253 lines
6.6 KiB
TeX
253 lines
6.6 KiB
TeX
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\documentclass[12pt,a4paper,german]{article}
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\usepackage{url}
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%\usepackage{graphics}
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\usepackage{times}
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\usepackage[T1]{fontenc}
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\usepackage{pifont}
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\usepackage{ngerman}
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\usepackage{float}
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\usepackage{diagbox}
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\usepackage[latin1]{inputenc}
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\usepackage{geometry}
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\usepackage{amsfonts}
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\usepackage{amsmath}
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\usepackage{delarray}
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% \usepackage{minted}
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\usepackage{csquotes}
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\usepackage{graphicx}
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\usepackage{epsfig}
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\usepackage{longtable}
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\usepackage{paralist}
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\geometry{left=2.0cm,textwidth=17cm,top=3.5cm,textheight=23cm}
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\graphicspath{.}
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%%%%%%%%%% Fill out the the definitions %%%%%%%%%
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\def \name {Valentin Brandl} %
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\def \matrikel {108018274494} %
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% \def \pname {Vorname2 Nachname2} %
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% \def \pmatrikel {Matrikelnummer2} %
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\def \gruppe {Gruppe 193} %
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\def \uebung {5} %
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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% DO NOT MODIFY THIS HEADER
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\newcommand{\hwsol}{
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\vspace*{-2cm}
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\noindent \matrikel \quad \name \hfill Gruppe:\gruppe \\
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% \noindent \pmatrikel \quad \pname \\
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\begin{center}{\Large \bf L\"osung f\"ur \"Ubung \# \uebung}\end{center}
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}
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\newcommand{\cmark}{\ding{51}}%
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\newcommand{\xmark}{\ding{55}}%
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\newcommand{\csquare}{\text{\rlap{$\checkmark$}}\square}%
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\begin{document}
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%Import header
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\hwsol
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\section*{Aufgabe 1}
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\begin{enumerate}[a)]
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\item Das National Bureau of Standards (NBS) (heute National Institute of Standards and Technology (NIST)) hat die
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Entwicklung des DES ausgeschrieben.
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\item DES wurde 1977 standardisiert.
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\item Die National Security Agency (NSA) hat an der Entwicklung des DES mitgewirkt.
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\item Die Kryptographen, die den Kandidaten eingereicht haben, geh<65>rten IBM an.
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\item Auf einen Feistel Netz mit einer Blockgr<67><72>e von 64 bit und einer Schl<68>ssell<6C>nge von 128 bit
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\item Die Schl<68>ssell<6C>nge von Lucifer ist 128 bit
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\item Die Schl<68>ssell<6C>nge des DES ist 56 bit und das Sicherheitsniveau ist 56 bit.
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\item Es werden 64 bit in einer DES Operation verschl<68>sselt.
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\item Abbildung \ref{feist_alg} und \ref{feist_round}
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\begin{figure}[h!]
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\centering
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\includegraphics[scale=0.5]{./build/school/intro-crypto/uebung/05/a1i.png}
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\caption{Allgemeine Struktur eines Feistel Netzes}
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\label{feist_alg}
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\end{figure}
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\begin{figure}[h!]
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\centering
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\includegraphics[width=\textwidth]{school/intro-crypto/uebung/05/a1i2.jpg}
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\caption{Struktur einer Feistel Runde}
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\label{feist_round}
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\end{figure}
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\end{enumerate}
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\section*{Aufgabe 2}
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\begin{enumerate}[a)]
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\item
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\begin{tabular}{|c|ccccc|}
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\hline
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$S_4$ & 0 & 1 & 2 & 3 & 4 \\\hline
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0 & 07 & 13 & 14 & 03 & 00 \\\hline
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1 & 13 & 08 & 11 & 05 & 06 \\\hline
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\end{tabular}
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\begin{tabular}{|c|ccccc|}
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\hline
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& 0 & 1 & 2 & 3 & 4 \\\hline
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$(y_1,y_2,y_3,y_4)$ & 0111 & 1101 & 1110 & 0011 & 0000 \\\hline
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$(y_2,y_1,y_4,y_3)$ & 1011 & 1110 & 1101 & 0011 & 0000 \\\hline
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$(y_2,y_1,y_4,y_3) \oplus (0,1,1,0)$ & 1101 & 1000 & 1011 & 0101 & 0110 \\\hline
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Dezimal & 13 & 8 & 11 & 5 & 6 \\\hline
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\end{tabular}
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Das Ergebnis entspricht genau der 1. Zeile in der S-Box $S_4$.
