From ca6e6e101547e5c586f13f7224e8b4fdf12f3a6d Mon Sep 17 00:00:00 2001 From: Valentin Brandl Date: Thu, 15 Nov 2018 11:54:38 +0100 Subject: [PATCH] Add intro-crypto exercise 04 --- school/intro-crypto/uebung/04/04.tex | 475 ++++++++++++++++++ school/intro-crypto/uebung/04/1a.jpg | Bin 0 -> 550328 bytes school/intro-crypto/uebung/04/1b.jpg | Bin 0 -> 3412471 bytes school/intro-crypto/uebung/04/1c.jpg | Bin 0 -> 663508 bytes school/intro-crypto/uebung/04/lfsr/Cargo.lock | 4 + school/intro-crypto/uebung/04/lfsr/Cargo.toml | 6 + .../intro-crypto/uebung/04/lfsr/src/main.rs | 177 +++++++ .../uebung/04/lfsr/target/.rustc_info.json | 1 + .../uebung/04/lfsr/target/debug/.cargo-lock | 0 .../bin-lfsr-19130ef987a3303b | 1 + .../bin-lfsr-19130ef987a3303b.json | 1 + .../dep-bin-lfsr-19130ef987a3303b | Bin 0 -> 12 bytes .../bin-lfsr-c5c66887bdea01a0 | 1 + .../bin-lfsr-c5c66887bdea01a0.json | 1 + .../dep-bin-lfsr-c5c66887bdea01a0 | Bin 0 -> 12 bytes .../target/debug/deps/lfsr-19130ef987a3303b | Bin 0 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+\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 {4} % +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + + % 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}}% + +\begin{document} +%Import header +\hwsol + + +\section*{Aufgabe 1} + +Grad $m = 6 \Rightarrow 2^m - 1 = 2^6 - 1 = 63$. + +Zustände und Tabellen wurden mit dem angehängten Code generiert. + +%{{{ a1 +\begin{enumerate}[a)] + + \item $x^5 + x^4 + x^2 + x + 1$ + + \begin{figure}[h] + \includegraphics[width=\textwidth]{1a} + \caption{Schaltbild des Schieberegisters für 1a)} + \end{figure} + + IV: $1 0 0 0 0 0$ + + \begin{tabular}{|cccccc|c|} + $x_5$ & $x_4$ & $x_3$ & $x_2$ & $x_1$ & $x_0$ & Output \\\hline + 1 & 0 & 0 & 0 & 0 & 0 & 0 \\ + 0 & 1 & 0 & 0 & 0 & 0 & 0 \\ + 1 & 0 & 1 & 0 & 0 & 0 & 0 \\ + 0 & 1 & 0 & 1 & 0 & 0 & 0 \\ + 0 & 0 & 1 & 0 & 1 & 0 & 0 \\ + 1 & 0 & 0 & 1 & 0 & 1 & 1 \\ + 0 & 1 & 0 & 0 & 1 & 0 & 0 \\ + 0 & 0 & 1 & 0 & 0 & 1 & 1 \\ + 1 & 0 & 0 & 1 & 0 & 0 & 0 \\ + 1 & 1 & 0 & 0 & 1 & 0 & 0 \\ + 0 & 1 & 1 & 0 & 0 & 1 & 1 \\ + 0 & 0 & 1 & 1 & 0 & 0 & 0 \\ + 1 & 0 & 0 & 1 & 1 & 0 & 0 \\ + 0 & 1 & 0 & 0 & 1 & 1 & 1 \\ + 1 & 0 & 1 & 0 & 0 & 1 & 1 \\ + 1 & 1 & 0 & 1 & 0 & 0 & 0 \\ + 0 & 1 & 1 & 0 & 1 & 0 & 0 \\ + 0 & 0 & 1 & 1 & 0 & 1 & 1 \\ + 0 & 0 & 0 & 1 & 1 & 0 & 0 \\ + 0 & 0 & 0 & 0 & 1 & 1 & 1 \\ + 0 & 0 & 0 & 0 & 0 & 1 & 1 \\ + \underline{1} & \underline{0} & \underline{0} & \underline{0} & \underline{0} & \underline{0} & 0 \\ + \end{tabular} + + Wiederholung nach 21 Iterationen. + + Neuer IV: $1 1 1 1 1 1$ + + \begin{tabular}{|cccccc|c|} + $x_5$ & $x_4$ & $x_3$ & $x_2$ & $x_1$ & $x_0$ & Output \\\hline + 1 & 1 & 1 & 1 & 1 & 1 & 1 \\ + 0 & 1 & 1 & 1 & 1 & 1 & 1 \\ + 0 & 0 & 1 & 1 & 1 & 1 & 1 \\ + 1 & 0 & 0 & 1 & 1 & 1 & 1 \\ + 1 & 1 & 0 & 0 & 1 & 1 & 1 \\ + 1 & 1 & 1 & 0 & 0 & 1 & 1 \\ + 0 & 1 & 1 & 1 & 0 & 0 & 0 \\ + 0 & 0 & 1 & 1 & 1 & 0 & 0 \\ + 0 & 0 & 0 & 1 & 1 & 1 & 1 \\ + 1 & 0 & 0 & 0 & 1 & 1 & 1 \\ + 0 & 1 & 0 & 0 & 0 & 1 & 1 \\ + 0 & 0 & 1 & 0 & 0 & 0 & 0 \\ + 0 & 0 & 0 & 1 & 0 & 0 & 0 \\ + 1 & 0 & 0 & 0 & 1 & 0 & 0 \\ + 1 & 1 & 0 & 0 & 0 & 1 & 1 \\ + 0 & 1 & 1 & 0 & 0 & 0 & 0 \\ + 1 & 0 & 1 & 1 & 0 & 0 & 0 \\ + 1 & 1 & 0 & 1 & 1 & 0 & 0 \\ + 1 & 1 & 1 & 0 & 1 & 1 & 1 \\ + 1 & 1 & 1 & 1 & 0 & 1 & 1 \\ + 1 & 1 & 1 & 1 & 1 & 0 & 0 \\ + \underline{1} & \underline{1} & \underline{1} & \underline{1} & \underline{1} & \underline{1} & 1 \\ + \end{tabular} + + Wiederholung wieder nach 21 Iterationen. + + $63 - 21 - 21 = 21$ Fehlende Zustände. + + Neuer IV: $1 1 0 0 0 0$ + + \begin{tabular}{|cccccc|c|} + $x_5$ & $x_4$ & $x_3$ & $x_2$ & $x_1$ & $x_0$ & Output \\\hline + 1 & 1 & 0 & 0 & 0 & 0 & 0 \\ + 1 & 1 & 1 & 0 & 0 & 0 & 0 \\ + 1 & 1 & 1 & 1 & 0 & 0 & 0 \\ + 0 & 1 & 1 & 1 & 1 & 0 & 0 \\ + 1 & 0 & 1 & 1 & 1 & 1 & 1 \\ + 1 & 1 & 0 & 1 & 1 & 1 & 1 \\ + 0 & 1 & 1 & 0 & 1 & 1 & 1 \\ + 1 & 0 & 1 & 1 & 0 & 1 & 1 \\ + 0 & 1 & 0 & 1 & 1 & 0 & 0 \\ + 1 & 0 & 1 & 0 & 1 & 1 & 1 \\ + 0 & 1 & 0 & 1 & 0 & 1 & 1 \\ + 1 & 0 & 1 & 0 & 1 & 0 & 0 \\ + 1 & 1 & 0 & 1 & 0 & 1 & 1 \\ + 1 & 1 & 1 & 0 & 1 & 0 & 0 \\ + 0 & 1 & 1 & 1 & 0 & 1 & 1 \\ + 1 & 0 & 1 & 1 & 1 & 0 & 0 \\ + 0 & 1 & 0 & 1 & 1 & 1 & 1 \\ + 0 & 0 & 1 & 0 & 1 & 1 & 1 \\ + 0 & 0 & 0 & 1 & 0 & 1 & 1 \\ + 0 & 0 & 0 & 0 & 1 & 0 & 0 \\ + 1 & 0 & 0 & 0 & 0 & 1 & 1 \\ + \underline{1} & \underline{1} & \underline{0} & \underline{0} & \underline{0} & \underline{0} & 0 \\ + \end{tabular} + + Wiederholung wieder nach 21 Iterationen. + + $63 - 21 - 21 - 21 = 0$ Fehlende Zustände. Alle möglichen Zustände wurden erzeugt. + + Keine Sequenz maximaler Länge aber Länge unabhängig von IV$\Rightarrow$ es liegt ein irreduzibles Polynom + zugrunde + + \item $x^5 + x + 1$ + + \begin{figure}[h] + \includegraphics[width=\textwidth]{1b} + \caption{Schaltbild des Schieberegisters für 1b)} + \end{figure} + + IV: $1 0 0 0 0 0$ + + \begin{longtable}{|cccccc|c|} + $x_5$ & $x_4$ & $x_3$ & $x_2$ & $x_1$ & $x_0$ & Output \\\hline + 1 & 0 & 0 & 0 & 0 & 0 & 0 \\ + 0 & 1 & 0 & 0 & 0 & 0 & 0 \\ + 0 & 0 & 1 & 0 & 0 & 0 & 0 \\ + 0 & 0 & 0 & 1 & 0 & 0 & 0 \\ + 0 & 0 & 0 & 0 & 1 & 0 & 0 \\ + 1 & 0 & 0 & 0 & 0 & 1 & 1 \\ + 1 & 1 & 0 & 0 & 0 & 0 & 0 \\ + 0 & 1 & 1 & 0 & 0 & 0 & 0 \\ + 0 & 0 & 1 & 1 & 0 & 0 & 0 \\ + 0 & 0 & 0 & 1 & 1 & 0 & 0 \\ + 1 & 0 & 0 & 0 & 1 & 1 & 1 \\ + 0 & 1 & 0 & 0 & 0 & 1 & 1 \\ + 1 & 0 & 1 & 0 & 0 & 0 & 0 \\ + 0 & 1 & 0 & 1 & 0 & 0 & 0 \\ + 0 & 0 & 1 & 0 & 1 & 0 & 0 \\ + 1 & 0 & 0 & 1 & 0 & 1 & 1 \\ + 1 & 1 & 0 & 0 & 1 & 0 & 0 \\ + 1 & 1 & 1 & 0 & 0 & 1 & 1 \\ + 1 & 1 & 1 & 1 & 0 & 0 & 0 \\ + 0 & 1 & 1 & 1 & 1 & 0 & 0 \\ + 1 & 0 & 1 & 1 & 1 & 1 & 1 \\ + 0 & 1 & 0 & 1 & 1 & 1 & 1 \\ + 0 & 0 & 1 & 0 & 1 & 1 & 1 \\ + 0 & 0 & 0 & 1 & 0 & 1 & 1 \\ + 1 & 0 & 0 & 0 & 1 & 0 & 0 \\ + 1 & 1 & 0 & 0 & 0 & 1 & 1 \\ + 1 & 1 & 1 & 0 & 0 & 0 & 0 \\ + 0 & 1 & 1 & 1 & 0 & 0 & 0 \\ + 0 & 0 & 1 & 1 & 1 & 0 & 0 \\ + 1 & 0 & 0 & 1 & 1 & 1 & 1 \\ + 0 & 1 & 0 & 0 & 1 & 1 & 1 \\ + 0 & 0 & 1 & 0 & 0 & 1 & 1 \\ + 1 & 0 & 0 & 1 & 0 & 0 & 0 \\ + 0 & 1 & 0 & 0 & 1 & 0 & 0 \\ + 1 & 0 & 1 & 0 & 0 & 1 & 1 \\ + 1 & 1 & 0 & 1 & 0 & 0 & 0 \\ + 0 & 1 & 1 & 0 & 1 & 0 & 0 \\ + 1 & 0 & 1 & 1 & 0 & 1 & 1 \\ + 1 & 1 & 0 & 1 & 1 & 0 & 0 \\ + 1 & 1 & 1 & 0 & 1 & 1 & 1 \\ + 0 & 1 & 1 & 1 & 0 & 1 & 1 \\ + 1 & 0 & 1 & 1 & 1 & 0 & 0 \\ + 1 & 1 & 0 & 1 & 1 & 1 & 1 \\ + 0 & 1 & 1 & 0 & 1 & 1 & 1 \\ + 0 & 0 & 1 & 1 & 0 & 1 & 1 \\ + 1 & 0 & 0 & 1 & 1 & 0 & 0 \\ + 1 & 1 & 0 & 0 & 1 & 1 & 1 \\ + 0 & 1 & 1 & 0 & 0 & 1 & 1 \\ + 1 & 0 & 1 & 1 & 0 & 0 & 0 \\ + 0 & 1 & 0 & 1 & 1 & 0 & 0 \\ + 1 & 0 & 1 & 0 & 1 & 1 & 1 \\ + 0 & 1 & 0 & 1 & 0 & 1 & 1 \\ + 1 & 0 & 1 & 0 & 1 & 0 & 0 \\ + 1 & 1 & 0 & 1 & 0 & 1 & 1 \\ + 1 & 1 & 1 & 0 & 1 & 0 & 0 \\ + 1 & 1 & 1 & 1 & 0 & 1 & 1 \\ + 1 & 1 & 1 & 1 & 1 & 0 & 0 \\ + 1 & 1 & 1 & 1 & 1 & 1 & 1 \\ + 0 & 1 & 1 & 1 & 1 & 1 & 1 \\ + 0 & 0 & 1 & 1 & 1 & 1 & 1 \\ + 0 & 0 & 0 & 1 & 1 & 1 & 1 \\ + 0 & 0 & 0 & 0 & 1 & 1 & 1 \\ + 0 & 0 & 0 & 0 & 0 & 1 & 1 \\ + \underline{1} & \underline{0} & \underline{0} & \underline{0} & \underline{0} & \underline{0} & 0 \\ + \end{longtable} + + Wiederholung nach 63 Iterationen, es wurden also eine Sequenz maximaler Länge erzeugt $\Rightarrow$ primitives + Polynom liegt zugrunde. + + \item $x^5 + x^3 + x^2 + x + 1$ + + \begin{figure}[h] + \includegraphics[width=\textwidth]{1c} + \caption{Schaltbild des Schieberegisters für 1c)} + \end{figure} + + IV: $1 0 0 0 0 0$ + + \begin{tabular}{|cccccc|c|} + $x_5$ & $x_4$ & $x_3$ & $x_2$ & $x_1$ & $x_0$ & Output \\\hline + 1 & 0 & 0 & 0 & 0 & 0 & 0 \\ + 0 & 1 & 0 & 0 & 0 & 0 & 0 \\ + 0 & 0 & 1 & 0 & 0 & 0 & 0 \\ + 1 & 0 & 0 & 1 & 0 & 0 & 0 \\ + 1 & 1 & 0 & 0 & 1 & 0 & 0 \\ + 1 & 1 & 1 & 0 & 0 & 1 & 1 \\ + 0 & 1 & 1 & 1 & 0 & 0 & 0 \\ + 0 & 0 & 1 & 1 & 1 & 0 & 0 \\ + 1 & 0 & 0 & 1 & 1 & 1 & 1 \\ + 1 & 1 & 0 & 0 & 1 & 1 & 1 \\ + 0 & 1 & 1 & 0 & 0 & 1 & 1 \\ + 0 & 0 & 1 & 1 & 0 & 0 & 0 \\ + 0 & 0 & 0 & 1 & 1 & 0 & 0 \\ + 0 & 0 & 0 & 0 & 1 & 1 & 1 \\ + 0 & 0 & 0 & 0 & 0 & 1 & 1 \\ + \underline{1} & \underline{0} & \underline{0} & \underline{0} & \underline{0} & \underline{0} & 0 \\ + \end{tabular} + + Wiederholung nach 15 Iterationen. + + Neuer IV: $1 1 1 1 1 1$ + + + \begin{tabular}{|cccccc|c|} + $x_5$ & $x_4$ & $x_3$ & $x_2$ & $x_1$ & $x_0$ & Output \\\hline + 1 & 1 & 1 & 1 & 1 & 1 & 1 \\ + 0 & 1 & 1 & 1 & 1 & 1 & 1 \\ + 0 & 0 & 1 & 1 & 1 & 1 & 1 \\ + 0 & 0 & 0 & 1 & 1 & 1 & 1 \\ + 1 & 0 & 0 & 0 & 1 & 1 & 1 \\ + 0 & 1 & 0 & 0 & 0 & 1 & 1 \\ + 1 & 0 & 1 & 0 & 0 & 0 & 0 \\ + 1 & 1 & 0 & 1 & 0 & 0 & 0 \\ + 1 & 1 & 1 & 0 & 1 & 0 & 0 \\ + 0 & 1 & 1 & 1 & 0 & 1 & 1 \\ + 1 & 0 & 1 & 1 & 1 & 0 & 0 \\ + 1 & 1 & 0 & 1 & 1 & 1 & 1 \\ + 1 & 1 & 1 & 0 & 1 & 1 & 1 \\ + 1 & 1 & 1 & 1 & 0 & 1 & 1 \\ + 1 & 1 & 1 & 1 & 1 & 0 & 0 \\ + \underline{1} & \underline{1} & \underline{1} & \underline{1} & \underline{1} & \underline{1} & 1 \\ + \end{tabular} + + Wiederholung nach 15 Iterationen. $63 - 15 - 15 = 33$ Fehlende Zustände. + + Neuer IV: $1 1 0 0 0 0$ + + \begin{tabular}{|cccccc|c|} + $x_5$ & $x_4$ & $x_3$ & $x_2$ & $x_1$ & $x_0$ & Output \\\hline + 1 & 1 & 0 & 0 & 0 & 0 & 0 \\ + 0 & 1 & 1 & 0 & 0 & 0 & 0 \\ + 1 & 0 & 1 & 1 & 0 & 0 & 0 \\ + 0 & 1 & 0 & 1 & 1 & 0 & 0 \\ + 0 & 0 & 1 & 0 & 1 & 1 & 1 \\ + 1 & 0 & 0 & 1 & 0 & 1 & 1 \\ + 0 & 1 & 0 & 0 & 1 & 0 & 0 \\ + 1 & 0 & 1 & 0 & 0 & 1 & 1 \\ + 0 & 1 & 0 & 1 & 0 & 0 & 0 \\ + 1 & 0 & 1 & 0 & 1 & 0 & 0 \\ + 0 & 1 & 0 & 1 & 0 & 1 & 1 \\ + 0 & 0 & 1 & 0 & 1 & 0 & 0 \\ + 0 & 0 & 0 & 1 & 0 & 1 & 1 \\ + 0 & 0 & 0 & 0 & 1 & 0 & 0 \\ + 1 & 0 & 0 & 0 & 0 & 1 & 1 \\ + \underline{1} & \underline{1} & \underline{0} & \underline{0} & \underline{0} & \underline{0} & 0 \\ + \end{tabular} + + Wiederholung nach 15 Iterationen. $63 - 15 - 15 - 15 = 18$ Fehlende Zustände. + + Neuer IV: $1 1 1 0 0 0$ + + \begin{tabular}{|cccccc|c|} + $x_5$ & $x_4$ & $x_3$ & $x_2$ & $x_1$ & $x_0$ & Output \\\hline + 1 & 1 & 1 & 0 & 0 & 0 & 0 \\ + 1 & 1 & 1 & 1 & 0 & 0 & 0 \\ + 0 & 1 & 1 & 1 & 1 & 0 & 0 \\ + 1 & 0 & 1 & 1 & 1 & 1 & 1 \\ + 0 & 1 & 0 & 1 & 1 & 1 & 1 \\ + 1 & 0 & 1 & 0 & 1 & 1 & 1 \\ + 1 & 1 & 0 & 1 & 0 & 1 & 1 \\ + 0 & 1 & 1 & 0 & 1 & 0 & 0 \\ + 0 & 0 & 1 & 1 & 0 & 1 & 1 \\ + 1 & 0 & 0 & 1 & 1 & 0 & 0 \\ + 0 & 1 & 0 & 0 & 1 & 1 & 1 \\ + 0 & 0 & 1 & 0 & 0 & 1 & 1 \\ + 0 & 0 & 0 & 1 & 0 & 0 & 0 \\ + 1 & 0 & 0 & 0 & 1 & 0 & 0 \\ + 1 & 1 & 0 & 0 & 0 & 1 & 1 \\ + \underline{1} & \underline{1} & \underline{1} & \underline{0} & \underline{0} & \underline{0} & 0 \\ + \end{tabular} + + Wiederholung nach 15 Iterationen. $63 - 15 - 15 - 15 - 15 = 3$ Fehlende Zustände. + + Letzter IV: $1 0 1 1 0 1$ + + \begin{tabular}{|cccccc|c|} + $x_5$ & $x_4$ & $x_3$ & $x_2$ & $x_1$ & $x_0$ & Output \\\hline + 1 & 0 & 1 & 1 & 0 & 1 & 1 \\ + 1 & 1 & 0 & 1 & 1 & 0 & 0 \\ + 0 & 1 & 1 & 0 & 1 & 1 & 1 \\ + \underline{1} & \underline{0} & \underline{1} & \underline{1} & \underline{0} & \underline{1} & 1 \\ + \end{tabular} + + Wiederholung nach 3 Iterathonen. $63 - 15 - 15 - 15 - 15 -3 = 0$ fehlende Zustände. + + Keine Sequenz maximaler Länge und Länge ist abhängig von IV $\Rightarrow$ reduzibles Polynom liegt zugrunde. + + +\end{enumerate} %}}} + +\section*{Aufgabe 2} + +\begin{eqnarray*} + s = 155 \text{ Mbits/sec} = 155 * 2^{20} \text{ bit/sec} \\ + 12h = 12 * 60 * 60 sec = 43200 sec \\ + 155 * 2^{20} \frac{bit}{sec} * 43200 sec = 7021264896000 bit +\end{eqnarray*} + +Gesucht $m \in \mathbb{N}$, so dass $2^m - 1 > 7021264896000$ (gelöst mit Wolframalpha) + +\begin{eqnarray*} + 2^m - 1 &> 7021264896000 \\ + m &> 42 +\end{eqnarray*} + +Vorausgesetzt, es handelt sich um ein primitives Polynom, ist der minimale Grad, der benötigt wird, dass eine +Wiederholung in der Schlüsselfolge frühestens nach 12 Stunden passiert $m = 43$. + +\section*{Aufgabe 3} + +\begin{enumerate}[a)] + + \item $m = 8 \Rightarrow 2^m - 1 = 2^8 - 1 = 255$ + + \item $2*m - 1 = 2 * 8 - 1 = 15$ + + \item + \begin{align*} + y_i &\equiv x_i + s_i &\mod 2 \\ + s_i &\equiv y_i + x_i &\mod 2 + \end{align*} + + Rekonstruieren der ersten 15 Bit des Schlüsselstroms mit Hilfe des known-plaintext \enquote{Mo} $\Rightarrow$ + 0x4d, 0x6f $\Rightarrow (01001101)_2, (01101111)_2$ + + Die ersten 2 Bytes des Ciphertext sind 0xEC, 0xD4 $\Rightarrow (11101100)_2, (11010100)_2$ + + Mit Hilfe des angehängten Programms wurden die folgenden 2 Schlüsselstrom Bytes berechnet: $(10100001)_2, + (10111011)_2 \Rightarrow (A1)_{16}, (BB)_{16}$ + + \item Folgendes System $(A\mid b)$ gilt es zu lösen: + + Die Matrix wurde mit Hilfe von \url{https://planetcalc.com/3324/} invertiert. + + \begin{align*} + \begin{array}({@{}cccccccc|c@{}}) + 1 