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\title[Code-Break-Party]{Code-Break-Party}
\author{Simon Pirkelmann}
\institute{\includegraphics[scale=0.5]{images/iR.pdf}}
\date{January 27th, 2020}


\AfterPreamble{\hypersetup{
  urlcolor=blue,
}}

\begin{document}

\begin{frame}
  \titlepage
\end{frame}

% Uncomment these lines for an automatically generated outline.
\begin{frame}{Outline}
  \tableofcontents
\end{frame}

\section{Substitutions-Chiffren}
\subsection{Cäsar Chiffre}
\begin{frame}{Cäsar Chiffre}
\begin{itemize}
\item Klartext (plain text): \texttt{ATTACKATDAWN}
\item Geheimtext (cipher text): \texttt{DWWDFNDWGDZQ}
\item Schlüssel: \texttt{3} $\rightarrow$ um \texttt{3} Stellen nach rechts verschieben
\end{itemize}
\includegraphics[scale=0.5]{images/caesar.jpg}
\end{frame}

\begin{frame}{Cäsar Kryptoanalyse}
\begin{itemize}
	\item Es gibt nur eine begrenzte Anzahl von Schlüsseln (nur \texttt{25} sinnvolle Verschiebungen)
	\item Brute-Force-Angriff $\rightarrow$ alle Kombinationen durchprobieren:\\[0.5cm]
	\begin{tabular}{c|c}
		Schlüssel & Entschlüsselter Text \\
		\hline
		0 & \texttt{DWWDFNDWGDZQ} \\
		1 & \texttt{CVVCEMCVFCYP} \\
		2 & \texttt{BUUBDLBUEBXO} \\
		3 & \texttt{\textcolor{darkgreen}{ATTACKATDAWN}} \\
		$\vdots$ & $\vdots$
	\end{tabular}
\end{itemize}
\end{frame}

\subsection{Monoalphabetische Substitution}
\begin{frame}{Monoalphabetische Substitution (Kryptogram)}
\begin{itemize}
	\item Anstelle für jeden Buchstaben den gleichen Offset zu verwenden, werden unterschiedliche Buchstaben verschieden verschoben
	\item Substitutionstabelle:
	\begin{tabular}{r|c}
Klartext Alphabet & \texttt{ABCDEFGHIJKLMNOPQRSTUVWXYZ} \\ \hline
 Geheimtext Alphabet & \texttt{MOSKAUBCDEFGHIJLNPQRTVWXYZ}
	\end{tabular}
\item Beispiel:\\
\begin{center}
	\texttt{FLEE AT ONCE. WE ARE DISCOVERED.} \\
\end{center}
wird zu\\
\begin{center}
	\texttt{UGAA MR JISA. WA MPA KDQSJVAPAK.}
\end{center}
\end{itemize}
\end{frame}

\begin{frame}{Frequenzanalyse}
\begin{itemize}
\item Buchstaben kommen in natürlicher Sprache mit unterschiedlicher Häufigkeit vor
\item Im Deutschen: \texttt{E, I, N} sind häufig, \texttt{Q, X, Y} sind selten
\end{itemize}
\begin{center}
	\includegraphics[scale=0.3]{images/frequency.jpg}
\end{center}
\begin{itemize}
\item Statistische Eigenschaften des Klartexts werden von einer Substitutionschiffre nicht verändert
\end{itemize}
\end{frame}

