100 lines
2.9 KiB
TeX
100 lines
2.9 KiB
TeX
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\documentclass[12pt,a4paper,german]{article}
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\usepackage{url}
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%\usepackage{graphics}
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\usepackage{times}
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\usepackage[T1]{fontenc}
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\usepackage{ngerman}
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\usepackage[latin1]{inputenc}
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\usepackage{geometry}
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\usepackage{amsfonts}
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\usepackage{amsmath}
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\usepackage{graphicx}
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\usepackage{epsfig}
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\usepackage{paralist}
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\geometry{left=2.0cm,textwidth=17cm,top=3.5cm,textheight=23cm}
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%%%%%%%%%% Fill out the the definitions %%%%%%%%%
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\def \name {Valentin Brandl} %
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\def \matrikel {108018274494} %
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\def \gruppe {VB} %
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\def \uebung {1} %
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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% DO NOT MODIFY THIS HEADER
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\newcommand{\hwsol}{
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\vspace*{-2cm}
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\noindent \matrikel \quad \name \hfill Gruppe:\gruppe \\
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% \noindent \pmatrikel \quad \pname \\
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\begin{center}{\Large \bf L\"osung f\"ur \"Ubung \# \uebung}\end{center}
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}
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\begin{document}
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%Import header
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\hwsol
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\section*{Aufgabe 1}
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\begin{enumerate}[(a)]
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\item
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\begin{itemize}
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\item Algorithmen sollen offengelegt werden, nur Schl<68>ssel werden geheim gehalten
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\item Es ist schwer, einen Algorithmus geheim zu halten
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\item Prinzip def vielen Augen: ein <20>ffentlicher Algorithmus wird ggf. analysiert und Schwachstellen gefunden
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\end{itemize}
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\item
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\begin{itemize}
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\item Kryptographie: Entwerfen von Algorithmen und Protokollen
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\item Kryptoanalyse: Schwachstellen in existierenden Verfahren suchen
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\end{itemize}
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\item
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\parbox{\linewidth}{\centering
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\includegraphics[width=\textwidth]{20181011_situation.png}
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}
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Ein Angreifer (Eve) kann die ausgetauschten Nachrichten mitlesen und ver<65>ndern
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\item
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\begin{itemize}
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\item Schl<68>ssel: $k$
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\item Verschl<68>sselung $e(\cdot)$
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\item Schl<68>sselraum $\#k = \vert k \vert$
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\item Chiffrat $y$
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\item Entschl<68>sselung $d(\cdot)$
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\item Klartext $x$
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\end{itemize}
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\end{enumerate}
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\section*{Aufgabe 2}
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\begin{enumerate}[(a)]
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\item $2^{128}$. Mit $2^{10} \approx 10^3 \to 2^{130} \approx 10^{39}$
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\item
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\begin{itemize}
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\item 80 Eur pro ASIC
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\item $10^6$ Eur Kapital
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\item $7 \cdot 10^8 \frac{k}{s}$ Leistung
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\end{itemize}
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\begin{eqnarray*}
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10^6 / 80 &=& 12500 \\
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7 \cdot 10^8 \cdot 12500 &=& 8.75 \cdot 10^{12} \frac{k}{s} \\
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\frac{2^{128}k}{8.75 \cdot 10^{12} \frac{k}{s}} &\approx{}& 3.89 \cdot 10^{25} s \\
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&\approx{}& 1.23 \cdot 10^{18} y
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\end{eqnarray*}
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\item
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\begin{eqnarray*}
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24 h &=& 86400 s \\
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\frac{2^{128}}{x} &=& 86400 \\
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\frac{2^{128}}{86400} &=& x \\
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x &\approx{}& 3.94 \cdot 10^{33} \text{ gesuchte $\frac{k}{s}$} \\
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\frac{x}{12500} &\approx{}& 3.15 \cdot 10^{29} \text{ gesuchte $\frac{k}{s}$ pro ASIC} \\
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\\
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(7 \cdot 10^8) \cdot 2^n &\geq{}& 3.15 \cdot 10^{29} \\
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n &\geq{}& 68.6 \approx 69 \text{ (Leistung muss sich 69 mal verdoppeln)} \\
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69 * 18m &=& 1242m = 103.5 y
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\end{eqnarray*}
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In $103.5$ Jahren w<>re man in der Lage alle $2^{128}$ Schl<68>ssel innerhlab von 24h durch zu probieren.
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\end{enumerate}
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\end{document}
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