diff --git a/school/intro-crypto/uebung/04/04.tex b/school/intro-crypto/uebung/04/04.tex new file mode 100644 index 0000000..aa1739e --- /dev/null +++ b/school/intro-crypto/uebung/04/04.tex @@ -0,0 +1,475 @@ +\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 {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 0000000..26f6494 Binary files /dev/null and b/school/intro-crypto/uebung/04/1a.jpg differ diff --git a/school/intro-crypto/uebung/04/1b.jpg b/school/intro-crypto/uebung/04/1b.jpg new file mode 100644 index 0000000..5f34c4a Binary files /dev/null and b/school/intro-crypto/uebung/04/1b.jpg differ diff --git a/school/intro-crypto/uebung/04/1c.jpg b/school/intro-crypto/uebung/04/1c.jpg new file mode 100644 index 0000000..d1bd456 Binary files /dev/null and b/school/intro-crypto/uebung/04/1c.jpg differ diff --git a/school/intro-crypto/uebung/04/lfsr/Cargo.lock b/school/intro-crypto/uebung/04/lfsr/Cargo.lock new file mode 100644 index 0000000..c4403b5 --- /dev/null +++ b/school/intro-crypto/uebung/04/lfsr/Cargo.lock @@ -0,0 +1,4 @@ +[[package]] +name = "lfsr" +version = "0.1.0" + diff --git a/school/intro-crypto/uebung/04/lfsr/Cargo.toml b/school/intro-crypto/uebung/04/lfsr/Cargo.toml new file mode 100644 index 0000000..03f2df8 --- /dev/null +++ b/school/intro-crypto/uebung/04/lfsr/Cargo.toml @@ -0,0 +1,6 @@ +[package] +name = "lfsr" +version = "0.1.0" +authors = ["Valentin Brandl "] + +[dependencies] diff --git a/school/intro-crypto/uebung/04/lfsr/src/main.rs b/school/intro-crypto/uebung/04/lfsr/src/main.rs new file mode 100644 index 0000000..43d493d --- /dev/null +++ b/school/intro-crypto/uebung/04/lfsr/src/main.rs @@ -0,0 +1,177 @@ +struct Lfsr { + reg: Vec, + p: Vec, +} + +impl Lfsr { + fn new(iv: &[bool], p: &[bool]) -> Self { + assert_eq!(iv.len(), p.len()); + Self { + reg: iv.iter().cloned().collect(), + p: p.iter().cloned().collect(), + } + } + + fn next(&mut self) -> bool { + // let res = self.reg[self.len - 1]; + let next = self + .reg + .iter() + .zip(self.p.iter()) + .map(|(n, m)| n & m) + .fold(false, |acc, v| acc ^ v); + self.reg.insert(0, next); + let ret = self.reg.pop().unwrap(); + assert_eq!(self.reg.len(), self.p.len()); + ret + } + + fn state(&self) -> &[bool] { + &self.reg + } +} + +fn convert_state(s: &[bool]) -> String { + s.iter() + .map(|x| if *x { "1".to_string() } else { "0".to_string() }) + .collect::>() + .join(" & ") +} + +/// helper for 3c) +fn recover_keystream(plain: &[bool], cipher: &[bool]) -> Vec { + assert_eq!(plain.len(), cipher.len()); + plain + .iter() + .zip(cipher.iter()) + .map(|(a, b)| a ^ b) + .collect() +} + +fn decrypt(l: &mut Lfsr, c: &[bool]) -> u8 { + let s: String = c + .into_iter() + .map(|c| c ^ l.next()) + .map(|c| if c { "1" } else { "0" }) + .collect(); + u8::from_str_radix(&s, 2).unwrap() +} + +/// main for 3d) +fn main() { + let p = &[false, true, true, false, false, false, true, true]; + // let s = &[true, false, true, true, true, false, true, true]; + // let s = &[true, false, true, false, false, false, false, true]; + // let s = &[true, false, false, false, false, true, false, true]; + let s = &[true, true, false, true, true, true, false, true]; + let mut l = Lfsr::new(s, p); + // for _ in 0..17 { + // println!("{}", if lfsr.next() { "1" } else { "0" }); + // } + // 00010011 + // 11010100 + let c = &[true, true, false, true, false, true, false, false]; + let d = decrypt(&mut l, c); + println!