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\item
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\begin{tabular}{|c|ccccc|}
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\hline
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$S_4$ & 0 & 1 & 2 & 3 & 4 \\\hline
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2 & 10 & 06 & 09 & 00 & 12 \\\hline
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3 & 03 & 15 & 00 & 06 & 10 \\\hline
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\end{tabular}
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Tabelle in bin<69>r:
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\begin{tabular}{|c|ccccc|}
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\hline
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$S_4$ & 0 & 1 & 2 & 3 & 4 \\\hline
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2 & 1010 & 0110 & 1001 & 0000 & 1100 \\\hline
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3 & 0011 & 1111 & 0000 & 0110 & 1010 \\\hline
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\end{tabular}
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Gesucht:
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\begin{itemize}
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\item Permutationsfunktion $f : (y_1,y_2,y_3,y_4) \to (y_1',y_2',y_3',y_4')$
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\item xor Parameter $x = (x_1,x_2,x_3,x_4)$
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\end{itemize}
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Der Ausgangswert von Spalte 3 (0000) bleibt von der Permutationsfunktion unver<65>ndert: $f(0000) = 0000 \Rightarrow x
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= 0000 \oplus 0110 = 0110$
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\begin{tabular}{|c|ccccc|}
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\hline
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$S_4$ & 0 & 1 & 2 & 3 & 4 \\\hline
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3 & 0011 & 1111 & 0000 & 0110 & 1010 \\\hline
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Zeile $3 \oplus 0110$ & 0101 & 1001 & 0110 & 0000 & 1100 \\\hline
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2 & 1010 & 0110 & 1001 & 0000 & 1100 \\\hline
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\end{tabular}
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Man kann sehen, dass wieder $y_1$ mit $y_2$ und $y_3$ mit $y_4$ vertauscht werden.
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$\Rightarrow$ Ableitung von Zeile 2 zu 3:
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\begin{align*}
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(y_1,y_2,y_3,y_4) \to (y_2,y_1,y_4,y_3) \oplus (0,1,1,0)
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\end{align*}
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\end{enumerate}
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\section*{Aufgabe 3}
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\begin{tabular}{|c|ccccccccc|}
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\hline
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& $x_1$ & $x_2$ & ... & $x_{56}$ & $x_{57}$ & $x_{58}$ & ... & $x_{63}$ & $x_{64}$ \\\hline
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Eingabe $x$ & 1 & 1 & ... & 1 & 0 & 1 & ... & 1 & 1 \\\hline
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$IP(x)$ & 1 & 1 & ... & 1 & 1 & 1 & ... & 0 & 1 \\\hline
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\end{tabular}
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$L_0 = 11111111111111111111111111111111$
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$R_0 = 11111111111111111111111111111101 = L_1$
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Das zu beobachtende Bit steht an Position $31$.
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$E(R_0) = 111111111111111111111111111111111111111111111011$
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\begin{enumerate}[a)]
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\item Auswirkungen:
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$S_1\ \square$
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$S_2\ \square$
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$S_3\ \square$
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$S_4\ \square$
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$S_5\ \square$
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$S_6\ \square$
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$S_7\ \square$
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$S_8\ \csquare$
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Eingangsbits: $E(R_0) \oplus 111111111111111111111111111111111111111111111111$
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S-Box $S_1$: $000000$
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S-Box $S_2$: $000000$
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S-Box $S_3$: $000000$
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S-Box $S_4$: $000000$
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S-Box $S_5$: $000000$
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S-Box $S_6$: $000000$
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S-Box $S_7$: $000000$
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S-Box $S_8$: $000100$
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\item
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Ausgabe der S-Boxen:
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S-Box $S_1$: $14 = 1110$
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S-Box $S_2$: $15 = 1111$
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S-Box $S_3$: $10 = 1010$
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S-Box $S_4$: $07 = 0111$
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S-Box $S_5$: $02 = 0010$
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S-Box $S_6$: $12 = 1100$
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S-Box $S_7$: $04 = 0100$
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S-Box $S_8$: $08 = 1000$
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Ausgabe nach allen S-Boxen: $s = 11101111101001110010110001001000$
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$P(s) = 10000010010110011101011100111011$ (berechnet mit Code im Anhang)
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$P(s) \oplus L_0 = 01111101101001100010100011000100 = R_1$
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\begin{align*}
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L_1 = R_0:\\
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11111111111111111111111111111101 \\
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R_1:\\
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01111101101001100010100011000100
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\end{align*}
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\item
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\begin{align*}
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L_1:\\
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R_1:\\
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\end{align*}
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\end{enumerate}
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\section*{Aufgabe 4}
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\end{document}
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