\begin{center} +\includegraphics[width=\textwidth]{../../buch/chapters/90-crypto/images/elliptic.pdf} +\end{center} +\end{column} +\begin{column}{0.48\textwidth} +\begin{block}{In speziellen Koordinaten} +\vspace{-12pt} +\[ +v^2 = u^3+Au+B +\] +\uncover<2->{invariant unter $v\mapsto -v$}% +\\ +\uncover<3->{{\color{red}geht nicht in $\mathbb{F}_2$}} +\end{block} +\uncover<4->{% +\begin{block}{Allgemein} +\vspace{-12pt} +\begin{align*} +Y^2+XY &= X^3 + aX+b +\\ +\uncover<5->{% +Y(Y+X) &= X^3 + aX + b} +\end{align*} +\uncover<6->{invariant unter} +\begin{align*} +\uncover<7->{X&\mapsto X,& Y&\mapsto -X-Y} +\\ +\uncover<8->{&&\Rightarrow X+Y&\mapsto -Y} +\end{align*} +\uncover<9->{Spezialfall $\mathbb{F}_2$: $Y\leftrightarrow X+Y$} +\end{block}} +\end{column} +\end{columns} +\end{frame} +\egroup |