\documentclass{beamer} % % Choose how your presentation looks. % % For more themes, color themes and font themes, see: % http://deic.uab.es/~iblanes/beamer_gallery/index_by_theme.html % \mode { \usetheme{Singapore} % or try Darmstadt, Madrid, Warsaw, ... \usecolortheme[RGB={3,138,94}]{structure} \usefonttheme{structurebold} % or try serif, structurebold, ... \setbeamertemplate{navigation symbols}{} \setbeamertemplate{headline}{} %\setbeamertemplate{caption}[numbered] \setbeamertemplate{footline}[frame number] } \usepackage[english]{babel} \usepackage[utf8x]{inputenc} \usepackage{fancyvrb} \usepackage{tcolorbox,listings} \usepackage{textpos} \usepackage{setspace} % Default fixed font does not support bold face \DeclareFixedFont{\ttb}{T1}{ascii}{m}{n}{7} % for bold \DeclareFixedFont{\ttm}{T1}{ascii}{m}{n}{7} % for normal % Custom colors \usepackage{color} \definecolor{deepblue}{rgb}{0,0,0.5} \definecolor{deepred}{rgb}{0.6,0,0} \definecolor{deepgreen}{rgb}{0,0.5,0} \definecolor{lightblue}{rgb}{0.6,0.8,1.0} \definecolor{teal}{rgb}{0.45,0.85,1.0} \fvset{frame=single,framesep=1mm,fontfamily=courier,fontsize=\scriptsize,framerule=.3mm,numbersep=1mm,commandchars=\\\{\}} \usepackage{color} \tcbuselibrary{listings,skins,breakable} \lstdefinestyle{commandline}{ basicstyle=\ttfamily\scriptsize, numbers=none, keywordstyle=\color{blue}, morekeywords={{git add}}, %numberstyle=\tiny, numbersep=2pt, moredelim=**[is][\color{darkgreen}]{_green_}{_green_}, moredelim=**[is][\color{red}]{_red_}{_red_}, moredelim=**[is][\color{blue}]{_blue_}{_blue_}, } % Python style for highlighting \newcommand\pythonstyle{ \lstset{ language=Python, basicstyle=\ttfamily\color{white}\tiny, otherkeywords={self}, % Add keywords here keywordstyle=\ttfamily\color{lightblue}, commentstyle=\ttfamily\color{teal}, emph={MyClass,__init__}, % Custom highlighting emphstyle=\ttfamily\color{deepred}, % Custom highlighting style stringstyle=\ttfamily\color{red}, frame=tb, % Any extra options here backgroundcolor = \color{black}, showstringspaces=false % }} \newtcblisting{ConsoleVerbatim}{ arc=0mm, top=-2mm, bottom=-2mm, left=0mm, right=0mm, width=\textwidth, boxrule=0.5pt, colupper=white, colback=black, spartan, listing only, listing options={style=commandline}, breakable } % Python environment \lstnewenvironment{python}[1][] { \pythonstyle \lstset{#1} } {} \lstdefinestyle{commandline}{ basicstyle=\ttfamily\tiny, numbers=none, keywordstyle=\color{blue}, morekeywords={{git add}}, %numberstyle=\tiny, numbersep=2pt, moredelim=**[is][\color{darkgreen}]{_green_}{_green_}, moredelim=**[is][\color{red}]{_red_}{_red_}, moredelim=**[is][\color{blue}]{_blue_}{_blue_}, } \newtcblisting{ConsoleVerbatimTiny}{ arc=0mm, top=-2mm, bottom=-2mm, left=0mm, right=0mm, width=\textwidth, boxrule=0.5pt, colupper=white, colback=black, spartan, listing only, listing options={style=commandline}, breakable } \newenvironment{reference}[2]{ % \begin{textblock*}{\textwidth}(#1,#2) % \rule{10cm}{0.5pt}\\ \tiny\bgroup\color{black}}{\egroup % for the emulated \end{textblock*}} \usepackage{hyperref} \definecolor{darkgreen}{rgb}{0.0,0.5,0.0} \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}. 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\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/} \url{https://projects.raspberrypi.org/en/projects/octapi-brute-force-enigma} \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}