("{}: {}", d, d as char); + + // 00010011 = 0x13 + let c = &[false, false, false, true, false, false, true, true]; + let d = decrypt(&mut l, c); + println!("{}: {}", d, d as char); + + // 00010000 = 0x10 + let c = &[false, false, false, true, false, false, false, false]; + let d = decrypt(&mut l, c); + println!("{}: {}", d, d as char); + + // 01110101 = 0x75 + let c = &[false, true, true, true, false, true, false, true]; + let d = decrypt(&mut l, c); + println!("{}: {}", d, d as char); + + // 01100000 = 0x60 + let c = &[false, true, true, false, false, false, false, false]; + let d = decrypt(&mut l, c); + println!("{}: {}", d, d as char); + + // 00000101 = 0x05 + let c = &[false, false, false, false, false, true, false, true]; + let d = decrypt(&mut l, c); + println!("{}: {}", d, d as char); + + // 01111100 = 0x7c + let c = &[false, true, true, true, true, true, false, false]; + let d = decrypt(&mut l, c); + println!("{}: {}", d, d as char); + + // 01010000 = 0x50 + let c = &[false, true, false, true, false, false, false, false]; + let d = decrypt(&mut l, c); + println!("{}: {}", d, d as char); + + // 11011011 = 0xdb + let c = &[true, true, false, true, true, false, true, true]; + let d = decrypt(&mut l, c); + println!("{}: {}", d, d as char); + + // 01110011 = 0x73 + let c = &[false, true, true, true, false, false, true, true]; + let d = decrypt(&mut l, c); + println!("{}: {}", d, d as char); +} + +// fn main() { +// let plain = &[ +// false, true, false, false, true, true, false, true, false, true, true, false, true, true, +// true, true, +// ]; +// let cipher = &[ +// true, true, true, false, true, true, false, false, true, true, false, true, false, true, +// false, false, +// ]; +// let key_stream = recover_keystream(plain, cipher); +// println!( +// "{}", +// key_stream +// .iter() +// .map(|k| if *k { "1, " } else { "0, " }) +// .collect::() +// ); +// } + +/// main for exercise 1 +fn main1() { + // 1a) + // let mut lfsr = Lfsr::new( + // &[true, true, false, false, false, false], + // // &[true, true, true, true, true, true], + // // &[true, false, false, false, false, false], + // &[false, true, false, true, true, true], + // ); + + // 1b) + // let mut lfsr = Lfsr::new( + // // &[true, true, true, true, true, true], + // &[true, false, false, false, false, false], + // &[false, false, false, false, true, true], + // ); + + // 1c) + let mut lfsr = Lfsr::new( + // &[true, true, true, false, false, false], + // &[true, true, false, false, false, false], + &[true, false, true, true, false, true], + // &[true, true, true, true, true, true], + // &[true, false, false, false, false, false], + &[false, false, true, true, true, true], + ); + let mut seen = Vec::new(); + let mut i = 0; + while !seen.contains(&lfsr.state().iter().cloned().collect::>()) { + seen.push(lfsr.state().iter().cloned().collect::>()); + print!("{}", convert_state(lfsr.state())); + println!(" & {} \\\\", if lfsr.next() { 1 } else { 0 }); + i += 1; + } + eprintln!("Repetition after {} iterations", i); +} diff --git a/school/intro-crypto/uebung/04/lfsr/target/.rustc_info.json b/school/intro-crypto/uebung/04/lfsr/target/.rustc_info.json new file mode 100644 index 0000000..9757f1a --- /dev/null +++ b/school/intro-crypto/uebung/04/lfsr/target/.rustc_info.json @@ -0,0 +1 @@ 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