\begin{frame}{Beispiel Frequenzanalyse}
	\begin{overlayarea}{\textwidth}{\textheight}
\only<1>{
\texttt{Tg stgsf Djia tf Ejnsg, nm dseqs stg Ajeetq. Gtiaq tg stgsf csriaqsg, piafrqythsg Djia, vj sp gmia Fjnso otsiaq rgn Vrofytkcsd ujg nsg Vmsgnsg asomeamsghsg, rgn mria gtiaq tg stgso qojibsgsg, bmadsg Pmgnhores jags Qtpias rgn Pqrsads, vj fmg ptia yrf Sppsg atgpsqysg bjsggqs: gstg, nmp Djia vmo stgs Ajeetqajsads, rgn nmp astppq, sp vmo psao bjfcjoqmesd.}
}
\only<2>{
\texttt{Tg \textcolor{darkgreen}{e}tg\textcolor{darkgreen}{e}f Djia tf Ejn\textcolor{darkgreen}{e}g, nm d\textcolor{darkgreen}{e}eq\textcolor{darkgreen}{e} \textcolor{darkgreen}{e}tg Ajeetq. Gtiaq tg \textcolor{darkgreen}{e}tg\textcolor{darkgreen}{e}f c\textcolor{darkgreen}{e}riaq\textcolor{darkgreen}{e}g, piafrqyth\textcolor{darkgreen}{e}g Djia, vj \textcolor{darkgreen}{e}p gmia Fjn\textcolor{darkgreen}{e}o ot\textcolor{darkgreen}{e}iaq rgn Vrofytkc\textcolor{darkgreen}{e}d ujg n\textcolor{darkgreen}{e}g Vm\textcolor{darkgreen}{e}gn\textcolor{darkgreen}{e}g a\textcolor{darkgreen}{e}omeam\textcolor{darkgreen}{e}gh\textcolor{darkgreen}{e}g, rgn mria gtiaq tg \textcolor{darkgreen}{e}tg\textcolor{darkgreen}{e}o qojib\textcolor{darkgreen}{e}g\textcolor{darkgreen}{e}g, bmad\textcolor{darkgreen}{e}g Pmgnhore\textcolor{darkgreen}{e} jag\textcolor{darkgreen}{e} Qtpia\textcolor{darkgreen}{e} rgn Pqr\textcolor{darkgreen}{e}ad\textcolor{darkgreen}{e}, vj fmg ptia yrf \textcolor{darkgreen}{E}pp\textcolor{darkgreen}{e}g atgp\textcolor{darkgreen}{e}qy\textcolor{darkgreen}{e}g bj\textcolor{darkgreen}{e}ggq\textcolor{darkgreen}{e}: g\textcolor{darkgreen}{e}tg, nmp Djia vmo \textcolor{darkgreen}{e}tg\textcolor{darkgreen}{e} Ajeetqaj\textcolor{darkgreen}{e}ad\textcolor{darkgreen}{e}, rgn nmp a\textcolor{darkgreen}{e}tppq, \textcolor{darkgreen}{e}p vmo p\textcolor{darkgreen}{e}ao bjfcjoqme\textcolor{darkgreen}{e}d.}
}
\only<3>{
	\texttt{T\textcolor{darkgreen}{n} \textcolor{darkgreen}{e}t\textcolor{darkgreen}{n}\textcolor{darkgreen}{e}f Djia tf Ejn\textcolor{darkgreen}{e}\textcolor{darkgreen}{n}, nm d\textcolor{darkgreen}{e}eq\textcolor{darkgreen}{e} \textcolor{darkgreen}{e}t\textcolor{darkgreen}{n} Ajeetq. \textcolor{darkgreen}{N}tiaq t\textcolor{darkgreen}{n} \textcolor{darkgreen}{e}t\textcolor{darkgreen}{n}\textcolor{darkgreen}{e}f c\textcolor{darkgreen}{e}riaq\textcolor{darkgreen}{e}\textcolor{darkgreen}{n}, piafrqyth\textcolor{darkgreen}{e}\textcolor{darkgreen}{n} Djia, vj \textcolor{darkgreen}{e}p \textcolor{darkgreen}{n}mia Fjn\textcolor{darkgreen}{e}o ot\textcolor{darkgreen}{e}iaq r\textcolor{darkgreen}{n}n Vrofytkc\textcolor{darkgreen}{e}d uj\textcolor{darkgreen}{n} n\textcolor{darkgreen}{e}\textcolor{darkgreen}{n} Vm\textcolor{darkgreen}{e}\textcolor{darkgreen}{n}n\textcolor{darkgreen}{e}\textcolor{darkgreen}{n} a\textcolor{darkgreen}{e}omeam\textcolor{darkgreen}{e}\textcolor{darkgreen}{n}h\textcolor{darkgreen}{e}\textcolor{darkgreen}{n}, r\textcolor{darkgreen}{n}n mria \textcolor{darkgreen}{n}tiaq t\textcolor{darkgreen}{n} \textcolor{darkgreen}{e}t\textcolor{darkgreen}{n}\textcolor{darkgreen}{e}o qojib\textcolor{darkgreen}{e}\textcolor{darkgreen}{n}\textcolor{darkgreen}{e}\textcolor{darkgreen}{n}, bmad\textcolor{darkgreen}{e}\textcolor{darkgreen}{n} Pm\textcolor{darkgreen}{n}nhore\textcolor{darkgreen}{e} ja\textcolor{darkgreen}{n}\textcolor{darkgreen}{e} Qtpia\textcolor{darkgreen}{e} r\textcolor{darkgreen}{n}n Pqr\textcolor{darkgreen}{e}ad\textcolor{darkgreen}{e}, vj fm\textcolor{darkgreen}{n} ptia yrf \textcolor{darkgreen}{E}pp\textcolor{darkgreen}{e}\textcolor{darkgreen}{n} at\textcolor{darkgreen}{n}p\textcolor{darkgreen}{e}qy\textcolor{darkgreen}{e}\textcolor{darkgreen}{n} bj\textcolor{darkgreen}{e}\textcolor{darkgreen}{n}\textcolor{darkgreen}{n}q\textcolor{darkgreen}{e}: \textcolor{darkgreen}{n}\textcolor{darkgreen}{e}t\textcolor{darkgreen}{n}, nmp Djia vmo \textcolor{darkgreen}{e}t\textcolor{darkgreen}{n}\textcolor{darkgreen}{e} Ajeetqaj\textcolor{darkgreen}{e}ad\textcolor{darkgreen}{e}, r\textcolor{darkgreen}{n}n nmp a\textcolor{darkgreen}{e}tppq, \textcolor{darkgreen}{e}p vmo p\textcolor{darkgreen}{e}ao bjfcjoqme\textcolor{darkgreen}{e}d.}
}
\only<4>{
		\texttt{\textcolor{darkgreen}{I}\textcolor{darkgreen}{n} \textcolor{darkgreen}{e}\textcolor{darkgreen}{i}\textcolor{darkgreen}{n}\textcolor{darkgreen}{e}f Djia \textcolor{darkgreen}{i}f Ejn\textcolor{darkgreen}{e}\textcolor{darkgreen}{n}, nm d\textcolor{darkgreen}{e}eq\textcolor{darkgreen}{e} \textcolor{darkgreen}{e}\textcolor{darkgreen}{i}\textcolor{darkgreen}{n} Ajee\textcolor{darkgreen}{i}q. \textcolor{darkgreen}{N}\textcolor{darkgreen}{i}iaq \textcolor{darkgreen}{i}\textcolor{darkgreen}{n} \textcolor{darkgreen}{e}\textcolor{darkgreen}{i}\textcolor{darkgreen}{n}\textcolor{darkgreen}{e}f c\textcolor{darkgreen}{e}riaq\textcolor{darkgreen}{e}\textcolor{darkgreen}{n}, piafrqy\textcolor{darkgreen}{i}h\textcolor{darkgreen}{e}\textcolor{darkgreen}{n} Djia, vj \textcolor{darkgreen}{e}p \textcolor{darkgreen}{n}mia Fjn\textcolor{darkgreen}{e}o o\textcolor{darkgreen}{i}\textcolor{darkgreen}{e}iaq r\textcolor{darkgreen}{n}n Vrofy\textcolor{darkgreen}{i}kc\textcolor{darkgreen}{e}d uj\textcolor{darkgreen}{n} n\textcolor{darkgreen}{e}\textcolor{darkgreen}{n} Vm\textcolor{darkgreen}{e}\textcolor{darkgreen}{n}n\textcolor{darkgreen}{e}\textcolor{darkgreen}{n} a\textcolor{darkgreen}{e}omeam\textcolor{darkgreen}{e}\textcolor{darkgreen}{n}h\textcolor{darkgreen}{e}\textcolor{darkgreen}{n}, r\textcolor{darkgreen}{n}n mria \textcolor{darkgreen}{n}\textcolor{darkgreen}{i}iaq \textcolor{darkgreen}{i}\textcolor{darkgreen}{n} \textcolor{darkgreen}{e}\textcolor{darkgreen}{i}\textcolor{darkgreen}{n}\textcolor{darkgreen}{e}o qojib\textcolor{darkgreen}{e}\textcolor{darkgreen}{n}\textcolor{darkgreen}{e}\textcolor{darkgreen}{n}, bmad\textcolor{darkgreen}{e}\textcolor{darkgreen}{n} Pm\textcolor{darkgreen}{n}nhore\textcolor{darkgreen}{e} ja\textcolor{darkgreen}{n}\textcolor{darkgreen}{e} Q\textcolor{darkgreen}{i}pia\textcolor{darkgreen}{e} r\textcolor{darkgreen}{n}n Pqr\textcolor{darkgreen}{e}ad\textcolor{darkgreen}{e}, vj fm\textcolor{darkgreen}{n} p\textcolor{darkgreen}{i}ia yrf \textcolor{darkgreen}{E}pp\textcolor{darkgreen}{e}\textcolor{darkgreen}{n} a\textcolor{darkgreen}{i}\textcolor{darkgreen}{n}p\textcolor{darkgreen}{e}qy\textcolor{darkgreen}{e}\textcolor{darkgreen}{n} bj\textcolor{darkgreen}{e}\textcolor{darkgreen}{n}\textcolor{darkgreen}{n}q\textcolor{darkgreen}{e}: \textcolor{darkgreen}{n}\textcolor{darkgreen}{e}\textcolor{darkgreen}{i}\textcolor{darkgreen}{n}, nmp Djia vmo \textcolor{darkgreen}{e}\textcolor{darkgreen}{i}\textcolor{darkgreen}{n}\textcolor{darkgreen}{e} Ajee\textcolor{darkgreen}{i}qaj\textcolor{darkgreen}{e}ad\textcolor{darkgreen}{e}, r\textcolor{darkgreen}{n}n nmp a\textcolor{darkgreen}{e}\textcolor{darkgreen}{i}ppq, \textcolor{darkgreen}{e}p vmo p\textcolor{darkgreen}{e}ao bjfcjoqme\textcolor{darkgreen}{e}d.}
}
\only<5>{
	\texttt{\textcolor{darkgreen}{I}\textcolor{darkgreen}{n} \textcolor{darkgreen}{e}\textcolor{darkgreen}{i}\textcolor{darkgreen}{n}\textcolor{darkgreen}{e}\textcolor{darkgreen}{m} Djia \textcolor{darkgreen}{i}\textcolor{darkgreen}{m} Ejn\textcolor{darkgreen}{e}\textcolor{darkgreen}{n}, nm d\textcolor{darkgreen}{e}eq\textcolor{darkgreen}{e} \textcolor{darkgreen}{e}\textcolor{darkgreen}{i}\textcolor{darkgreen}{n} Ajee\textcolor{darkgreen}{i}q. \textcolor{darkgreen}{N}\textcolor{darkgreen}{i}iaq \textcolor{darkgreen}{i}\textcolor{darkgreen}{n} \textcolor{darkgreen}{e}\textcolor{darkgreen}{i}\textcolor{darkgreen}{n}\textcolor{darkgreen}{e}\textcolor{darkgreen}{m} c\textcolor{darkgreen}{e}riaq\textcolor{darkgreen}{e}\textcolor{darkgreen}{n}, pia\textcolor{darkgreen}{m}rqy\textcolor{darkgreen}{i}h\textcolor{darkgreen}{e}\textcolor{darkgreen}{n} Djia, vj \textcolor{darkgreen}{e}p \textcolor{darkgreen}{n}mia \textcolor{darkgreen}{M}jn\textcolor{darkgreen}{e}o o\textcolor{darkgreen}{i}\textcolor{darkgreen}{e}iaq r\textcolor{darkgreen}{n}n Vro\textcolor{darkgreen}{m}y\textcolor{darkgreen}{i}kc\textcolor{darkgreen}{e}d uj\textcolor{darkgreen}{n} n\textcolor{darkgreen}{e}\textcolor{darkgreen}{n} Vm\textcolor{darkgreen}{e}\textcolor{darkgreen}{n}n\textcolor{darkgreen}{e}\textcolor{darkgreen}{n} a\textcolor{darkgreen}{e}omeam\textcolor{darkgreen}{e}\textcolor{darkgreen}{n}h\textcolor{darkgreen}{e}\textcolor{darkgreen}{n}, r\textcolor{darkgreen}{n}n mria \textcolor{darkgreen}{n}\textcolor{darkgreen}{i}iaq \textcolor{darkgreen}{i}\textcolor{darkgreen}{n} \textcolor{darkgreen}{e}\textcolor{darkgreen}{i}\textcolor{darkgreen}{n}\textcolor{darkgreen}{e}o qojib\textcolor{darkgreen}{e}\textcolor{darkgreen}{n}\textcolor{darkgreen}{e}\textcolor{darkgreen}{n}, bmad\textcolor{darkgreen}{e}\textcolor{darkgreen}{n} Pm\textcolor{darkgreen}{n}nhore\textcolor{darkgreen}{e} ja\textcolor{darkgreen}{n}\textcolor{darkgreen}{e} Q\textcolor{darkgreen}{i}pia\textcolor{darkgreen}{e} r\textcolor{darkgreen}{n}n Pqr\textcolor{darkgreen}{e}ad\textcolor{darkgreen}{e}, vj \textcolor{darkgreen}{m}m\textcolor{darkgreen}{n} p\textcolor{darkgreen}{i}ia yr\textcolor{darkgreen}{m} \textcolor{darkgreen}{E}pp\textcolor{darkgreen}{e}\textcolor{darkgreen}{n} a\textcolor{darkgreen}{i}\textcolor{darkgreen}{n}p\textcolor{darkgreen}{e}qy\textcolor{darkgreen}{e}\textcolor{darkgreen}{n} bj\textcolor{darkgreen}{e}\textcolor{darkgreen}{n}\textcolor{darkgreen}{n}q\textcolor{darkgreen}{e}: \textcolor{darkgreen}{n}\textcolor{darkgreen}{e}\textcolor{darkgreen}{i}\textcolor{darkgreen}{n}, nmp Djia vmo \textcolor{darkgreen}{e}\textcolor{darkgreen}{i}\textcolor{darkgreen}{n}\textcolor{darkgreen}{e} Ajee\textcolor{darkgreen}{i}qaj\textcolor{darkgreen}{e}ad\textcolor{darkgreen}{e}, r\textcolor{darkgreen}{n}n nmp a\textcolor{darkgreen}{e}\textcolor{darkgreen}{i}ppq, \textcolor{darkgreen}{e}p vmo p\textcolor{darkgreen}{e}ao bj\textcolor{darkgreen}{m}cjoqme\textcolor{darkgreen}{e}d.}
