Initial commit
This commit is contained in:
Valentin Brandl
28
school/intro-crypto/20181011-classification.dot
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28
school/intro-crypto/20181011-classification.dot
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@ -0,0 +1,28 @@
|
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digraph classification {
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edge [ arrowhead="none" ];
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1 [ label="Kryptologie" ];
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||||
2 [ label="Kryptographie" ];
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||||
3 [ label="Kryptoanalyse" ];
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||||
4 [ label="symmetrische\nChiffren" ];
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||||
5 [ label="asymmetrische\nChiffren" ];
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||||
6 [ label="Protokolle\n& Sonstiges" ];
|
||||
|
||||
{
|
||||
rank=same;
|
||||
2;
|
||||
3;
|
||||
}
|
||||
{
|
||||
rank=same;
|
||||
4;
|
||||
5;
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||||
6;
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||||
}
|
||||
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||||
1 -> 2;
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1 -> 3;
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||||
|
||||
2 -> 4;
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2 -> 5;
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2 -> 6;
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||||
}
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||||
26
school/intro-crypto/20181011_1-intro.md
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26
school/intro-crypto/20181011_1-intro.md
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@ -0,0 +1,26 @@
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||||
---
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||||
title: Intro
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date: 2018-10-11
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---
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||||
|
||||
# Moodle
|
||||
|
||||
**Kursnummer**: 141022
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||||
|
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**Passwort** : krypto1819
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||||
|
||||
# Klausur
|
||||
|
||||
* 10% Bonus durch Übungen, nur wenn bestanden (>49%)
|
||||
* Anmeldung im Prüfungsamt
|
||||
|
||||
## Hilfsmittel
|
||||
|
||||
* Taschenrechner
|
||||
* 1 Seite handschriftlich
|
||||
|
||||
# Übungen
|
||||
|
||||
**Abgabe**: Donnerstag 12:14 Uhr
|
||||
|
||||
Handschriftlich oder LaTeX (Vorlage vorhanden)
|
||||
59
school/intro-crypto/20181011_2-klassifikation.md
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59
school/intro-crypto/20181011_2-klassifikation.md
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@ -0,0 +1,59 @@
|
||||
---
|
||||
title: Klassifikation, Grundlagen, Substitutionschiffre
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date: 2018-10-11
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---
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||||
|
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# Klassifikation der "Kryptographie"
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||||
|
||||
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||||
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## Anwendungen
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* WhatsApp
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* Auto
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* Mensa Karte
|
||||
* Medizinische Geräte
|
||||
* Kreditkarten
|
||||
* mobile Kommunikation
|
||||
* IoT
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||||
* BitCoin
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||||
* Flugzeuge
|
||||
* E-Mail
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||||
* (Schadsoftware)
|
||||
|
||||
# Grundlagen symmetrischer Chiffren
|
||||
|
||||
Einfache Ausgangssituation:
|
||||
|
||||
|
||||
|
||||
* $e \widehat{=}$ Verschlüsselung oder Chiffrierung
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||||
* $d \widehat{=}$ Entschlüsselung oder Dechiffrierung
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||||
* $x \widehat{=}$ Klartext
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||||
* $y \widehat{=}$ Chiffrat
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||||
* $k \widehat{=}$ Schlüssel
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* $\vert k \vert \widehat{=}$ Schlüsselraum
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||||
|
||||
## Kerckhoffs' Prinzip
|
||||
|
||||
> Ein Kryptosystem muss auch dann sicher sein, wenn der Angreifer alle Deteils kennt, bis auf den Schlüssel.
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||||
|
||||
Bei Verletzung der Prinzips: `Security by Obscurity`.
|
||||
|
||||
# Substitutionschiffre
|
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|
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* operiert auf Buchstaben
|
||||
* Prinzip:
|
||||
$$
|
||||
A \to l \\
|
||||
B \to d \\
|
||||
C \to w \\
|
||||
...
