537 lines
56 KiB
TeX
537 lines
56 KiB
TeX
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\usepackage{hyperref}
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\definecolor{darkgreen}{rgb}{0.0,0.5,0.0}
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\title[Code-Break-Party]{Code-Break-Party}
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\author{}
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\institute{\includegraphics[scale=0.5]{images/iR.pdf}}
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\date{January 27th, 2020}
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\AfterPreamble{\hypersetup{
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urlcolor=blue,
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}}
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\begin{document}
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\begin{frame}
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\titlepage
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\end{frame}
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% Uncomment these lines for an automatically generated outline.
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\begin{frame}{Outline}
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\tableofcontents
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\end{frame}
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\section{Substitutions-Chiffren}
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\subsection{Cäsar Chiffre}
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\begin{frame}{Cäsar Chiffre}
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\begin{itemize}
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\item Klartext (plain text): \texttt{ATTACKATDAWN}
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\item Geheimtext (cipher text): \texttt{DWWDFNDWGDZQ}
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\item Schlüssel: \texttt{3} $\rightarrow$ um \texttt{3} Stellen nach rechts verschieben
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\end{itemize}
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\includegraphics[scale=0.5]{images/caesar.jpg}
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\end{frame}
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\begin{frame}{Cäsar Kryptoanalyse}
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\begin{itemize}
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\item Es gibt nur eine begrenzte Anzahl von Schlüsseln (nur \texttt{25} sinnvolle Verschiebungen)
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\item Brute-Force-Angriff $\rightarrow$ alle Kombinationen durchprobieren:\\[0.5cm]
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\begin{tabular}{c|c}
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Schlüssel & Entschlüsselter Text \\
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\hline
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0 & \texttt{DWWDFNDWGDZQ} \\
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1 & \texttt{CVVCEMCVFCYP} \\
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2 & \texttt{BUUBDLBUEBXO} \\
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3 & \texttt{\textcolor{darkgreen}{ATTACKATDAWN}} \\
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$\vdots$ & $\vdots$
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\end{tabular}
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\end{itemize}
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\end{frame}
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\begin{frame}{Monoalphabetische Substitution (Kryptogram)}
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\begin{itemize}
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\item Anstelle für jeden Buchstaben den gleichen Offset zu verwenden, werden unterschiedliche Buchstaben verschieden verschoben
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\item Substitutionstabelle:
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\begin{tabular}{r|c}
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Klartext Alphabet & \texttt{ABCDEFGHIJKLMNOPQRSTUVWXYZ} \\ \hline
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Geheimtext Alphabet & \texttt{MOSKAUBCDEFGHIJLNPQRTVWXYZ}
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\end{tabular}
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\item Beispiel:\\
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\begin{center}
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\texttt{FLEE AT ONCE. WE ARE DISCOVERED.} \\
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\end{center}
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wird zu\\
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\begin{center}
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\texttt{UGAA MR JISA. WA MPA KDQSJVAPAK.}
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\end{center}
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\end{itemize}
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\end{frame}
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\begin{frame}{Frequenzanalyse}
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\begin{itemize}
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\item Buchstaben kommen in natürlicher Sprache mit unterschiedlicher Häufigkeit vor
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\item Im Deutschen: \texttt{E, I, N} sind häufig, \texttt{Q, X, Y} sind selten
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\end{itemize}
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\begin{center}
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\includegraphics[scale=0.3]{images/frequency.jpg}
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\end{center}
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\begin{itemize}
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\item Statistische Eigenschaften des Klartexts werden von einer Substitutionschiffre nicht verändert
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\end{itemize}
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\end{frame}
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\begin{frame}{Beispiel Frequenzanalyse}
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\begin{overlayarea}{\textwidth}{\textheight}
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\only<1>{
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\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.}
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}
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\only<2>{
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\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.}
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}
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\only<3>{
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\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.}
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}
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\only<4>{
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\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.}
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}
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\only<5>{
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\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.}
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}
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\only<6>{
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\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.}
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\only<7>{
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\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.}
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\only<8>{
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\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.}
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\only<9>{
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\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.}
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\only<10>{
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\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.}
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\only<11>{
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\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}
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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
|
|
\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}
|
|
Use implementation py-enigma\\
|
|
crib attack\\
|
|
Brute force without plug board
|
|
\end{frame}
|
|
|
|
\begin{frame}
|
|
More topics
|
|
\begin{itemize}
|
|
\item Book cipher
|
|
\item known plaintext attack
|
|
\item key reuse attack (for one-time-pad)
|
|
\end{itemize}
|
|
https://www.cryptool.org/en/cto-ciphers/caesar
|
|
\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}
|