}
\only<6>{
	\texttt{\textcolor{darkgreen}{I}\textcolor{darkgreen}{n} \textcolor{darkgreen}{e}\textcolor{darkgreen}{i}\textcolor{darkgreen}{n}\textcolor{darkgreen}{e}\textcolor{darkgreen}{m} Djia \textcolor{darkgreen}{i}\textcolor{darkgreen}{m} Ejn\textcolor{darkgreen}{e}\textcolor{darkgreen}{n}, n\textcolor{darkgreen}{a} d\textcolor{darkgreen}{e}eq\textcolor{darkgreen}{e} \textcolor{darkgreen}{e}\textcolor{darkgreen}{i}\textcolor{darkgreen}{n} Ajee\textcolor{darkgreen}{i}q. \textcolor{darkgreen}{N}\textcolor{darkgreen}{i}iaq \textcolor{darkgreen}{i}\textcolor{darkgreen}{n} \textcolor{darkgreen}{e}\textcolor{darkgreen}{i}\textcolor{darkgreen}{n}\textcolor{darkgreen}{e}\textcolor{darkgreen}{m} c\textcolor{darkgreen}{e}riaq\textcolor{darkgreen}{e}\textcolor{darkgreen}{n}, pia\textcolor{darkgreen}{m}rqy\textcolor{darkgreen}{i}h\textcolor{darkgreen}{e}\textcolor{darkgreen}{n} Djia, vj \textcolor{darkgreen}{e}p \textcolor{darkgreen}{n}\textcolor{darkgreen}{a}ia \textcolor{darkgreen}{M}jn\textcolor{darkgreen}{e}o o\textcolor{darkgreen}{i}\textcolor{darkgreen}{e}iaq r\textcolor{darkgreen}{n}n Vro\textcolor{darkgreen}{m}y\textcolor{darkgreen}{i}kc\textcolor{darkgreen}{e}d uj\textcolor{darkgreen}{n} n\textcolor{darkgreen}{e}\textcolor{darkgreen}{n} V\textcolor{darkgreen}{a}\textcolor{darkgreen}{e}\textcolor{darkgreen}{n}n\textcolor{darkgreen}{e}\textcolor{darkgreen}{n} a\textcolor{darkgreen}{e}o\textcolor{darkgreen}{a}ea\textcolor{darkgreen}{a}\textcolor{darkgreen}{e}\textcolor{darkgreen}{n}h\textcolor{darkgreen}{e}\textcolor{darkgreen}{n}, r\textcolor{darkgreen}{n}n \textcolor{darkgreen}{a}ria \textcolor{darkgreen}{n}\textcolor{darkgreen}{i}iaq \textcolor{darkgreen}{i}\textcolor{darkgreen}{n} \textcolor{darkgreen}{e}\textcolor{darkgreen}{i}\textcolor{darkgreen}{n}\textcolor{darkgreen}{e}o qojib\textcolor{darkgreen}{e}\textcolor{darkgreen}{n}\textcolor{darkgreen}{e}\textcolor{darkgreen}{n}, b\textcolor{darkgreen}{a}ad\textcolor{darkgreen}{e}\textcolor{darkgreen}{n} P\textcolor{darkgreen}{a}\textcolor{darkgreen}{n}nhore\textcolor{darkgreen}{e} ja\textcolor{darkgreen}{n}\textcolor{darkgreen}{e} Q\textcolor{darkgreen}{i}pia\textcolor{darkgreen}{e} r\textcolor{darkgreen}{n}n Pqr\textcolor{darkgreen}{e}ad\textcolor{darkgreen}{e}, vj \textcolor{darkgreen}{m}\textcolor{darkgreen}{a}\textcolor{darkgreen}{n} p\textcolor{darkgreen}{i}ia yr\textcolor{darkgreen}{m} \textcolor{darkgreen}{E}pp\textcolor{darkgreen}{e}\textcolor{darkgreen}{n} a\textcolor{darkgreen}{i}\textcolor{darkgreen}{n}p\textcolor{darkgreen}{e}qy\textcolor{darkgreen}{e}\textcolor{darkgreen}{n} bj\textcolor{darkgreen}{e}\textcolor{darkgreen}{n}\textcolor{darkgreen}{n}q\textcolor{darkgreen}{e}: \textcolor{darkgreen}{n}\textcolor{darkgreen}{e}\textcolor{darkgreen}{i}\textcolor{darkgreen}{n}, n\textcolor{darkgreen}{a}p Djia v\textcolor{darkgreen}{a}o \textcolor{darkgreen}{e}\textcolor{darkgreen}{i}\textcolor{darkgreen}{n}\textcolor{darkgreen}{e} Ajee\textcolor{darkgreen}{i}qaj\textcolor{darkgreen}{e}ad\textcolor{darkgreen}{e}, r\textcolor{darkgreen}{n}n n\textcolor{darkgreen}{a}p a\textcolor{darkgreen}{e}\textcolor{darkgreen}{i}ppq, \textcolor{darkgreen}{e}p v\textcolor{darkgreen}{a}o p\textcolor{darkgreen}{e}ao bj\textcolor{darkgreen}{m}cjoq\textcolor{darkgreen}{a}e\textcolor{darkgreen}{e}d.}
}
\only<7>{
	\texttt{\textcolor{darkgreen}{I}\textcolor{darkgreen}{n} \textcolor{darkgreen}{e}\textcolor{darkgreen}{i}\textcolor{darkgreen}{n}\textcolor{darkgreen}{e}\textcolor{darkgreen}{m} Djia \textcolor{darkgreen}{i}\textcolor{darkgreen}{m} Ej\textcolor{darkgreen}{d}\textcolor{darkgreen}{e}\textcolor{darkgreen}{n}, \textcolor{darkgreen}{d}\textcolor{darkgreen}{a} d\textcolor{darkgreen}{e}eq\textcolor{darkgreen}{e} \textcolor{darkgreen}{e}\textcolor{darkgreen}{i}\textcolor{darkgreen}{n} Ajee\textcolor{darkgreen}{i}q. \textcolor{darkgreen}{N}\textcolor{darkgreen}{i}iaq \textcolor{darkgreen}{i}\textcolor{darkgreen}{n} \textcolor{darkgreen}{e}\textcolor{darkgreen}{i}\textcolor{darkgreen}{n}\textcolor{darkgreen}{e}\textcolor{darkgreen}{m} c\textcolor{darkgreen}{e}\textcolor{darkgreen}{u}iaq\textcolor{darkgreen}{e}\textcolor{darkgreen}{n}, pia\textcolor{darkgreen}{m}\textcolor{darkgreen}{u}qy\textcolor{darkgreen}{i}h\textcolor{darkgreen}{e}\textcolor{darkgreen}{n} Djia, vj \textcolor{darkgreen}{e}p \textcolor{darkgreen}{n}\textcolor{darkgreen}{a}ia \textcolor{darkgreen}{M}j\textcolor{darkgreen}{d}\textcolor{darkgreen}{e}o o\textcolor{darkgreen}{i}\textcolor{darkgreen}{e}iaq \textcolor{darkgreen}{u}\textcolor{darkgreen}{n}\textcolor{darkgreen}{d} V\textcolor{darkgreen}{u}o\textcolor{darkgreen}{m}y\textcolor{darkgreen}{i}kc\textcolor{darkgreen}{e}d uj\textcolor{darkgreen}{n} \textcolor{darkgreen}{d}\textcolor{darkgreen}{e}\textcolor{darkgreen}{n} V\textcolor{darkgreen}{a}\textcolor{darkgreen}{e}\textcolor{darkgreen}{n}\textcolor{darkgreen}{d}\textcolor{darkgreen}{e}\textcolor{darkgreen}{n} a\textcolor{darkgreen}{e}o\textcolor{darkgreen}{a}ea\textcolor{darkgreen}{a}\textcolor{darkgreen}{e}\textcolor{darkgreen}{n}h\textcolor{darkgreen}{e}\textcolor{darkgreen}{n}, \textcolor{darkgreen}{u}\textcolor{darkgreen}{n}\textcolor{darkgreen}{d} \textcolor{darkgreen}{a}\textcolor{darkgreen}{u}ia \textcolor{darkgreen}{n}\textcolor{darkgreen}{i}iaq \textcolor{darkgreen}{i}\textcolor{darkgreen}{n} \textcolor{darkgreen}{e}\textcolor{darkgreen}{i}\textcolor{darkgreen}{n}\textcolor{darkgreen}{e}o qojib\textcolor{darkgreen}{e}\textcolor{darkgreen}{n}\textcolor{darkgreen}{e}\textcolor{darkgreen}{n}, b\textcolor{darkgreen}{a}ad\textcolor{darkgreen}{e}\textcolor{darkgreen}{n} P\textcolor{darkgreen}{a}\textcolor{darkgreen}{n}\textcolor{darkgreen}{d}ho\textcolor{darkgreen}{u}e\textcolor{darkgreen}{e} ja\textcolor{darkgreen}{n}\textcolor{darkgreen}{e} Q\textcolor{darkgreen}{i}pia\textcolor{darkgreen}{e} \textcolor{darkgreen}{u}\textcolor{darkgreen}{n}\textcolor{darkgreen}{d} Pq\textcolor{darkgreen}{u}\textcolor{darkgreen}{e}ad\textcolor{darkgreen}{e}, vj \textcolor{darkgreen}{m}\textcolor{darkgreen}{a}\textcolor{darkgreen}{n} p\textcolor{darkgreen}{i}ia y\textcolor{darkgreen}{u}\textcolor{darkgreen}{m} \textcolor{darkgreen}{E}pp\textcolor{darkgreen}{e}\textcolor{darkgreen}{n} a\textcolor{darkgreen}{i}\textcolor{darkgreen}{n}p\textcolor{darkgreen}{e}qy\textcolor{darkgreen}{e}\textcolor{darkgreen}{n} bj\textcolor{darkgreen}{e}\textcolor{darkgreen}{n}\textcolor{darkgreen}{n}q\textcolor{darkgreen}{e}: \textcolor{darkgreen}{n}\textcolor{darkgreen}{e}\textcolor{darkgreen}{i}\textcolor{darkgreen}{n}, \textcolor{darkgreen}{d}\textcolor{darkgreen}{a}p Djia v\textcolor{darkgreen}{a}o \textcolor{darkgreen}{e}\textcolor{darkgreen}{i}\textcolor{darkgreen}{n}\textcolor{darkgreen}{e} Ajee\textcolor{darkgreen}{i}qaj\textcolor{darkgreen}{e}ad\textcolor{darkgreen}{e}, \textcolor{darkgreen}{u}\textcolor{darkgreen}{n}\textcolor{darkgreen}{d} \textcolor{darkgreen}{d}\textcolor{darkgreen}{a}p a\textcolor{darkgreen}{e}\textcolor{darkgreen}{i}ppq, \textcolor{darkgreen}{e}p v\textcolor{darkgreen}{a}o p\textcolor{darkgreen}{e}ao bj\textcolor{darkgreen}{m}cjoq\textcolor{darkgreen}{a}e\textcolor{darkgreen}{e}d.}
}
\only<8>{