|
||||
$$
|
||||
|
||||
**Beispiel**: $ABBA \to^e lddl$
|
||||
|
||||
## Angriffe
|
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|
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1. Häufigkeitsanalyse (Übung)
|
||||
2. Vollständige Schlüsselsuche (Bruteforce): $\vert k \vert = 26! \approx 2^{88}$ Möglichkeiten
|
||||
51
school/intro-crypto/20181011_situation.dot
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51
school/intro-crypto/20181011_situation.dot
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@ -0,0 +1,51 @@
|
||||
digraph situation {
|
||||
rankdir=LR;
|
||||
a [ label="Alice" shape="none" ];
|
||||
b [ label="Bob" shape="none" ];
|
||||
o [ label="Oscar" shape="none" ];
|
||||
i [ label="unsicherer\nKanal" ];
|
||||
e [ label="e" shape="box" ];
|
||||
d [ label="d" shape="box" ];
|
||||
g [ label="Gen" shape="box"];
|
||||
1 [ style="invisible" shape="point" width=0 ];
|
||||
2 [ style="invisible" shape="point" width=0 ];
|
||||
3 [ style="invisible" shape="point" width=0 ];
|
||||
4 [ style="invisible" shape="point" width=0 ];
|
||||
|
||||
{
|
||||
rank=same;
|
||||
a;
|
||||
g;
|
||||
}
|
||||
|
||||
{
|
||||
rank=same;
|
||||
e;
|
||||
1;
|
||||
}
|
||||
|
||||
{
|
||||
rank=same;
|
||||
d;
|
||||
2;
|
||||
}
|
||||
|
||||
{
|
||||
rank=same;
|
||||
i; o;
|
||||
}
|
||||
|
||||
a -> e [ label="x" ];
|
||||
e -> i [ label="y" ];
|
||||
i -> d [ label="y" ];
|
||||
d -> b [ label="x" ];
|
||||
|
||||
g -> 1 [ arrowhead="none" ];
|
||||
1 -> e [ label="k" ];
|
||||
1 -> 3 [ arrowhead="none" ];
|
||||
3 -> 4 [ arrowhead="none"; penwidth=10; label="sicherer Kanal\n " ];
|
||||
4 -> 2 [ arrowhead="none" ];
|
||||
2 -> d [ label="k" ];
|
||||
|
||||
i -> o [ label="y" ];
|
||||
}
|
||||
51
school/intro-crypto/aufgaben/1/20181011_situation.dot
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51
school/intro-crypto/aufgaben/1/20181011_situation.dot
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@ -0,0 +1,51 @@
|
||||
digraph situation {
|
||||
rankdir=LR;
|
||||
a [ label="Alice" shape="none" ];
|
||||
b [ label="Bob" shape="none" ];
|
||||
o [ label="Oscar" shape="none" ];
|
||||
i [ label="unsicherer\nKanal" ];
|
||||
e [ label="e" shape="box" ];
|
||||
d [ label="d" shape="box" ];
|
||||
g [ label="Gen" shape="box"];
|
||||
1 [ style="invisible" shape="point" width=0 ];
|
||||
2 [ style="invisible" shape="point" width=0 ];
|
||||
3 [ style="invisible" shape="point" width=0 ];
|
||||
4 [ style="invisible" shape="point" width=0 ];
|
||||
|
||||
{
|
||||
rank=same;
|
||||
a;
|
||||
g;
|
||||
}
|
||||
|
||||
{
|
||||
rank=same;
|
||||
e;
|
||||
1;
|
||||
}
|
||||
|
||||
{
|
||||
rank=same;
|
||||
d;
|
||||
2;
|
||||
}
|
||||
|
||||
{
|
||||
rank=same;
|
||||
i; o;
|
||||
}
|
||||
|
||||
a -> e [ label="x" ];
|
||||
e -> i [ label="y" ];
|
||||
i -> d [ label="y" ];
|
||||
d -> b [ label="x" ];
|
||||
|
||||
g -> 1 [ arrowhead="none" ];
|
||||
1 -> e [ label="k" ];
|
||||
1 -> 3 [ arrowhead="none" ];
|
||||
3 -> 4 [ arrowhead="none"; penwidth=10; label="sicherer Kanal\n " ];
|
||||
4 -> 2 [ arrowhead="none" ];
|
||||
2 -> d [ label="k" ];
|
||||
|
||||
i -> o [ label="y" ];
|
||||
}
|
||||
BIN
school/intro-crypto/aufgaben/1/Präsenzübung_1_EK1_WS1819.pdf
Normal file
BIN
school/intro-crypto/aufgaben/1/Präsenzübung_1_EK1_WS1819.pdf
Normal file
Binary file not shown.
