From ff5bbc1a8a7e3b522ab242e5c21e2aee67cdf105 Mon Sep 17 00:00:00 2001 From: Valentin Brandl Date: Tue, 27 Nov 2018 22:28:37 +0100 Subject: [PATCH] Add crypto exercise --- school/intro-crypto/uebung/05/05.tex | 252 ++++++++++++++++++ school/intro-crypto/uebung/05/a1i.dot | 46 ++++ school/intro-crypto/uebung/05/a1i2.jpg | Bin 0 -> 3606478 bytes school/intro-crypto/uebung/05/p/Cargo.lock | 4 + school/intro-crypto/uebung/05/p/Cargo.toml | 6 + school/intro-crypto/uebung/05/p/src/main.rs | 39 +++ .../uebung/05/p/target/.rustc_info.json | 1 + .../uebung/05/p/target/debug/.cargo-lock | 0 .../p-317830ef682f5c46/bin-p-317830ef682f5c46 | 1 + .../bin-p-317830ef682f5c46.json | 1 + .../dep-bin-p-317830ef682f5c46 | Bin 0 -> 12 bytes .../p-a8d68fe4b06c3a8a/bin-p-a8d68fe4b06c3a8a | 1 + .../bin-p-a8d68fe4b06c3a8a.json | 1 + .../dep-bin-p-a8d68fe4b06c3a8a | Bin 0 -> 12 bytes .../debug/deps/libp-317830ef682f5c46.rmeta | 0 .../p/target/debug/deps/p-317830ef682f5c46.d | 5 + 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index 0000000..6a40f56 --- /dev/null +++ b/school/intro-crypto/uebung/05/05.tex @@ -0,0 +1,252 @@ +\documentclass[12pt,a4paper,german]{article} +\usepackage{url} +%\usepackage{graphics} +\usepackage{times} +\usepackage[T1]{fontenc} +\usepackage{pifont} +\usepackage{ngerman} +\usepackage{float} +\usepackage{diagbox} +\usepackage[latin1]{inputenc} +\usepackage{geometry} +\usepackage{amsfonts} +\usepackage{amsmath} +\usepackage{delarray} +% \usepackage{minted} +\usepackage{csquotes} +\usepackage{graphicx} +\usepackage{epsfig} +\usepackage{longtable} +\usepackage{paralist} +\geometry{left=2.0cm,textwidth=17cm,top=3.5cm,textheight=23cm} + +\graphicspath{.} + +%%%%%%%%%% Fill out the the definitions %%%%%%%%% +\def \name {Valentin Brandl} % +\def \matrikel {108018274494} % +% \def \pname {Vorname2 Nachname2} % +% \def \pmatrikel {Matrikelnummer2} % +\def \gruppe {Gruppe 193} % +\def \uebung {5} % +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + + % DO NOT MODIFY THIS HEADER +\newcommand{\hwsol}{ +\vspace*{-2cm} +\noindent \matrikel \quad \name \hfill Gruppe:\gruppe \\ +% \noindent \pmatrikel \quad \pname \\ +\begin{center}{\Large \bf L\"osung f\"ur \"Ubung \# \uebung}\end{center} +} + +\newcommand{\cmark}{\ding{51}}% +\newcommand{\xmark}{\ding{55}}% +\newcommand{\csquare}{\text{\rlap{$\checkmark$}}\square}% + +\begin{document} +%Import header +\hwsol + + +\section*{Aufgabe 1} + +\begin{enumerate}[a)] + + \item Das National Bureau of Standards (NBS) (heute National Institute of Standards and Technology (NIST)) hat die + Entwicklung des DES ausgeschrieben. + + \item DES wurde 1977 standardisiert. + + \item Die National Security Agency (NSA) hat an der Entwicklung des DES mitgewirkt. + + \item Die Kryptographen, die den Kandidaten eingereicht haben, gehörten IBM an. + + \item Auf einen Feistel Netz mit einer Blockgröße von 64 bit und einer Schlüssellänge von 128 bit + + \item Die Schlüssellänge von Lucifer ist 128 bit + + \item Die Schlüssellänge des DES ist 56 bit und das Sicherheitsniveau ist 56 bit. + + \item Es werden 64 bit in einer DES Operation verschlüsselt. + + \item Abbildung \ref{feist_alg} und \ref{feist_round} + + \begin{figure}[h!] + \centering + \includegraphics[scale=0.5]{./build/school/intro-crypto/uebung/05/a1i.png} + \caption{Allgemeine Struktur eines Feistel Netzes} + \label{feist_alg} + \end{figure} + \begin{figure}[h!] + \centering + \includegraphics[width=\textwidth]{school/intro-crypto/uebung/05/a1i2.jpg} + \caption{Struktur einer Feistel Runde} + \label{feist_round} + \end{figure} + +\end{enumerate} + +\section*{Aufgabe 