	\texttt{\textcolor{darkgreen}{I}\textcolor{darkgreen}{n} \textcolor{darkgreen}{e}\textcolor{darkgreen}{i}\textcolor{darkgreen}{n}\textcolor{darkgreen}{e}\textcolor{darkgreen}{m} Djia \textcolor{darkgreen}{i}\textcolor{darkgreen}{m} Ej\textcolor{darkgreen}{d}\textcolor{darkgreen}{e}\textcolor{darkgreen}{n}, \textcolor{darkgreen}{d}\textcolor{darkgreen}{a} d\textcolor{darkgreen}{e}eq\textcolor{darkgreen}{e} \textcolor{darkgreen}{e}\textcolor{darkgreen}{i}\textcolor{darkgreen}{n} Ajee\textcolor{darkgreen}{i}q. \textcolor{darkgreen}{N}\textcolor{darkgreen}{i}iaq \textcolor{darkgreen}{i}\textcolor{darkgreen}{n} \textcolor{darkgreen}{e}\textcolor{darkgreen}{i}\textcolor{darkgreen}{n}\textcolor{darkgreen}{e}\textcolor{darkgreen}{m} c\textcolor{darkgreen}{e}\textcolor{darkgreen}{u}iaq\textcolor{darkgreen}{e}\textcolor{darkgreen}{n}, \textcolor{darkgreen}{s}ia\textcolor{darkgreen}{m}\textcolor{darkgreen}{u}qy\textcolor{darkgreen}{i}h\textcolor{darkgreen}{e}\textcolor{darkgreen}{n} Djia, vj \textcolor{darkgreen}{e}\textcolor{darkgreen}{s} \textcolor{darkgreen}{n}\textcolor{darkgreen}{a}ia \textcolor{darkgreen}{M}j\textcolor{darkgreen}{d}\textcolor{darkgreen}{e}o o\textcolor{darkgreen}{i}\textcolor{darkgreen}{e}iaq \textcolor{darkgreen}{u}\textcolor{darkgreen}{n}\textcolor{darkgreen}{d} V\textcolor{darkgreen}{u}o\textcolor{darkgreen}{m}y\textcolor{darkgreen}{i}kc\textcolor{darkgreen}{e}d uj\textcolor{darkgreen}{n} \textcolor{darkgreen}{d}\textcolor{darkgreen}{e}\textcolor{darkgreen}{n} V\textcolor{darkgreen}{a}\textcolor{darkgreen}{e}\textcolor{darkgreen}{n}\textcolor{darkgreen}{d}\textcolor{darkgreen}{e}\textcolor{darkgreen}{n} a\textcolor{darkgreen}{e}o\textcolor{darkgreen}{a}ea\textcolor{darkgreen}{a}\textcolor{darkgreen}{e}\textcolor{darkgreen}{n}h\textcolor{darkgreen}{e}\textcolor{darkgreen}{n}, \textcolor{darkgreen}{u}\textcolor{darkgreen}{n}\textcolor{darkgreen}{d} \textcolor{darkgreen}{a}\textcolor{darkgreen}{u}ia \textcolor{darkgreen}{n}\textcolor{darkgreen}{i}iaq \textcolor{darkgreen}{i}\textcolor{darkgreen}{n} \textcolor{darkgreen}{e}\textcolor{darkgreen}{i}\textcolor{darkgreen}{n}\textcolor{darkgreen}{e}o qojib\textcolor{darkgreen}{e}\textcolor{darkgreen}{n}\textcolor{darkgreen}{e}\textcolor{darkgreen}{n}, b\textcolor{darkgreen}{a}ad\textcolor{darkgreen}{e}\textcolor{darkgreen}{n} \textcolor{darkgreen}{S}\textcolor{darkgreen}{a}\textcolor{darkgreen}{n}\textcolor{darkgreen}{d}ho\textcolor{darkgreen}{u}e\textcolor{darkgreen}{e} ja\textcolor{darkgreen}{n}\textcolor{darkgreen}{e} Q\textcolor{darkgreen}{i}\textcolor{darkgreen}{s}ia\textcolor{darkgreen}{e} \textcolor{darkgreen}{u}\textcolor{darkgreen}{n}\textcolor{darkgreen}{d} \textcolor{darkgreen}{S}q\textcolor{darkgreen}{u}\textcolor{darkgreen}{e}ad\textcolor{darkgreen}{e}, vj \textcolor{darkgreen}{m}\textcolor{darkgreen}{a}\textcolor{darkgreen}{n} \textcolor{darkgreen}{s}\textcolor{darkgreen}{i}ia y\textcolor{darkgreen}{u}\textcolor{darkgreen}{m} \textcolor{darkgreen}{E}\textcolor{darkgreen}{s}\textcolor{darkgreen}{s}\textcolor{darkgreen}{e}\textcolor{darkgreen}{n} a\textcolor{darkgreen}{i}\textcolor{darkgreen}{n}\textcolor{darkgreen}{s}\textcolor{darkgreen}{e}qy\textcolor{darkgreen}{e}\textcolor{darkgreen}{n} bj\textcolor{darkgreen}{e}\textcolor{darkgreen}{n}\textcolor{darkgreen}{n}q\textcolor{darkgreen}{e}: \textcolor{darkgreen}{n}\textcolor{darkgreen}{e}\textcolor{darkgreen}{i}\textcolor{darkgreen}{n}, \textcolor{darkgreen}{d}\textcolor{darkgreen}{a}\textcolor{darkgreen}{s} Djia v\textcolor{darkgreen}{a}o \textcolor{darkgreen}{e}\textcolor{darkgreen}{i}\textcolor{darkgreen}{n}\textcolor{darkgreen}{e} Ajee\textcolor{darkgreen}{i}qaj\textcolor{darkgreen}{e}ad\textcolor{darkgreen}{e}, \textcolor{darkgreen}{u}\textcolor{darkgreen}{n}\textcolor{darkgreen}{d} \textcolor{darkgreen}{d}\textcolor{darkgreen}{a}\textcolor{darkgreen}{s} a\textcolor{darkgreen}{e}\textcolor{darkgreen}{i}\textcolor{darkgreen}{s}\textcolor{darkgreen}{s}q, \textcolor{darkgreen}{e}\textcolor{darkgreen}{s} v\textcolor{darkgreen}{a}o \textcolor{darkgreen}{s}\textcolor{darkgreen}{e}ao bj\textcolor{darkgreen}{m}cjoq\textcolor{darkgreen}{a}e\textcolor{darkgreen}{e}d.}
}
\only<9>{
	\texttt{\textcolor{darkgreen}{I}\textcolor{darkgreen}{n} \textcolor{darkgreen}{e}\textcolor{darkgreen}{i}\textcolor{darkgreen}{n}\textcolor{darkgreen}{e}\textcolor{darkgreen}{m} Djia \textcolor{darkgreen}{i}\textcolor{darkgreen}{m} Ej\textcolor{darkgreen}{d}\textcolor{darkgreen}{e}\textcolor{darkgreen}{n}, \textcolor{darkgreen}{d}\textcolor{darkgreen}{a} d\textcolor{darkgreen}{e}eq\textcolor{darkgreen}{e} \textcolor{darkgreen}{e}\textcolor{darkgreen}{i}\textcolor{darkgreen}{n} Ajee\textcolor{darkgreen}{i}q. \textcolor{darkgreen}{N}\textcolor{darkgreen}{i}iaq \textcolor{darkgreen}{i}\textcolor{darkgreen}{n} \textcolor{darkgreen}{e}\textcolor{darkgreen}{i}\textcolor{darkgreen}{n}\textcolor{darkgreen}{e}\textcolor{darkgreen}{m} c\textcolor{darkgreen}{e}\textcolor{darkgreen}{u}iaq\textcolor{darkgreen}{e}\textcolor{darkgreen}{n}, \textcolor{darkgreen}{s}ia\textcolor{darkgreen}{m}\textcolor{darkgreen}{u}q\textcolor{darkgreen}{z}\textcolor{darkgreen}{i}h\textcolor{darkgreen}{e}\textcolor{darkgreen}{n} Djia, vj \textcolor{darkgreen}{e}\textcolor{darkgreen}{s} \textcolor{darkgreen}{n}\textcolor{darkgreen}{a}ia \textcolor{darkgreen}{M}j\textcolor{darkgreen}{d}\textcolor{darkgreen}{e}o o\textcolor{darkgreen}{i}\textcolor{darkgreen}{e}iaq \textcolor{darkgreen}{u}\textcolor{darkgreen}{n}\textcolor{darkgreen}{d} V\textcolor{darkgreen}{u}o\textcolor{darkgreen}{m}\textcolor{darkgreen}{z}\textcolor{darkgreen}{i}kc\textcolor{darkgreen}{e}d uj\textcolor{darkgreen}{n} \textcolor{darkgreen}{d}\textcolor{darkgreen}{e}\textcolor{darkgreen}{n} V\textcolor{darkgreen}{a}\textcolor{darkgreen}{e}\textcolor{darkgreen}{n}\textcolor{darkgreen}{d}\textcolor{darkgreen}{e}\textcolor{darkgreen}{n} a\textcolor{darkgreen}{e}o\textcolor{darkgreen}{a}ea\textcolor{darkgreen}{a}\textcolor{darkgreen}{e}\textcolor{darkgreen}{n}h\textcolor{darkgreen}{e}\textcolor{darkgreen}{n}, \textcolor{darkgreen}{u}\textcolor{darkgreen}{n}\textcolor{darkgreen}{d} \textcolor{darkgreen}{a}\textcolor{darkgreen}{u}ia \textcolor{darkgreen}{n}\textcolor{darkgreen}{i}iaq \textcolor{darkgreen}{i}\textcolor{darkgreen}{n} \textcolor{darkgreen}{e}\textcolor{darkgreen}{i}\textcolor{darkgreen}{n}\textcolor{darkgreen}{e}o qojib\textcolor{darkgreen}{e}\textcolor{darkgreen}{n}\textcolor{darkgreen}{e}\textcolor{darkgreen}{n}, b\textcolor{darkgreen}{a}ad\textcolor{darkgreen}{e}\textcolor{darkgreen}{n} \textcolor{darkgreen}{S}\textcolor{darkgreen}{a}\textcolor{darkgreen}{n}\textcolor{darkgreen}{d}ho\textcolor{darkgreen}{u}e\textcolor{darkgreen}{e} ja\textcolor{darkgreen}{n}\textcolor{darkgreen}{e} Q\textcolor{darkgreen}{i}\textcolor{darkgreen}{s}ia\textcolor{darkgreen}{e} \textcolor{darkgreen}{u}\textcolor{darkgreen}{n}\textcolor{darkgreen}{d} \textcolor{darkgreen}{S}q\textcolor{darkgreen}{u}\textcolor{darkgreen}{e}ad\textcolor{darkgreen}{e}, vj \textcolor{darkgreen}{m}\textcolor{darkgreen}{a}\textcolor{darkgreen}{n} \textcolor{darkgreen}{s}\textcolor{darkgreen}{i}ia \textcolor{darkgreen}{z}\textcolor{darkgreen}{u}\textcolor{darkgreen}{m} \textcolor{darkgreen}{E}\textcolor{darkgreen}{s}\textcolor{darkgreen}{s}\textcolor{darkgreen}{e}\textcolor{darkgreen}{n} a\textcolor{darkgreen}{i}\textcolor{darkgreen}{n}\textcolor{darkgreen}{s}\textcolor{darkgreen}{e}q\textcolor{darkgreen}{z}\textcolor{darkgreen}{e}\textcolor{darkgreen}{n} bj\textcolor{darkgreen}{e}\textcolor{darkgreen}{n}\textcolor{darkgreen}{n}q\textcolor{darkgreen}{e}: \textcolor{darkgreen}{n}\textcolor{darkgreen}{e}\textcolor{darkgreen}{i}\textcolor{darkgreen}{n}, \textcolor{darkgreen}{d}\textcolor{darkgreen}{a}\textcolor{darkgreen}{s} Djia v\textcolor{darkgreen}{a}o \textcolor{darkgreen}{e}\textcolor{darkgreen}{i}\textcolor{darkgreen}{n}\textcolor{darkgreen}{e} Ajee\textcolor{darkgreen}{i}qaj\textcolor{darkgreen}{e}ad\textcolor{darkgreen}{e}, \textcolor{darkgreen}{u}\textcolor{darkgreen}{n}\textcolor{darkgreen}{d} \textcolor{darkgreen}{d}\textcolor{darkgreen}{a}\textcolor{darkgreen}{s} a\textcolor{darkgreen}{e}\textcolor{darkgreen}{i}\textcolor{darkgreen}{s}\textcolor{darkgreen}{s}q, \textcolor{darkgreen}{e}\textcolor{darkgreen}{s} v\textcolor{darkgreen}{a}o \textcolor{darkgreen}{s}\textcolor{darkgreen}{e}ao bj\textcolor{darkgreen}{m}cjoq\textcolor{darkgreen}{a}e\textcolor{darkgreen}{e}d.}
}
\only<10>{