99
school/intro-crypto/aufgaben/1/a1.tex
Normal file
99
school/intro-crypto/aufgaben/1/a1.tex
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@ -0,0 +1,99 @@
|
||||
\documentclass[12pt,a4paper,german]{article}
|
||||
\usepackage{url}
|
||||
%\usepackage{graphics}
|
||||
\usepackage{times}
|
||||
\usepackage[T1]{fontenc}
|
||||
\usepackage{ngerman}
|
||||
\usepackage[latin1]{inputenc}
|
||||
\usepackage{geometry}
|
||||
\usepackage{amsfonts}
|
||||
\usepackage{amsmath}
|
||||
\usepackage{graphicx}
|
||||
\usepackage{epsfig}
|
||||
\usepackage{paralist}
|
||||
\geometry{left=2.0cm,textwidth=17cm,top=3.5cm,textheight=23cm}
|
||||
|
||||
%%%%%%%%%% Fill out the the definitions %%%%%%%%%
|
||||
\def \name {Valentin Brandl} %
|
||||
\def \matrikel {108018274494} %
|
||||
\def \gruppe {VB} %
|
||||
\def \uebung {1} %
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
|
||||
% 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}
|
||||
}
|
||||
|
||||
\begin{document}
|
||||
%Import header
|
||||
\hwsol
|
||||
|
||||
|
||||
\section*{Aufgabe 1}
|
||||
\begin{enumerate}[(a)]
|
||||
\item
|
||||
\begin{itemize}
|
||||
\item Algorithmen sollen offengelegt werden, nur Schl<68>ssel werden geheim gehalten
|
||||
\item Es ist schwer, einen Algorithmus geheim zu halten
|
||||
\item Prinzip def vielen Augen: ein <20>ffentlicher Algorithmus wird ggf. analysiert und Schwachstellen gefunden
|
||||
\end{itemize}
|
||||
\item
|
||||
\begin{itemize}
|
||||
\item Kryptographie: Entwerfen von Algorithmen und Protokollen
|
||||
\item Kryptoanalyse: Schwachstellen in existierenden Verfahren suchen
|
||||
\end{itemize}
|
||||
|
||||
\item
|
||||
\parbox{\linewidth}{\centering
|
||||
\includegraphics[width=\textwidth]{20181011_situation.png}
|
||||
}
|
||||
Ein Angreifer (Eve) kann die ausgetauschten Nachrichten mitlesen und ver<65>ndern
|
||||
\item
|
||||
\begin{itemize}
|
||||
\item Schl<68>ssel: $k$
|
||||
\item Verschl<68>sselung $e(\cdot)$
|
||||
\item Schl<68>sselraum $\#k = \vert k \vert$
|
||||
\item Chiffrat $y$
|
||||
\item Entschl<68>sselung $d(\cdot)$
|
||||
\item Klartext $x$
|
||||
\end{itemize}
|
||||
\end{enumerate}
|
||||
|
||||
\section*{Aufgabe 2}
|
||||
\begin{enumerate}[(a)]
|
||||
\item $2^{128}$. Mit $2^{10} \approx 10^3 \to 2^{130} \approx 10^{39}$
|
||||
|
||||
\item
|
||||
\begin{itemize}
|
||||
\item 80 Eur pro ASIC
|
||||
\item $10^6$ Eur Kapital
|
||||
\item $7 \cdot 10^8 \frac{k}{s}$ Leistung
|
||||
\end{itemize}
|
||||
\begin{eqnarray*}
|
||||
10^6 / 80 &=& 12500 \\
|
||||
7 \cdot 10^8 \cdot 12500 &=& 8.75 \cdot 10^{12} \frac{k}{s} \\
|
||||
\frac{2^{128}k}{8.75 \cdot 10^{12} \frac{k}{s}} &\approx{}& 3.89 \cdot 10^{25} s \\
|
||||
&\approx{}& 1.23 \cdot 10^{18} y
|
||||
\end{eqnarray*}
|
||||
|
||||
\item
|
||||
\begin{eqnarray*}
|
||||
24 h &=& 86400 s \\
|
||||
\frac{2^{128}}{x} &=& 86400 \\
|
||||
\frac{2^{128}}{86400} &=& x \\
|
||||
x &\approx{}& 3.94 \cdot 10^{33} \text{ gesuchte $\frac{k}{s}$} \\
|
||||
\frac{x}{12500} &\approx{}& 3.15 \cdot 10^{29} \text{ gesuchte $\frac{k}{s}$ pro ASIC} \\
|
||||
\\
|
||||
(7 \cdot 10^8) \cdot 2^n &\geq{}& 3.15 \cdot 10^{29} \\
|
||||
n &\geq{}& 68.6 \approx 69 \text{ (Leistung muss sich 69 mal verdoppeln)} \\
|
||||
69 * 18m &=& 1242m = 103.5 y
|
||||
\end{eqnarray*}
|
||||
In $103.5$ Jahren w<>re man in der Lage alle $2^{128}$ Schl<68>ssel innerhlab von 24h durch zu probieren.
