finished vigenere cryptoanalysis
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presentation.pdf
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presentation.pdf
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presentation.tex
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presentation.tex
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@ -261,31 +261,32 @@ wird zu\\
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\includegraphics[scale=0.3]{images/hobbit-plain-freq.png}
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}
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\end{center}
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\vspace{-0.2cm}
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\begin{tabular}{r|l}
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Ciphertext alphabet & \texttt{ABCDEFGHIJKLMNOPQRSTUVWXYZ} \\ \hline
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\only<2>{Plaintext alphabet &
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Ciphertext Alphabet & \texttt{ABCDEFGHIJKLMNOPQRSTUVWXYZ} \\ \hline
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\only<2>{Plaintext Alphabet &
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\texttt{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ E\ \ \ \ \ \ \ \ }}
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\only<3>{Plaintext alphabet &
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\only<3>{Plaintext Alphabet &
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\texttt{\ \ \ \ \ \ N\ \ \ \ \ \ \ \ \ \ \ E\ \ \ \ \ \ \ \ }}
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\only<4>{Plaintext alphabet &
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\only<4>{Plaintext Alphabet &
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\texttt{\ \ \ \ \ \ N\ \ \ \ \ \ \ \ \ \ \ EI\ \ \ \ \ \ }}
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\only<5>{Plaintext alphabet &
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\only<5>{Plaintext Alphabet &
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\texttt{\ \ \ \ \ MN\ \ \ \ \ \ \ \ \ \ \ EI\ \ \ \ \ \ }}
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\only<6>{Plaintext alphabet &
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\only<6>{Plaintext Alphabet &
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\texttt{\ \ \ \ \ MN\ \ \ \ \ A\ \ \ \ \ EI\ \ \ \ \ \ }}
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\only<7>{Plaintext alphabet &
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\only<7>{Plaintext Alphabet &
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\texttt{\ \ \ \ \ MN\ \ \ \ \ AD\ \ \ UEI\ \ \ \ \ \ }}
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\only<8>{Plaintext alphabet &
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\only<8>{Plaintext Alphabet &
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\texttt{\ \ \ \ \ MN\ \ \ \ \ AD\ S\ UEI\ \ \ \ \ \ }}
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\only<9>{Plaintext alphabet &
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\only<9>{Plaintext Alphabet &
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\texttt{\ \ \ \ \ MN\ \ \ \ \ AD\ S\ UEI\ \ \ \ Z\ }}
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\only<10>{Plaintext alphabet &
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\only<10>{Plaintext Alphabet &
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\texttt{\ \ \ \ \ MN\ \ \ \ \ ADRS\ UEI\ \ \ \ Z\ }}
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\only<11>{Plaintext alphabet &
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\only<11>{Plaintext Alphabet &
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\texttt{H\ \ \ \ MN\ \ \ \ \ ADRSTUEI\ \ \ \ Z\ }}
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\only<12>{Plaintext alphabet &
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\only<12>{Plaintext Alphabet &
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\texttt{HK\ \ \ MNGCO\ \ ADRSTUEI\ \ \ \ Z\ }}
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\only<13>{Plaintext alphabet &
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\only<13>{Plaintext Alphabet &
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\texttt{HKFLBMNGCOP\ ADRSTUEIVW\ \ Z\ }}
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\end{tabular}
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\end{overlayarea}
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@ -317,13 +318,142 @@ $\rightarrow$ Gleiche Buchstaben werden nicht immer gleich verschlüsselt
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\end{center}
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\end{frame}
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\begin{frame}{Vigenère-Chiffre Kryptoanalyse}
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content...
