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