|
||||
\end{enumerate}
|
||||
|
||||
\end{document}
|
||||
|
||||
67
school/intro-crypto/aufgaben/template.tex
Normal file
67
school/intro-crypto/aufgaben/template.tex
Normal file
@ -0,0 +1,67 @@
|
||||
\documentclass[12pt,a4paper,german]{article}
|
||||
\usepackage{url}
|
||||
%\usepackage{graphics}
|
||||
\usepackage{times}
|
||||
\usepackage[T1]{fontenc}
|
||||
\usepackage{ngerman}
|
||||
\usepackage[latin1]{inputenc}
|
||||
\usepackage{geometry}
|
||||
\usepackage{amsfonts}
|
||||
\usepackage{graphicx}
|
||||
\usepackage{epsfig}
|
||||
\usepackage{paralist}
|
||||
\geometry{left=2.0cm,textwidth=17cm,top=3.5cm,textheight=23cm}
|
||||
|
||||
%%%%%%%%%% Fill out the the definitions %%%%%%%%%
|
||||
\def \name {Vorname1 Nachname1} %
|
||||
\def \matrikel {Matrikelnummer1} %
|
||||
\def \pname {Vorname2 Nachname2} %
|
||||
\def \pmatrikel {Matrikelnummer2} %
|
||||
\def \gruppe {Gruppenkuerzel} %
|
||||
\def \uebung {1} %
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
|
||||
% 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}
|
||||
}
|
||||
|
||||
\begin{document}
|
||||
%Import header
|
||||
\hwsol
|
||||
|
||||
|
||||
\section*{Aufgabe 1}
|
||||
\begin{enumerate}[(a)]
|
||||
\item Beispielantwort
|
||||
\item Hier k\"onnte deine Antwort auf diese Teilaufgabe stehen.
|
||||
\item F<>r das Beispiel gilt $b_1=2^4+1=17=(10001)_2$ und $b_2=2^4-1=15=(1111)_2$.
|
||||
\end{enumerate}
|
||||
|
||||
\section*{Aufgabe 2}
|
||||
Notation von mathematischen L\"osungen:
|
||||
\begin{eqnarray*}
|
||||
r_{0} &=& \beta^{K_{X}} \bmod n\\
|
||||
r_{1} &=& \alpha^{K_{X}+1} = \alpha \cdot \alpha^{K_{n}} = \alpha \cdot r_{1} \bmod p\\
|
||||
r_{2} &=& (a_{1}-d \cdot q_{1}) \cdot z_{E}^{-1} \bmod p-1 \Leftrightarrow d = (x_{1}-s_{1} \cdot o_{E}) \cdot r_{1}^{-1} \bmod p-1\\
|
||||
\end{eqnarray*}
|
||||
|
||||
\section*{Aufgabe 3}
|
||||
\begin{center}
|
||||
\begin{tabular}{|c|c|c|c|}
|
||||
\hline
|
||||
Tabellenzeile & Tabellenzeile & Tabellenzeile & Tabellenzeile \\
|
||||
\hline
|
||||
e & f & g & h \\
|
||||
\hline
|
||||
i & j & k & l \\
|
||||
\hline
|
||||
m & n & o & p \\
|
||||
\hline
|
||||
\end{tabular}
|
||||
\end{center}
|
||||
\end{document}
|
||||
|
||||
248
school/intro-crypto/uebung/01/01.tex
Normal file
248
school/intro-crypto/uebung/01/01.tex
Normal file
@ -0,0 +1,248 @@
|
||||
\documentclass[12pt,a4paper,german]{article}