	\texttt{\textcolor{darkgreen}{I}\textcolor{darkgreen}{n} \textcolor{darkgreen}{e}\textcolor{darkgreen}{i}\textcolor{darkgreen}{n}\textcolor{darkgreen}{e}\textcolor{darkgreen}{m} Djia \textcolor{darkgreen}{i}\textcolor{darkgreen}{m} Ej\textcolor{darkgreen}{d}\textcolor{darkgreen}{e}\textcolor{darkgreen}{n}, \textcolor{darkgreen}{d}\textcolor{darkgreen}{a} d\textcolor{darkgreen}{e}eq\textcolor{darkgreen}{e} \textcolor{darkgreen}{e}\textcolor{darkgreen}{i}\textcolor{darkgreen}{n} Ajee\textcolor{darkgreen}{i}q. \textcolor{darkgreen}{N}\textcolor{darkgreen}{i}iaq \textcolor{darkgreen}{i}\textcolor{darkgreen}{n} \textcolor{darkgreen}{e}\textcolor{darkgreen}{i}\textcolor{darkgreen}{n}\textcolor{darkgreen}{e}\textcolor{darkgreen}{m} c\textcolor{darkgreen}{e}\textcolor{darkgreen}{u}iaq\textcolor{darkgreen}{e}\textcolor{darkgreen}{n}, \textcolor{darkgreen}{s}ia\textcolor{darkgreen}{m}\textcolor{darkgreen}{u}q\textcolor{darkgreen}{z}\textcolor{darkgreen}{i}h\textcolor{darkgreen}{e}\textcolor{darkgreen}{n} Djia, vj \textcolor{darkgreen}{e}\textcolor{darkgreen}{s} \textcolor{darkgreen}{n}\textcolor{darkgreen}{a}ia \textcolor{darkgreen}{M}j\textcolor{darkgreen}{d}\textcolor{darkgreen}{e}\textcolor{darkgreen}{r} \textcolor{darkgreen}{r}\textcolor{darkgreen}{i}\textcolor{darkgreen}{e}iaq \textcolor{darkgreen}{u}\textcolor{darkgreen}{n}\textcolor{darkgreen}{d} V\textcolor{darkgreen}{u}\textcolor{darkgreen}{r}\textcolor{darkgreen}{m}\textcolor{darkgreen}{z}\textcolor{darkgreen}{i}kc\textcolor{darkgreen}{e}d uj\textcolor{darkgreen}{n} \textcolor{darkgreen}{d}\textcolor{darkgreen}{e}\textcolor{darkgreen}{n} V\textcolor{darkgreen}{a}\textcolor{darkgreen}{e}\textcolor{darkgreen}{n}\textcolor{darkgreen}{d}\textcolor{darkgreen}{e}\textcolor{darkgreen}{n} a\textcolor{darkgreen}{e}\textcolor{darkgreen}{r}\textcolor{darkgreen}{a}ea\textcolor{darkgreen}{a}\textcolor{darkgreen}{e}\textcolor{darkgreen}{n}h\textcolor{darkgreen}{e}\textcolor{darkgreen}{n}, \textcolor{darkgreen}{u}\textcolor{darkgreen}{n}\textcolor{darkgreen}{d} \textcolor{darkgreen}{a}\textcolor{darkgreen}{u}ia \textcolor{darkgreen}{n}\textcolor{darkgreen}{i}iaq \textcolor{darkgreen}{i}\textcolor{darkgreen}{n} \textcolor{darkgreen}{e}\textcolor{darkgreen}{i}\textcolor{darkgreen}{n}\textcolor{darkgreen}{e}\textcolor{darkgreen}{r} q\textcolor{darkgreen}{r}jib\textcolor{darkgreen}{e}\textcolor{darkgreen}{n}\textcolor{darkgreen}{e}\textcolor{darkgreen}{n}, b\textcolor{darkgreen}{a}ad\textcolor{darkgreen}{e}\textcolor{darkgreen}{n} \textcolor{darkgreen}{S}\textcolor{darkgreen}{a}\textcolor{darkgreen}{n}\textcolor{darkgreen}{d}h\textcolor{darkgreen}{r}\textcolor{darkgreen}{u}e\textcolor{darkgreen}{e} ja\textcolor{darkgreen}{n}\textcolor{darkgreen}{e} Q\textcolor{darkgreen}{i}\textcolor{darkgreen}{s}ia\textcolor{darkgreen}{e} \textcolor{darkgreen}{u}\textcolor{darkgreen}{n}\textcolor{darkgreen}{d} \textcolor{darkgreen}{S}q\textcolor{darkgreen}{u}\textcolor{darkgreen}{e}ad\textcolor{darkgreen}{e}, vj \textcolor{darkgreen}{m}\textcolor{darkgreen}{a}\textcolor{darkgreen}{n} \textcolor{darkgreen}{s}\textcolor{darkgreen}{i}ia \textcolor{darkgreen}{z}\textcolor{darkgreen}{u}\textcolor{darkgreen}{m} \textcolor{darkgreen}{E}\textcolor{darkgreen}{s}\textcolor{darkgreen}{s}\textcolor{darkgreen}{e}\textcolor{darkgreen}{n} a\textcolor{darkgreen}{i}\textcolor{darkgreen}{n}\textcolor{darkgreen}{s}\textcolor{darkgreen}{e}q\textcolor{darkgreen}{z}\textcolor{darkgreen}{e}\textcolor{darkgreen}{n} bj\textcolor{darkgreen}{e}\textcolor{darkgreen}{n}\textcolor{darkgreen}{n}q\textcolor{darkgreen}{e}: \textcolor{darkgreen}{n}\textcolor{darkgreen}{e}\textcolor{darkgreen}{i}\textcolor{darkgreen}{n}, \textcolor{darkgreen}{d}\textcolor{darkgreen}{a}\textcolor{darkgreen}{s} Djia v\textcolor{darkgreen}{a}\textcolor{darkgreen}{r} \textcolor{darkgreen}{e}\textcolor{darkgreen}{i}\textcolor{darkgreen}{n}\textcolor{darkgreen}{e} Ajee\textcolor{darkgreen}{i}qaj\textcolor{darkgreen}{e}ad\textcolor{darkgreen}{e}, \textcolor{darkgreen}{u}\textcolor{darkgreen}{n}\textcolor{darkgreen}{d} \textcolor{darkgreen}{d}\textcolor{darkgreen}{a}\textcolor{darkgreen}{s} a\textcolor{darkgreen}{e}\textcolor{darkgreen}{i}\textcolor{darkgreen}{s}\textcolor{darkgreen}{s}q, \textcolor{darkgreen}{e}\textcolor{darkgreen}{s} v\textcolor{darkgreen}{a}\textcolor{darkgreen}{r} \textcolor{darkgreen}{s}\textcolor{darkgreen}{e}a\textcolor{darkgreen}{r} bj\textcolor{darkgreen}{m}cj\textcolor{darkgreen}{r}q\textcolor{darkgreen}{a}e\textcolor{darkgreen}{e}d.}
}
\only<11>{
	\texttt{\textcolor{darkgreen}{I}\textcolor{darkgreen}{n} \textcolor{darkgreen}{e}\textcolor{darkgreen}{i}\textcolor{darkgreen}{n}\textcolor{darkgreen}{e}\textcolor{darkgreen}{m} Dji\textcolor{darkgreen}{h} \textcolor{darkgreen}{i}\textcolor{darkgreen}{m} Ej\textcolor{darkgreen}{d}\textcolor{darkgreen}{e}\textcolor{darkgreen}{n}, \textcolor{darkgreen}{d}\textcolor{darkgreen}{a} d\textcolor{darkgreen}{e}e\textcolor{darkgreen}{t}\textcolor{darkgreen}{e} \textcolor{darkgreen}{e}\textcolor{darkgreen}{i}\textcolor{darkgreen}{n} \textcolor{darkgreen}{H}jee\textcolor{darkgreen}{i}\textcolor{darkgreen}{t}. \textcolor{darkgreen}{N}\textcolor{darkgreen}{i}i\textcolor{darkgreen}{h}\textcolor{darkgreen}{t} \textcolor{darkgreen}{i}\textcolor{darkgreen}{n} \textcolor{darkgreen}{e}\textcolor{darkgreen}{i}\textcolor{darkgreen}{n}\textcolor{darkgreen}{e}\textcolor{darkgreen}{m} c\textcolor{darkgreen}{e}\textcolor{darkgreen}{u}i\textcolor{darkgreen}{h}\textcolor{darkgreen}{t}\textcolor{darkgreen}{e}\textcolor{darkgreen}{n}, \textcolor{darkgreen}{s}i\textcolor{darkgreen}{h}\textcolor{darkgreen}{m}\textcolor{darkgreen}{u}\textcolor{darkgreen}{t}\textcolor{darkgreen}{z}\textcolor{darkgreen}{i}h\textcolor{darkgreen}{e}\textcolor{darkgreen}{n} Dji\textcolor{darkgreen}{h}, vj \textcolor{darkgreen}{e}\textcolor{darkgreen}{s} \textcolor{darkgreen}{n}\textcolor{darkgreen}{a}i\textcolor{darkgreen}{h} \textcolor{darkgreen}{M}j\textcolor{darkgreen}{d}\textcolor{darkgreen}{e}\textcolor{darkgreen}{r} \textcolor{darkgreen}{r}\textcolor{darkgreen}{i}\textcolor{darkgreen}{e}i\textcolor{darkgreen}{h}\textcolor{darkgreen}{t} \textcolor{darkgreen}{u}\textcolor{darkgreen}{n}\textcolor{darkgreen}{d} V\textcolor{darkgreen}{u}\textcolor{darkgreen}{r}\textcolor{darkgreen}{m}\textcolor{darkgreen}{z}\textcolor{darkgreen}{i}kc\textcolor{darkgreen}{e}d uj\textcolor{darkgreen}{n} \textcolor{darkgreen}{d}\textcolor{darkgreen}{e}\textcolor{darkgreen}{n} V\textcolor{darkgreen}{a}\textcolor{darkgreen}{e}\textcolor{darkgreen}{n}\textcolor{darkgreen}{d}\textcolor{darkgreen}{e}\textcolor{darkgreen}{n} \textcolor{darkgreen}{h}\textcolor{darkgreen}{e}\textcolor{darkgreen}{r}\textcolor{darkgreen}{a}e\textcolor{darkgreen}{h}\textcolor{darkgreen}{a}\textcolor{darkgreen}{e}\textcolor{darkgreen}{n}h\textcolor{darkgreen}{e}\textcolor{darkgreen}{n}, \textcolor{darkgreen}{u}\textcolor{darkgreen}{n}\textcolor{darkgreen}{d} \textcolor{darkgreen}{a}\textcolor{darkgreen}{u}i\textcolor{darkgreen}{h} \textcolor{darkgreen}{n}\textcolor{darkgreen}{i}i\textcolor{darkgreen}{h}\textcolor{darkgreen}{t} \textcolor{darkgreen}{i}\textcolor{darkgreen}{n} \textcolor{darkgreen}{e}\textcolor{darkgreen}{i}\textcolor{darkgreen}{n}\textcolor{darkgreen}{e}\textcolor{darkgreen}{r} \textcolor{darkgreen}{t}\textcolor{darkgreen}{r}jib\textcolor{darkgreen}{e}\textcolor{darkgreen}{n}\textcolor{darkgreen}{e}\textcolor{darkgreen}{n}, b\textcolor{darkgreen}{a}\textcolor{darkgreen}{h}d\textcolor{darkgreen}{e}\textcolor{darkgreen}{n} \textcolor{darkgreen}{S}\textcolor{darkgreen}{a}\textcolor{darkgreen}{n}\textcolor{darkgreen}{d}h\textcolor{darkgreen}{r}\textcolor{darkgreen}{u}e\textcolor{darkgreen}{e} j\textcolor{darkgreen}{h}\textcolor{darkgreen}{n}\textcolor{darkgreen}{e} \textcolor{darkgreen}{T}\textcolor{darkgreen}{i}\textcolor{darkgreen}{s}i\textcolor{darkgreen}{h}\textcolor{darkgreen}{e} \textcolor{darkgreen}{u}\textcolor{darkgreen}{n}\textcolor{darkgreen}{d} \textcolor{darkgreen}{S}\textcolor{darkgreen}{t}\textcolor{darkgreen}{u}\textcolor{darkgreen}{e}\textcolor{darkgreen}{h}d\textcolor{darkgreen}{e}, vj \textcolor{darkgreen}{m}\textcolor{darkgreen}{a}\textcolor{darkgreen}{n} \textcolor{darkgreen}{s}\textcolor{darkgreen}{i}i\textcolor{darkgreen}{h} \textcolor{darkgreen}{z}\textcolor{darkgreen}{u}\textcolor{darkgreen}{m} \textcolor{darkgreen}{E}\textcolor{darkgreen}{s}\textcolor{darkgreen}{s}\textcolor{darkgreen}{e}\textcolor{darkgreen}{n} \textcolor{darkgreen}{h}\textcolor{darkgreen}{i}\textcolor{darkgreen}{n}\textcolor{darkgreen}{s}\textcolor{darkgreen}{e}\textcolor{darkgreen}{t}\textcolor{darkgreen}{z}\textcolor{darkgreen}{e}\textcolor{darkgreen}{n} bj\textcolor{darkgreen}{e}\textcolor{darkgreen}{n}\textcolor{darkgreen}{n}\textcolor{darkgreen}{t}\textcolor{darkgreen}{e}: \textcolor{darkgreen}{n}\textcolor{darkgreen}{e}\textcolor{darkgreen}{i}\textcolor{darkgreen}{n}, \textcolor{darkgreen}{d}\textcolor{darkgreen}{a}\textcolor{darkgreen}{s} Dji\textcolor{darkgreen}{h} v\textcolor{darkgreen}{a}\textcolor{darkgreen}{r} \textcolor{darkgreen}{e}\textcolor{darkgreen}{i}\textcolor{darkgreen}{n}\textcolor{darkgreen}{e} \textcolor{darkgreen}{H}jee\textcolor{darkgreen}{i}\textcolor{darkgreen}{t}\textcolor{darkgreen}{h}j\textcolor{darkgreen}{e}\textcolor{darkgreen}{h}d\textcolor{darkgreen}{e}, \textcolor{darkgreen}{u}\textcolor{darkgreen}{n}\textcolor{darkgreen}{d} \textcolor{darkgreen}{d}\textcolor{darkgreen}{a}\textcolor{darkgreen}{s} \textcolor{darkgreen}{h}\textcolor{darkgreen}{e}\textcolor{darkgreen}{i}\textcolor{darkgreen}{s}\textcolor{darkgreen}{s}\textcolor{darkgreen}{t}, \textcolor{darkgreen}{e}\textcolor{darkgreen}{s} v\textcolor{darkgreen}{a}\textcolor{darkgreen}{r} \textcolor{darkgreen}{s}\textcolor{darkgreen}{e}\textcolor{darkgreen}{h}\textcolor{darkgreen}{r} bj\textcolor{darkgreen}{m}cj\textcolor{darkgreen}{r}\textcolor{darkgreen}{t}\textcolor{darkgreen}{a}e\textcolor{darkgreen}{e}d.}