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\begin{frame}{Vigenère Kryptoanalyse: Kasiski test}
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\begin{overlayarea}{\textwidth}{\textheight}
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\begin{footnotesize}
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\begin{itemize}
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\item Schwachstelle der Vigenère-Chiffre: wiederholender Schlüssel
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\item<2-> Angenommen wir kennen die Schlüssellänge $K$:
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\begin{itemize}
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\item<3-> Text in $K$ Blöcke aufteilen (Beispiel: $K=3$)
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\only<3>{
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\texttt{PPKAMJELQHPIAHLWYPKDDNBGPMJELQHPIAHZWUYJH...}
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}
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\only<4->{
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\texttt{
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\textcolor{red}{P}\textcolor{blue}{P}\textcolor{darkgreen}{K}\textcolor{red}{A}\textcolor{blue}{M}\textcolor{darkgreen}{J}\textcolor{red}{E}\textcolor{blue}{L}\textcolor{darkgreen}{Q}\textcolor{red}{H}\textcolor{blue}{P}\textcolor{darkgreen}{I}\textcolor{red}{A}\textcolor{blue}{H}\textcolor{darkgreen}{L}\textcolor{red}{W}\textcolor{blue}{Y}\textcolor{darkgreen}{P}\textcolor{red}{K}\textcolor{blue}{D}\textcolor{darkgreen}{D}\textcolor{red}{N}\textcolor{blue}{B}\textcolor{darkgreen}{G}\textcolor{red}{P}\textcolor{blue}{M}\textcolor{darkgreen}{J}\textcolor{red}{E}\textcolor{blue}{L}\textcolor{darkgreen}{Q}\textcolor{red}{H}\textcolor{blue}{P}\textcolor{darkgreen}{I}\textcolor{red}{A}\textcolor{blue}{H}\textcolor{darkgreen}{Z}\textcolor{red}{W}\textcolor{blue}{U}\textcolor{darkgreen}{Y}\textcolor{red}{J}\textcolor{blue}{H}...
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}
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}
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\item<5-> Auf jedem Block eigene Häufigkeitsanalyse:
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\only<5->{
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\begin{tabular}{c|c|c}
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\texttt{\textcolor{red}{PAEHAWKNPEHAWJ}} & \texttt{\textcolor{blue}{PMLPHYDBMLPHUH}} & \texttt{\textcolor{darkgreen}{KJQILPDGJQIZY}}
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\end{tabular}
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}
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\end{itemize}
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\item<6-> Problem: Wie findet man die Schlüssellänge?\\
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\only<7->{\textbf{Kasiski Test:}\\
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\only<7>{
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\texttt{PPKAMJELQHPIAHLWYPKDDNBGPMJELQHPIAHZWUYJH...}
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}
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\only<8->{
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\texttt{PPKA\textcolor{red}{MJELQHPIAH}LWYPKDDNBGP\textcolor{red}{MJELQHPIAH}ZWUYJH...}\\
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}
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\onslide<9->{
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\hspace{0.9cm}index = $4$ \hspace{2.4cm} index = $25$
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}
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\begin{itemize}
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\item<7-> Suche nach wiederholenden Buchstabengruppen ($N$-Gramme)
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\item<9-> Bestimme Abstand zwischen den Wiederholungen \\
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(hier: $d = 25 - 4 = 21$)
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\item<10-> Schlüssellänge Teiler des Abstands:
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$d = 3 \cdot 7$ $\rightarrow$ $K=3$ oder $7$
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\end{itemize}
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}
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\item<11->Grund: Gleiche Wörter (oder Teile davon) manchmal gleich verschlüsselt
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\begin{tabular}{rl}
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Klartext&\texttt{TIME\textcolor{blue}{FLIESLIKEA}NARROWFRUIT\textcolor{red}{FLIESLIKEA}BANANA}\\
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Schlüssel&\texttt{WHYWHYWHYWHYWHYWHYWHYWHYWHYWHYWHYWHYWHYWH}\\
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Geheimtext&\texttt{PPKA\textcolor{blue}{MJELQHPIAH}LWYPKDDNBGP\textcolor{red}{MJELQHPIAH}ZWUYJH...}
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\end{tabular}
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\end{itemize}
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\end{footnotesize}
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\end{overlayarea}
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\end{frame}
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\begin{frame}{Kasiski test}
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content...