|
||||
\usepackage{url}
|
||||
%\usepackage{graphics}
|
||||
\usepackage{times}
|
||||
\usepackage[T1]{fontenc}
|
||||
\usepackage{ngerman}
|
||||
\usepackage{float}
|
||||
\usepackage{diagbox}
|
||||
\usepackage[latin1]{inputenc}
|
||||
\usepackage{geometry}
|
||||
\usepackage{amsfonts}
|
||||
\usepackage{amsmath}
|
||||
\usepackage{csquotes}
|
||||
\usepackage{graphicx}
|
||||
\usepackage{epsfig}
|
||||
\usepackage{paralist}
|
||||
\geometry{left=2.0cm,textwidth=17cm,top=3.5cm,textheight=23cm}
|
||||
|
||||
%%%%%%%%%% Fill out the the definitions %%%%%%%%%
|
||||
\def \name {Valentin Brandl} %
|
||||
\def \matrikel {108018274494} %
|
||||
% \def \pname {Vorname2 Nachname2} %
|
||||
% \def \pmatrikel {Matrikelnummer2} %
|
||||
\def \gruppe {Gruppenkuerzel} %
|
||||
\def \uebung {1} %
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
|
||||
% 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}
|
||||
}
|
||||
|
||||
\begin{document}
|
||||
%Import header
|
||||
\hwsol
|
||||
|
||||
|
||||
\section*{Aufgabe 2}
|
||||
\begin{enumerate}[(a)]
|
||||
\item
|
||||
\begin{eqnarray*}
|
||||
A &\text{:}& 23 \to{} 0.02 \\
|
||||
B &\text{:}& 5 \to{} 0.00 \\
|
||||
C &\text{:}& 22 \to{} 0.02 \\
|
||||
D &\text{:}& 8 \to{} 0.01 \\
|
||||
E &\text{:}& 17 \to{} 0.02 \\
|
||||
F &\text{:}& 2 \to{} 0.00 \\
|
||||
G &\text{:}& 80 \to{} 0.07 \\
|
||||
J &\text{:}& 66 \to{} 0.06 \\
|
||||
K &\text{:}& 39 \to{} 0.04 \\
|
||||
L &\text{:}& 47 \to{} 0.04 \\
|
||||
M &\text{:}& 2 \to{} 0.00 \\
|
||||
N &\text{:}& 17 \to{} 0.02 \\
|
||||
O &\text{:}& 63 \to{} 0.06 \\
|
||||
P &\text{:}& 80 \to{} 0.07 \\
|
||||
Q &\text{:}& 62 \to{} 0.06 \\
|
||||
R &\text{:}& 57 \to{} 0.05 \\
|
||||
S &\text{:}& 136 \to{} 0.12 \\
|
||||
T &\text{:}& 6 \to{} 0.01 \\
|
||||
U &\text{:}& 57 \to{} 0.05 \\
|
||||
V &\text{:}& 6 \to{} 0.01 \\
|
||||
W &\text{:}& 76 \to{} 0.07 \\
|
||||
X &\text{:}& 25 \to{} 0.02 \\
|
||||
Y &\text{:}& 8 \to{} 0.01 \\
|
||||
Z &\text{:}& 83 \to{} 0.08 \\
|
||||
\text{\"A} &\text{:}& 43 \to{} 0.04 \\
|
||||
\text{\"O} &\text{:}& 14 \to{} 0.01 \\
|
||||
\text{\"U} &\text{:}& 28 \to{} 0.03 \\
|
||||
\text{<EFBFBD>} &\text{:}& 18 \to{} 0.02 \\
|
||||
sum &\text{:}& 1090
|
||||
\end{eqnarray*}
|
||||
|
||||
\item
|
||||
\begin{displayquote}
|
||||
gr<67>ndlich durchgecheckt steht sie da \\
|
||||
und wartet auf den start - alles klar! \\