}
\only<12>{
	\texttt{\textcolor{darkgreen}{I}\textcolor{darkgreen}{n} \textcolor{darkgreen}{e}\textcolor{darkgreen}{i}\textcolor{darkgreen}{n}\textcolor{darkgreen}{e}\textcolor{darkgreen}{m} D\textcolor{darkgreen}{o}\textcolor{darkgreen}{c}\textcolor{darkgreen}{h} \textcolor{darkgreen}{i}\textcolor{darkgreen}{m} E\textcolor{darkgreen}{o}\textcolor{darkgreen}{d}\textcolor{darkgreen}{e}\textcolor{darkgreen}{n}, \textcolor{darkgreen}{d}\textcolor{darkgreen}{a} d\textcolor{darkgreen}{e}e\textcolor{darkgreen}{t}\textcolor{darkgreen}{e} \textcolor{darkgreen}{e}\textcolor{darkgreen}{i}\textcolor{darkgreen}{n} \textcolor{darkgreen}{H}\textcolor{darkgreen}{o}ee\textcolor{darkgreen}{i}\textcolor{darkgreen}{t}. \textcolor{darkgreen}{N}\textcolor{darkgreen}{i}\textcolor{darkgreen}{c}\textcolor{darkgreen}{h}\textcolor{darkgreen}{t} \textcolor{darkgreen}{i}\textcolor{darkgreen}{n} \textcolor{darkgreen}{e}\textcolor{darkgreen}{i}\textcolor{darkgreen}{n}\textcolor{darkgreen}{e}\textcolor{darkgreen}{m} c\textcolor{darkgreen}{e}\textcolor{darkgreen}{u}\textcolor{darkgreen}{c}\textcolor{darkgreen}{h}\textcolor{darkgreen}{t}\textcolor{darkgreen}{e}\textcolor{darkgreen}{n}, \textcolor{darkgreen}{s}\textcolor{darkgreen}{c}\textcolor{darkgreen}{h}\textcolor{darkgreen}{m}\textcolor{darkgreen}{u}\textcolor{darkgreen}{t}\textcolor{darkgreen}{z}\textcolor{darkgreen}{i}\textcolor{darkgreen}{g}\textcolor{darkgreen}{e}\textcolor{darkgreen}{n} D\textcolor{darkgreen}{o}\textcolor{darkgreen}{c}\textcolor{darkgreen}{h}, v\textcolor{darkgreen}{o} \textcolor{darkgreen}{e}\textcolor{darkgreen}{s} \textcolor{darkgreen}{n}\textcolor{darkgreen}{a}\textcolor{darkgreen}{c}\textcolor{darkgreen}{h} \textcolor{darkgreen}{M}\textcolor{darkgreen}{o}\textcolor{darkgreen}{d}\textcolor{darkgreen}{e}\textcolor{darkgreen}{r} \textcolor{darkgreen}{r}\textcolor{darkgreen}{i}\textcolor{darkgreen}{e}\textcolor{darkgreen}{c}\textcolor{darkgreen}{h}\textcolor{darkgreen}{t} \textcolor{darkgreen}{u}\textcolor{darkgreen}{n}\textcolor{darkgreen}{d} V\textcolor{darkgreen}{u}\textcolor{darkgreen}{r}\textcolor{darkgreen}{m}\textcolor{darkgreen}{z}\textcolor{darkgreen}{i}kc\textcolor{darkgreen}{e}d u\textcolor{darkgreen}{o}\textcolor{darkgreen}{n} \textcolor{darkgreen}{d}\textcolor{darkgreen}{e}\textcolor{darkgreen}{n} V\textcolor{darkgreen}{a}\textcolor{darkgreen}{e}\textcolor{darkgreen}{n}\textcolor{darkgreen}{d}\textcolor{darkgreen}{e}\textcolor{darkgreen}{n} \textcolor{darkgreen}{h}\textcolor{darkgreen}{e}\textcolor{darkgreen}{r}\textcolor{darkgreen}{a}e\textcolor{darkgreen}{h}\textcolor{darkgreen}{a}\textcolor{darkgreen}{e}\textcolor{darkgreen}{n}\textcolor{darkgreen}{g}\textcolor{darkgreen}{e}\textcolor{darkgreen}{n}, \textcolor{darkgreen}{u}\textcolor{darkgreen}{n}\textcolor{darkgreen}{d} \textcolor{darkgreen}{a}\textcolor{darkgreen}{u}\textcolor{darkgreen}{c}\textcolor{darkgreen}{h} \textcolor{darkgreen}{n}\textcolor{darkgreen}{i}\textcolor{darkgreen}{c}\textcolor{darkgreen}{h}\textcolor{darkgreen}{t} \textcolor{darkgreen}{i}\textcolor{darkgreen}{n} \textcolor{darkgreen}{e}\textcolor{darkgreen}{i}\textcolor{darkgreen}{n}\textcolor{darkgreen}{e}\textcolor{darkgreen}{r} \textcolor{darkgreen}{t}\textcolor{darkgreen}{r}\textcolor{darkgreen}{o}\textcolor{darkgreen}{c}\textcolor{darkgreen}{k}\textcolor{darkgreen}{e}\textcolor{darkgreen}{n}\textcolor{darkgreen}{e}\textcolor{darkgreen}{n}, \textcolor{darkgreen}{k}\textcolor{darkgreen}{a}\textcolor{darkgreen}{h}d\textcolor{darkgreen}{e}\textcolor{darkgreen}{n} \textcolor{darkgreen}{S}\textcolor{darkgreen}{a}\textcolor{darkgreen}{n}\textcolor{darkgreen}{d}\textcolor{darkgreen}{g}\textcolor{darkgreen}{r}\textcolor{darkgreen}{u}e\textcolor{darkgreen}{e} \textcolor{darkgreen}{o}\textcolor{darkgreen}{h}\textcolor{darkgreen}{n}\textcolor{darkgreen}{e} \textcolor{darkgreen}{T}\textcolor{darkgreen}{i}\textcolor{darkgreen}{s}\textcolor{darkgreen}{c}\textcolor{darkgreen}{h}\textcolor{darkgreen}{e} \textcolor{darkgreen}{u}\textcolor{darkgreen}{n}\textcolor{darkgreen}{d} \textcolor{darkgreen}{S}\textcolor{darkgreen}{t}\textcolor{darkgreen}{u}\textcolor{darkgreen}{e}\textcolor{darkgreen}{h}d\textcolor{darkgreen}{e}, v\textcolor{darkgreen}{o} \textcolor{darkgreen}{m}\textcolor{darkgreen}{a}\textcolor{darkgreen}{n} \textcolor{darkgreen}{s}\textcolor{darkgreen}{i}\textcolor{darkgreen}{c}\textcolor{darkgreen}{h} \textcolor{darkgreen}{z}\textcolor{darkgreen}{u}\textcolor{darkgreen}{m} \textcolor{darkgreen}{E}\textcolor{darkgreen}{s}\textcolor{darkgreen}{s}\textcolor{darkgreen}{e}\textcolor{darkgreen}{n} \textcolor{darkgreen}{h}\textcolor{darkgreen}{i}\textcolor{darkgreen}{n}\textcolor{darkgreen}{s}\textcolor{darkgreen}{e}\textcolor{darkgreen}{t}\textcolor{darkgreen}{z}\textcolor{darkgreen}{e}\textcolor{darkgreen}{n} \textcolor{darkgreen}{k}\textcolor{darkgreen}{o}\textcolor{darkgreen}{e}\textcolor{darkgreen}{n}\textcolor{darkgreen}{n}\textcolor{darkgreen}{t}\textcolor{darkgreen}{e}: \textcolor{darkgreen}{n}\textcolor{darkgreen}{e}\textcolor{darkgreen}{i}\textcolor{darkgreen}{n}, \textcolor{darkgreen}{d}\textcolor{darkgreen}{a}\textcolor{darkgreen}{s} D\textcolor{darkgreen}{o}\textcolor{darkgreen}{c}\textcolor{darkgreen}{h} v\textcolor{darkgreen}{a}\textcolor{darkgreen}{r} \textcolor{darkgreen}{e}\textcolor{darkgreen}{i}\textcolor{darkgreen}{n}\textcolor{darkgreen}{e} \textcolor{darkgreen}{H}\textcolor{darkgreen}{o}ee\textcolor{darkgreen}{i}\textcolor{darkgreen}{t}\textcolor{darkgreen}{h}\textcolor{darkgreen}{o}\textcolor{darkgreen}{e}\textcolor{darkgreen}{h}d\textcolor{darkgreen}{e}, \textcolor{darkgreen}{u}\textcolor{darkgreen}{n}\textcolor{darkgreen}{d} \textcolor{darkgreen}{d}\textcolor{darkgreen}{a}\textcolor{darkgreen}{s} \textcolor{darkgreen}{h}\textcolor{darkgreen}{e}\textcolor{darkgreen}{i}\textcolor{darkgreen}{s}\textcolor{darkgreen}{s}\textcolor{darkgreen}{t}, \textcolor{darkgreen}{e}\textcolor{darkgreen}{s} v\textcolor{darkgreen}{a}\textcolor{darkgreen}{r} \textcolor{darkgreen}{s}\textcolor{darkgreen}{e}\textcolor{darkgreen}{h}\textcolor{darkgreen}{r} \textcolor{darkgreen}{k}\textcolor{darkgreen}{o}\textcolor{darkgreen}{m}c\textcolor{darkgreen}{o}\textcolor{darkgreen}{r}\textcolor{darkgreen}{t}\textcolor{darkgreen}{a}e\textcolor{darkgreen}{e}d.}
}
\only<13>{
\texttt{\textcolor{darkgreen}{In einem Loch im Boden, da lebte ein Hobbit. Nicht in einem feuchten, schmutzigen Loch, wo es nach Moder riecht und Wurmzipfel von den Waenden herabhaengen, und auch nicht in einer trockenen, kahlen Sandgrube ohne Tische und Stuehle, wo man sich zum Essen hinsetzen koennte: nein, das Loch war eine Hobbithoehle, und das heisst, es war sehr komfortabel.}}
}
\vspace{-0.25cm}
\begin{center}
\includegraphics[scale=0.3]{images/hobbit-cipher-freq.png}
\onslide<13>{
\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 & 	
	\texttt{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ E\ \ \ \ \ \ \ \ }}
	\only<3>{Plaintext Alphabet & 	
	\texttt{\ \ \ \ \ \ N\ \ \ \ \ \ \ \ \ \ \ E\ \ \ \ \ \ \ \ }}
	\only<4>{Plaintext Alphabet & 	
	\texttt{\ \ \ \ \ \ N\ \ \ \ \ \ \ \ \ \ \ EI\ \ \ \ \ \ }}
	\only<5>{Plaintext Alphabet & 	
		\texttt{\ \ \ \ \ MN\ \ \ \ \ \ \ \ \ \ \ EI\ \ \ \ \ \ }}
	\only<6>{Plaintext Alphabet & 	
		\texttt{\ \ \ \ \ MN\ \ \ \ \ A\ \ \ \ \ EI\ \ \ \ \ \ }}
	\only<7>{Plaintext Alphabet & 	
		\texttt{\ \ \ \ \ MN\ \ \ \ \ AD\ \ \ UEI\ \ \ \ \ \ }}
	\only<8>{Plaintext Alphabet & 	
			\texttt{\ \ \ \ \ MN\ \ \ \ \ AD\ S\ UEI\ \ \ \ \ \ }}
	\only<9>{Plaintext Alphabet & 	
			\texttt{\ \ \ \ \ MN\ \ \ \ \ AD\ S\ UEI\ \ \ \ Z\ }}
	\only<10>{Plaintext Alphabet & 	
			\texttt{\ \ \ \ \ MN\ \ \ \ \ ADRS\ UEI\ \ \ \ Z\ }}
	\only<11>{Plaintext Alphabet & 	
			\texttt{H\ \ \ \ MN\ \ \ \ \ ADRSTUEI\ \ \ \ Z\ }}
	\only<12>{Plaintext Alphabet & 	
		\texttt{HK\ \ \ MNGCO\ \ ADRSTUEI\ \ \ \ Z\ }}
	\only<13>{Plaintext Alphabet & 	
		\texttt{HKFLBMNGCOP\ ADRSTUEIVW\ \ Z\ }}
\end{tabular}
\end{overlayarea}
\end{frame}

