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author | Andreas Müller <andreas.mueller@ost.ch> | 2021-06-14 07:26:10 +0200 |
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committer | GitHub <noreply@github.com> | 2021-06-14 07:26:10 +0200 |
commit | 114633b43a0f1ebedbc5dfd85f75ede9841f26fd (patch) | |
tree | 18e61c7d69883a1c9b69098b7d36856abaed5c1e /vorlesungen/slides/a/ecc/oakley.tex | |
parent | Delete buch.pdf (diff) | |
parent | Fix references.bib (diff) | |
download | SeminarMatrizen-114633b43a0f1ebedbc5dfd85f75ede9841f26fd.tar.gz SeminarMatrizen-114633b43a0f1ebedbc5dfd85f75ede9841f26fd.zip |
Merge branch 'master' into master
Diffstat (limited to 'vorlesungen/slides/a/ecc/oakley.tex')
-rw-r--r-- | vorlesungen/slides/a/ecc/oakley.tex | 85 |
1 files changed, 85 insertions, 0 deletions
diff --git a/vorlesungen/slides/a/ecc/oakley.tex b/vorlesungen/slides/a/ecc/oakley.tex new file mode 100644 index 0000000..6980c10 --- /dev/null +++ b/vorlesungen/slides/a/ecc/oakley.tex @@ -0,0 +1,85 @@ +% +% oakley.tex -- Oakley Gruppen +% +% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +% +\bgroup +\begin{frame}[t] +\setlength{\abovedisplayskip}{5pt} +\setlength{\belowdisplayskip}{5pt} +\frametitle{Oakley-Gruppen} +\only<1>{% +\small +\verbatiminput{../slides/a/ecc/oakley1.txt} +$\approx 1.55252\cdot 10^{231}$ +} +\only<2>{% +\begin{block}{$\mathbb{F}_p$} +Endlicher Körper mit $p = $ +\verbatiminput{../slides/a/ecc/prime1.txt} +\end{block} +} +\only<3>{% +\small +\verbatiminput{../slides/a/ecc/oakley2.txt} +} +\only<4>{% +\begin{block}{$\mathbb{F}_p$} +Endlicher Körper mit $p = $ +\verbatiminput{../slides/a/ecc/prime2.txt} +$\approx 1.7977\cdot 10^{308}$ +\end{block} +} +\only<5>{% +\small +\verbatiminput{../slides/a/ecc/oakley3.txt} +} +\only<6>{% +\begin{block}{Oakley Gruppe 3} +\begin{align*} +m(x) &= x^{155} + x^{62} + 1 +\\ +a &= 0 +\\ +b &= \texttt{0x07338f} +\\ +g_x &= 0x7b = x^6 + x^5 + x^4 + x^3 + x + 1 +\\ +&= +x^{18}+x^{17}+x^{16} ++ +x^{13}+x^{12} ++ +x^{9}+x^{8}+x^{7} ++ +x^{3}+x^{1}+x^{1}+1 +\\ +|G|&=45671926166590716193865565914344635196769237316 = 4.5672\cdot 10^{46} +\\ +\log_2|G|&=155\,\text{bit} +\end{align*} +\end{block}} +\only<7>{% +\small +\verbatiminput{../slides/a/ecc/oakley4.txt} +} +\only<8>{% +\begin{block}{Oakley Gruppe 4} +\begin{align*} +m(x) &= x^{185} + x^{69} + 1 +\\ +a &= 0 +\\ +b &= \texttt{0x1ee9} = x^{12} + x^{11}+x^{10}+x^9 + x^7+x^6+x^5 + x^3+1 +\\ +g_x &= \texttt{0x18} = x^4+x^3 +\\ +|G| &= 49039857307708443467467104857652682248052385001045053116 +\\ +&= 4.9040\cdot 10^{55} +\\ +\log_2|G| &= 185 +\end{align*} +\end{block}} +\end{frame} +\egroup |