|
||||
experten streiten sich um ein paar daten \\
|
||||
die crew hat da noch ein paar fragen \\
|
||||
doch der countdown l<>uft \\
|
||||
\end{displayquote}
|
||||
|
||||
\item
|
||||
\begin{tabular}{|c|c|}
|
||||
\hline
|
||||
von & zu \\\hline
|
||||
A & f \\
|
||||
B & <20> \\
|
||||
C & g \\
|
||||
D & j \\
|
||||
E & <20> \\
|
||||
F & x \\
|
||||
G & n \\
|
||||
J & i \\
|
||||
K & m \\
|
||||
L & c \\
|
||||
M & <20> \\
|
||||
N & v \\
|
||||
O & d \\
|
||||
P & r \\
|
||||
Q & a \\
|
||||
R & l \\
|
||||
S & e \\
|
||||
T & <20> \\
|
||||
U & h \\
|
||||
V & z \\
|
||||
W & t \\
|
||||
X & w \\
|
||||
Y & p \\
|
||||
Z & s \\
|
||||
<09> & o \\
|
||||
<09> & b \\
|
||||
<09> & u \\
|
||||
<09> & k \\
|
||||
H/I & q/y \\
|
||||
\hline
|
||||
\end{tabular}
|
||||
|
||||
Weder H noch I kommen im Ciphertext vor, daher ist es nicht m<>glich, die Substitution von H/I eindeutig zu
|
||||
bestimmen. Da jedoch auch weder q noch y im Plaintext vorkommen, muss entweder $H \to q \text{ und } I \to y$
|
||||
oder $H \to y \text{ und } I \to q$ gelten.
|
||||
|
||||
\item $30! = \vert \{A,B,...Z,\text{<EFBFBD>},\text{<EFBFBD>},\text{<EFBFBD>},\text{<EFBFBD>}\} \vert!$
|
||||
|
||||
\item Name des Textes: Major Tom (v<>llig losgel<65>st) \\
|
||||
Erscheinungsjahr: 1982
|
||||
|
||||
\end{enumerate}
|
||||
|
||||
\section*{Aufgabe 3}
|
||||
\begin{enumerate}[(a)]
|
||||
\item $2^{63} = 9,223,372,036,854,775,808$
|
||||
\item $2^{63} * 0.03g = 276,701,161,105,643,260g \approx 276,701,161,106t$ \\
|
||||
$277 \cdot 10^9 / 460 \cdot 10^6 \approx 602 \Rightarrow$ mehr als das 600-fache der j<>hrlichen Reisernte
|
||||
|
||||
\item $2^{10} * 0.1mm = 102.4mm = 1.204m$
|
||||
|
||||
\item
|
||||
\begin{eqnarray*}
|
||||
2^n * 0.1mm &\geq{}& 1,000,000mm \\
|
||||
2^n &\geq{}& 10000000 \\
|
||||
n &\geq{}& 24
|
||||
\end{eqnarray*}
|
||||
Man muss das Blatt 24 mal falten.
|
||||
|
||||
\item
|
||||
\begin{eqnarray*}
|
||||
2^n * 0.1mm &\geq{}& 384,400,000,000mm \\
|
||||
2^n &\geq{}& 3,844,000,000,000 \\
|
||||
n &\geq{}& 42
|
||||
\end{eqnarray*}
|
||||
Man muss das Blatt 42 mal falten.
|
||||
|
||||
\item
|
||||
\begin{eqnarray*}
|
||||
2^n * 0.1mm &\geq{}& 9,460,730,472,580,800,000mm \\
|
||||
2^n &\geq{}& 94,607,304,725,808,000,000mm \\
|
||||
n &\geq{}& 67
|
||||
\end{eqnarray*}
|
||||
Man muss das Blatt 67 mal falten.