\subsection{Vigenère-Chiffre}
\begin{frame}{Vigenère-Chiffre}
\begin{itemize}
\item Poly-alphabetische Substitution
\item Verwendet unterschiedliche Cäsar-Chiffren für aufeinanderfolgende Buchstaben
\item Beispiel: \\
\begin{tabular}{r|l}
Schlüsselwort & \texttt{B A \ Y \ R E \ U \ T H} \\
Cäser mit Schlüssel & \texttt{1 0 24 17 4 20 19 7}
\end{tabular}\\[0.5cm]
Verschlüsselung:
\begin{tabular}{r|l}
	Klartext   &  \texttt{ES WAR EINMAL VOR LANGER, LANGER ZEIT, ...} \\
	Schlüssel  & \texttt{BA YRE UTHBAY REU THBAYR,\ EUTHBA YREU,\ ...} \\
	Geheimtext & \texttt{FS URV YBUNAJ MSL EHOGCI,\ PUGNFR XVMN,\ ...}
\end{tabular}
\end{itemize}
$\rightarrow$ Gleiche Buchstaben werden nicht immer gleich verschlüsselt
\end{frame}

\begin{frame}{Tabula recta}
\begin{center}
	\includegraphics[scale=0.225]{images/vigenere-square.png}
\end{center}
\end{frame}