2} + +\begin{enumerate}[a)] + + \item + \begin{tabular}{|c|ccccc|} + \hline + $S_4$ & 0 & 1 & 2 & 3 & 4 \\\hline + 0 & 07 & 13 & 14 & 03 & 00 \\\hline + 1 & 13 & 08 & 11 & 05 & 06 \\\hline + \end{tabular} + + \begin{tabular}{|c|ccccc|} + \hline + & 0 & 1 & 2 & 3 & 4 \\\hline + $(y_1,y_2,y_3,y_4)$ & 0111 & 1101 & 1110 & 0011 & 0000 \\\hline + $(y_2,y_1,y_4,y_3)$ & 1011 & 1110 & 1101 & 0011 & 0000 \\\hline + $(y_2,y_1,y_4,y_3) \oplus (0,1,1,0)$ & 1101 & 1000 & 1011 & 0101 & 0110 \\\hline + Dezimal & 13 & 8 & 11 & 5 & 6 \\\hline + \end{tabular} + + Das Ergebnis entspricht genau der 1. Zeile in der S-Box $S_4$. + + \item + \begin{tabular}{|c|ccccc|} + \hline + $S_4$ & 0 & 1 & 2 & 3 & 4 \\\hline + 2 & 10 & 06 & 09 & 00 & 12 \\\hline + 3 & 03 & 15 & 00 & 06 & 10 \\\hline + \end{tabular} + + Tabelle in binär: + + \begin{tabular}{|c|ccccc|} + \hline + $S_4$ & 0 & 1 & 2 & 3 & 4 \\\hline + 2 & 1010 & 0110 & 1001 & 0000 & 1100 \\\hline + 3 & 0011 & 1111 & 0000 & 0110 & 1010 \\\hline + \end{tabular} + + Gesucht: + + \begin{itemize} + \item Permutationsfunktion $f : (y_1,y_2,y_3,y_4) \to (y_1',y_2',y_3',y_4')$ + \item xor Parameter $x = (x_1,x_2,x_3,x_4)$ + \end{itemize} + + Der Ausgangswert von Spalte 3 (0000) bleibt von der Permutationsfunktion unverändert: $f(0000) = 0000 \Rightarrow x + = 0000 \oplus 0110 = 0110$ + + \begin{tabular}{|c|ccccc|} + \hline + $S_4$ & 0 & 1 & 2 & 3 & 4 \\\hline + 3 & 0011 & 1111 & 0000 & 0110 & 1010 \\\hline + Zeile $3 \oplus 0110$ & 0101 & 1001 & 0110 & 0000 & 1100 \\\hline + 2 & 1010 & 0110 & 1001 & 0000 & 1100 \\\hline + \end{tabular} + + Man kann sehen, dass wieder $y_1$ mit $y_2$ und $y_3$ mit $y_4$ vertauscht werden. + + $\Rightarrow$ Ableitung von Zeile 2 zu 3: + + \begin{align*} + (y_1,y_2,y_3,y_4) \to (y_2,y_1,y_4,y_3) \oplus (0,1,1,0) + \end{align*} + + +\end{enumerate} + +\section*{Aufgabe 3} + + +\begin{tabular}{|c|ccccccccc|} + \hline + & $x_1$ & $x_2$ & ... & $x_{56}$ & $x_{57}$ & $x_{58}$ & ... & $x_{63}$ & $x_{64}$ \\\hline + Eingabe $x$ & 1 & 1 & ... & 1 & 0 & 1 & ... & 1 & 1 \\\hline + $IP(x)$ & 1 & 1 & ... & 1 & 1 & 1 & ... & 0 & 1 \\\hline +\end{tabular} + +$L_0 = 11111111111111111111111111111111$ + +$R_0 = 11111111111111111111111111111101 = L_1$ + +Das zu beobachtende Bit steht an Position $31$. + +$E(R_0) = 111111111111111111111111111111111111111111111011$ + + +\begin{enumerate}[a)] + + \item Auswirkungen: + + $S_1\ \square$ + $S_2\ \square$ + $S_3\ \square$ + $S_4\ \square$ + $S_5\ \square$ + $S_6\ \square$ + $S_7\ \square$ + $S_8\ \csquare$ + + Eingangsbits: $E(R_0) \oplus 111111111111111111111111111111111111111111111111$ + + S-Box $S_1$: $000000$ + + S-Box $S_2$: $000000$ + + S-Box $S_3$: $000000$ + + S-Box $S_4$: $000000$ + + S-Box $S_5$: $000000$ + + S-Box $S_6$: $000000$ + + S-Box $S_7$: $000000$ + + S-Box $S_8$: $000100$ + + \item + Ausgabe der S-Boxen: + + S-Box $S_1$: $14 = 1110$ + + S-Box $S_2$: $15 = 1111$ + + S-Box $S_3$: $10 = 1010$ + + S-Box $S_4$: $07 = 0111$ + + S-Box $S_5$: $02 = 0010$ + + S-Box $S_6$: $12 = 1100$ + + S-Box $S_7$: $04 = 0100$ + + S-Box $S_8$: $08 = 1000$ + + Ausgabe nach allen S-Boxen: $s = 11101111101001110010110001001000$ + + $P(s) = 10000010010110011101011100111011$ (berechnet mit Code im Anhang) + + $P(s) \oplus L_0 = 01111101101001100010100011000100 = R_1$ + + \begin{align*} + L_1 = R_0:\\ + 11111111111111111111111111111101 \\ + R_1:\\ + 01111101101001100010100011000100 + \end{align*} + + \item + + \begin{align*} + L_1:\\ + R_1:\\ + \end{align*} + +\end{enumerate} + +\section*{Aufgabe 4} + +\end{document} + diff --git 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