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & 1 \\ + 1 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 0 \\ + 0 & 1 & 1 & 0 & 0 & 0 & 0 & 1 & 1 \\ + 1 & 0 & 1 & 1 & 0 & 0 & 0 & 0 & 1 \\ + 1 & 1 & 0 & 1 & 1 & 0 & 0 & 0 & 1 \\ + 1 & 1 & 1 & 0 & 1 & 1 & 0 & 0 & 0 \\ + 0 & 1 & 1 & 1 & 0 & 1 & 1 & 0 & 1 \\ + 1 & 0 & 1 & 1 & 1 & 0 & 1 & 1 & 1 + \end{array} \\ + Ax = b \Rightarrow A^{-1}b = x \\ + A^{-1} = + \begin{matrix} + 0 & 1 & 0 & 0 & 1 & 1 & 1 & 0 \\ + 0 & 0 & 1 & 0 & 0 & 1 & 1 & 1 \\ + 1 & 0 & 0 & 1 & 1 & 0 & 1 & 1 \\ + 1 & 1 & 0 & 0 & 0 & 1 & 0 & 1 \\ + 1 & 0 & 1 & 0 & 0 & 1 & 0 & 0 \\ + 0 & 1 & 0 & 1 & 0 & 0 & 1 & 0 \\ + 0 & 0 & 1 & 0 & 1 & 0 & 0 & 1 \\ + 1 & 0 & 0 & 1 & 1 & 1 & 0 & 0 + \end{matrix} \\ + b = + \begin{matrix} + 1\\ + 0\\ + 1\\ + 1\\ + 1\\ + 0\\ + 1\\ + 1\\ + \end{matrix}\\ + x = + \begin{array}({@{}cccccccc@{}}) + 0 & 1 & 1 & 0 & 0 & 0 & 1 & 1 + \end{array} \\ + p_0 = 1 \\ + p_1 = 1 \\ + p_2 = 0 \\ + p_3 = 0 \\ + p_4 = 0 \\ + p_5 = 1 \\ + p_6 = 1 \\ + p_7 = 0 \\ + \end{align*} + + \item Der Klartext ist \enquote{Mondl4ndunG}. + + Berechnet mit dem Code im Anhang. + + \item Die erste unsanfte und unbemannte Mondlandung war am 13.09.1959 (Lunik 2). + + Die erste sanfte und unbemannte Mondlandung am 03.02.1966 (Luna 9) + + Die erste bemannte Mondlandung war am 21.07.1969 (Apollo 11). + + (Quelle: \url{https://de.wikipedia.org/wiki/Mondlandung}) + +\end{enumerate} + +% \section*{Code} + +% \inputminted{rust}{./school/intro-crypto/uebung/04/lfsr/src/main.rs} + +\end{document} + diff --git a/school/intro-crypto/uebung/04/1a.jpg b/school/intro-crypto/uebung/04/1a.jpg new file mode 100644 index 0000000000000000000000000000000000000000..26f64942c030621b1962c145ccd977f93e705eb8 GIT binary patch literal 550328 zcmbTeeOyy_o%D4>LMW_} zU-!OV_pf^|zVsg<=i&SPem?J~5C8Sye_cfxwi;^_+BdHtI>J6JSHfkPuY_m?6wK*#@JMY_DvmYmNGqVbwC?Nhv(YBIp*;^i^ALQ){u>Jm35N4}SPJ z|9fN0vwydHkC$m}+uz=C;NYRo?xQaqJO0z3ai@Aiubl4dKNB7vi3rirv*&*CPrr$c z|Ms6J&i~81@4X+Np1JtJzlwA7|Gw~t5C6FM+0wP^|FL}I=E|+Rf4aAJ|G`&Z|M}ti 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