\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}{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}

\section{Enigma}
\begin{frame}{Enigma}
	\begin{itemize}
		\item Von den Deutschen im 2.~Weltkrieg zur Verschlüsselung verwendet
		\item Von den Alliierten gebrochen (ohne Wissen der Deutschen)
	\end{itemize}
	\begin{center}
\includegraphics[scale=0.2]{images/enigma.jpg}
	\end{center}
\end{frame}

\begin{frame}{Enigma Funktionsweise}
	\begin{itemize}
	\item Grundlage: Substitutionschiffre
	\begin{center}
		\includegraphics[scale=0.2]{images/enigma-substitution.png}
	\end{center}
	\item Rotoren ändern die Substitution nach jedem Buchstaben
		\begin{center}
			\includegraphics[scale=0.2]{images/enigma-rotation.png}
			\hspace{0.0cm}
			\includegraphics[scale=0.296]{images/enigma-rotor.jpg}
		\end{center}
	\item Anfangsposition der Rotoren entspricht dem Schlüssel
	\begin{center}
		\includegraphics[scale=0.3]{images/enigma-alphabet-ring.jpg}
	\end{center}
	\end{itemize}
\end{frame}

\begin{frame}{Enigma Funktionsweise}
	\begin{itemize}
		\item Aus den Anfangspositionen der Rotoren erhält man $$26 \cdot 26 \cdot 26 = 17\ 576$$ mögliche Verschlüsselungen für einen Buchstaben
		\item Es gibt mehrere mögliche Rotoren (numeriert mit \texttt{I} bis \texttt{VII}) von denen $3$ Stück (in beliebiger Reihenfolge) ausgewählt werden
		$$\rightarrow 8 \cdot 7 \cdot 6 = 336\text{ Möglichkeiten}$$
		Insgesamt: $17\ 576 \cdot 336 = 5\ 905\ 536$ Möglichkeiten
	\end{itemize}
\end{frame}

\begin{frame}{Enigma: Innerer Aufbau}
		\begin{center}
			\includegraphics[scale=0.45]{images/enigma-circuit.png}
		\end{center}
\end{frame}

\begin{frame}{Enigma: Steckerbrett}
	\begin{center}
		\includegraphics[width=5cm,height=4cm]{images/enigma-plugboard.jpg}
		\hspace{0cm}
		\includegraphics[scale=0.3]{images/enigma-plugboard-circuit.png}
	\end{center}
	$\rightarrow$ bis zu $158\ 962\ 555\ 217\ 826\ 360\ 000$ Möglichkeiten
\end{frame}

\begin{frame}
	\begin{itemize}		
		\item Verwende \texttt{Python3} Implementation\texttt{pyenigma}\\
		\item Crib attack (Teil des Klartexts ist bekannt)\\
		\item Brute force ohne Steckerbrett
	\end{itemize}
	Die folgende Nachricht wurde abgefangen. Wir wissen, dass irgendwo in der Nachricht der Wetterbericht steht. Heute hat es geregnet. 
	
	Der Rest der Nachricht enthält den letzten Voucher. 
	
	\texttt{OXSTMZLWDZYSCHIZOUFKTLRYHWNDPBNOQLBVWLQMUT
		WPYBHFICHBCFABQBBPUZKHSWGAJAPJRETCRABZLFJT}
	\\[1cm]
	Hier der gleiche Text mit einer anderen Walzenstellung:
	\texttt{JJSSHINCLYLAQUVENENTYRQOYYLNOLNVCUFPWYHIPH
		TLWUZBRJXEJNOHLUTIXAWFEQRPBHYFILLPDAUJDQTP}
	
\end{frame}

\begin{frame}
Weitere Themen
\begin{itemize}
	\item Buch-Verschlüsselung
	\item Known Plaintext Angriffe
	\item RSA
\end{itemize}
Webseiten zum Thema:

\url{https://www.cryptool.org/en/cto-ciphers/caesar}
\url{https://cryptii.com/}
\url{https://www.guballa.de/substitution-solver}
\url{https://www.dcode.fr/en}
\url{https://hackaday.com/2017/08/22/the-enigma-enigma-how-the-enigma-machine-worked/}
\end{frame}


%\section{Public-key Cryptography}
%\begin{frame}{RSA}
%	content...
%\end{frame}

%\section{Some more puzzles}
%Undeciphered historical codes and ciphers $\rightarrow$ Wikipedia
\end{document}