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\begin{frame}{Vigenère Kryptoanalyse: Friedman Test}
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\begin{overlayarea}{\textwidth}{\textheight}
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\begin{itemize}
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\item Statistischer Test zur Bestimmung der Schlüssellänge:
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\begin{tabular}{c|l}
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$\kappa_p$ & Wahrscheinlichkeit, dass zwei zufällig gewählte Buchstaben \\
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& eines Textes gleich sind \\
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\hline
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$\kappa_r$ & Wahrscheinlichkeit, dass zwei Buchstaben eines zufälligen\\ & gleichverteilten Textes übereinstimmen
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\end{tabular}
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\item Im Englischen (monocase, 26 Buchstaben)):
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\begin{equation*}
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\kappa_p = 0.067 \hspace{1cm} \kappa_r = \frac{1}{26} = 0.0385
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\end{equation*}
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\item Abschätzung der Schlüssellänge:
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\begin{equation*}
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K \approx \frac{\kappa_p - \kappa_r}{\kappa_o - \kappa_r}
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\end{equation*}
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mit der beobachteten Koinzidenzrate
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\begin{equation*}
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\kappa_o = \frac{\sum_{i=1}^{26} n_i(n_i - 1)}{N (N-1)}
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\end{equation*}
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\begin{tabular}{c|l}
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$N$ & Länge des Texts\\
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\hline
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$n_i$ & Vorkommen des Buchstabens im Text
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\end{tabular}
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\end{itemize}
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\end{overlayarea}
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\end{frame}
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\begin{frame}{Friedman Test: Anwendung}
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\begin{tiny}
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\hspace{-0.8cm}
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\begin{minipage}[t][3cm]{\textwidth}
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\only<1>{
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\input{vigenere/friedman_0.tex}
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}
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\only<2-4>{
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\input{vigenere/friedman_4.tex}
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}
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\only<5->{
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\input{vigenere/friedman_5.tex}
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}
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\end{minipage}
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\only<3-4>{
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\begin{minipage}[b][1.4cm]{0.22\textwidth}
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\input{vigenere/friedman_4_red.tex}\\
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\end{minipage}
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\begin{minipage}[b][0cm]{0.22\textwidth}
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\input{vigenere/friedman_4_blue.tex}\\
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\end{minipage}
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\begin{minipage}[b][0cm]{0.22\textwidth}
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\input{vigenere/friedman_4_darkgreen.tex}\\
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\end{minipage}
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\begin{minipage}[b][0cm]{0.22\textwidth}
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\input{vigenere/friedman_4_orange.tex}\\
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\end{minipage}
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}
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\only<5->{
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\begin{minipage}[b][1.6cm]{0.18\textwidth}
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\input{vigenere/friedman_5_red.tex}\\
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\end{minipage}
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\begin{minipage}[b][0cm]{0.18\textwidth}
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\input{vigenere/friedman_5_blue.tex}\\
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\end{minipage}
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\begin{minipage}[b][0cm]{0.18\textwidth}
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\input{vigenere/friedman_5_darkgreen.tex}\\
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\end{minipage}
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\begin{minipage}[b][0cm]{0.18\textwidth}
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\input{vigenere/friedman_5_orange.tex}\\
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\end{minipage}
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\begin{minipage}[b][0cm]{0.18\textwidth}
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\input{vigenere/friedman_5_black.tex}\\
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\end{minipage}
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}
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\end{tiny}
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\begin{itemize}
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\item<1-> Rateversuch: Schlüssellänge \only<1-4>{$K = 4$}\only<5->{$K = 5$}
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\item<2-> Teile Text in \only<1-4>{$4$}\only<5->{$5$} Blöcke auf
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\item<3-> Bestimme Koinzidenzindex für jeden Block \\
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\onslide<4->{Erinnerung: $$\kappa_p = 0.067 \text{ (englisch)}, \;\;\;\kappa_r = 0.0385 \text{ (zufällig)}$$}
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\end{itemize}
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\end{frame}
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\begin{frame}
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