|
||||
\end{enumerate}
|
||||
|
||||
\section*{Aufgabe 4}
|
||||
\begin{enumerate}[(a)]
|
||||
\item $2^n$
|
||||
|
||||
\item $\frac{2^n}{2}$
|
||||
|
||||
\item Gerechnet mit $1y = 365d$
|
||||
\begin{figure}[h]
|
||||
\begin{tabular}{|l|l|l|l|}
|
||||
\hline
|
||||
\diagbox{Case}{$n$} & 80 & 112 & 192 \\\hline
|
||||
Worst Case & $2.50 * 10^8y$ & $1.08 * 10^{18}y$ & $1.30 * 10^{42}y$ \\\hline
|
||||
Average Case & $1.25 * 10^8y$ & $5.38 * 10^{17}y$ & $6.50 * 10^{41}y$ \\\hline
|
||||
\end{tabular}
|
||||
\caption{GPU}
|
||||
\end{figure}
|
||||
|
||||
\begin{figure}[h]
|
||||
\begin{tabular}{|l|l|l|l|}
|
||||
\hline
|
||||
\diagbox{Case}{$n$} & 80 & 112 & 192 \\\hline
|
||||
Worst Case & $5.81 * 10^7y$ & $2.49 * 10^{17}y$ & $3.02 * 10^{41}y$ \\\hline
|
||||
Average Case & $2.90 * 10^7y$ & $1.25 * 10^{17}y$ & $1.51 * 10^{41}y$ \\\hline
|
||||
\end{tabular}
|
||||
\caption{Amazon Cloud}
|
||||
\end{figure}
|
||||
|
||||
\begin{figure}[h]
|
||||
\begin{tabular}{|l|l|l|l|}
|
||||
\hline
|
||||
\diagbox{Case}{$n$} & 80 & 112 & 192 \\\hline
|
||||
Worst Case & $3.41 * 10^7y$ & $1.46 * 10^{17}y$ & $1.77 * 10^{41}y$ \\\hline
|
||||
Average Case & $1.70 * 10^7y$ & $7.32 * 10^{16}y$ & $8.85 * 10^{40}y$ \\\hline
|
||||
\end{tabular}
|
||||
\caption{FPGA}
|
||||
\end{figure}
|
||||
|
||||
\item Unter Anwendung der Erkenntnisse aus e):
|
||||
\begin{eqnarray*}
|
||||
n &=& 80 \\
|
||||
n + w &=& 112 \\
|
||||
w &=& 32 \\
|
||||
x &=& \frac{2^{112} - 2^{80}}{r} \\
|
||||
\end{eqnarray*}
|
||||
|
||||
\begin{itemize}
|
||||
\item $r_{GPU} = 15.3 * 10^7 \frac{k}{s}$
|
||||
\item $r_{Amazon} = 66 * 10^7 \frac{k}{s}$
|
||||
\item $r_{FPGA} = 11.25 * 10^8 \frac{k}{s}$
|
||||
\end{itemize}
|
||||
|
||||
\begin{eqnarray*}
|
||||
x_{GPU} &=& 1.06 * 10^{18}y \\
|
||||
x_{Amazon} &=& 2.49 * 10^{17}y \\
|
||||
x_{FPGA} &=& 1.46 * 10^{17}y \\
|
||||
\end{eqnarray*}
|
||||
|
||||
\item
|
||||
\begin{itemize}
|
||||
\item $r$: Anzahl der Versuche pro Sekunde
|
||||
\item $n$: Aktuelle Bit L<>nge der Schl<68>ssel
|
||||
\item $w$: Verl<72>ngerung der Schl<68>ssell<6C>nge um $w$ Bit
|
||||
\item $x$: Gesucht: Wie viel langsamer der Angriff wird
|
||||
\end{itemize}
|
||||
\begin{eqnarray*}
|
||||
\frac{2^n}{r} + x &=& \frac{2^{n+w}}{r} \\
|
||||
x &=& \frac{2^{n+w} - 2^n}{r} \\
|
||||
x &=& \frac{2^n(2^w-1)}{r}
|
||||
\end{eqnarray*}
|
||||
|
||||
\item
|
||||
\begin{eqnarray*}
|
||||
183d &=& 4392h \\\\
|
||||
\frac{4392}{2^n} &\leq{}& 1 \\
|
||||
n &\geq{}& 13 \Rightarrow \text{ 13 Verdoppelungen der Rechenleistung} \\\\
|
||||
13 * 18m &=& 234 m = 19.5y \approx 20y \\
|
||||
1992 + 20 &=& 2012
|
||||
\end{eqnarray*}
|
||||
|
||||
Seit dem Jahr 2012 sollte es m<>glich sein, 50-bit Keys in weniger als 1 Stunde zu Bruteforcen.
|
||||
\end{enumerate}
|
||||
|
||||
\end{document}
|
||||
|
||||
60
school/intro-crypto/uebung/01/chiffrat.txt
Normal file
60
school/intro-crypto/uebung/01/chiffrat.txt
Normal file
@ -0,0 +1,60 @@
|
||||
CPTGORJLU OÜPLUCSLUSLßW ZWSUW ZJS OQ
|
||||
ÜGO XQPWSW QÜA OSG ZWQPW - QRRSZ ßRQP!
|
||||
SFYSPWSG ZWPSJWSG ZJLU ÜK SJG YQQP OQWSG
|
||||
OJS LPSX UQW OQ GÄLU SJG YQQP APQCSG
|
||||
OÄLU OSP LÄÜGWOÄXG RBÜAW
|
||||
|
||||
SAASßWJNJWBW ÖSZWJKKW OQZ UQGOSRG
|
||||
KQG NSPRBZZW ZJLU ÖRJGO QÜA OSG QGOSP'G
|
||||
DSOSP XSJM CSGQÜ, XQZ NÄG JUK QÖUBGCW
|
||||
DSOSP JZW JK ZWPSZZ, OÄLU KQDÄP WÄK
|
||||
KQLUW SJGSG ZLUSPV
|
||||
OQGG USÖW SP QÖ ÜGO
|
||||
|
||||
NERRJC RÄZCSREZW
|
||||
NÄG OSP SPOS
|
||||
ZLUXSÖW OQZ PQÜKZLUJAA
|
||||
NERRJC ZLUXSPSRÄZ
|
||||
|
||||
|
||||
OJS SPOQGVJSUÜGCZßPQAW JZW TÖSPXÜGOSG
|
||||
QRRSZ RBÜAW YSPASßW, ZLUÄG ZSJW ZWÜGOSG
|
||||
XJZZSGZLUQAWRJLUS SFYSPJKSGWS
|
||||
OÄLU XQZ GTWVSG OJS QK SGOS, OSGßW
|
||||
ZJLU KQDÄP WÄK
|
||||
|
||||
JK ßÄGWPÄRRVSGWPÜK, OQ XJPO KQG YQGJZLU
|
||||
OSP ßÜPZ OSP ßQYZSR, OSP ZWJKKW DQ CQP GJLUW
|
||||
"UQRRÄ KQDÄP WÄK, ßEGGSG ZJS UEPSG
|
||||
XÄRR'G ZJS OQZ YPÄDSßW OSGG ZÄ VSPZWEPSG?"
|
||||
OÄLU SP ßQGG GJLUWZ UEP'G
|
||||
SP ZLUXSÖW XSJWSP
|
||||
|
||||
NERRJC RÄZCSREZW
|
||||
NÄG OSP SPOS
|
||||
ZLUXSÖW OQZ PQÜKZLUJAA
|
||||
NERRJC ZLUXSPSRÄZ
|
||||
|
||||
OJS SPOS ZLUJKKSPW ÖRQÜ, ZSJG RSWVWSP AÜGß ßÄKKW
|
||||
"CPTMW KJP KSJGS APQÜ", ÜGO SP NSPZWÜKKW
|
||||
|
||||
ÜGWSG WPQÜSPG GÄLU OJS SCÄJZWSG
|
||||
KQDÄP WÄK OSGßW ZJLU, XSGG OJS XTZZWSG
|
||||
KJLU ATUPW UJSP SJG RJLUW OÜPLU OQZ QRR
|
||||
OQZ ßSGGW JUP GÄLU GJLUW, JLU ßÄKKS ÖQRO
|
||||
KJP XJPO ßQRW
|
||||
|
||||
NERRJC RÄZCSREZW
|
||||
NÄG OSP SPOS
|
||||
ZLUXSÖW OQZ PQÜKZLUJAA
|
||||
ZLUXSPSRÄZ
|
||||
|
||||
NERRJC RÄZCSREZW
|
||||
NÄG OSP SPOS
|
||||
ZLUXSÖW OQZ PQÜKZLUJAA
|
||||
ZLUXSPSRÄZ
|
||||
|
||||
NERRJC RÄZCSREZW
|
||||
NÄG OSP SPOS
|
||||
ZLUXSÖW OQZ PQÜKZLUJAA
|
||||
NERRJC ZLUXSPSRÄZ
|
||||
30
school/intro-crypto/uebung/01/table.txt
Normal file
30
school/intro-crypto/uebung/01/table.txt
Normal file
@ -0,0 +1,30 @@
|
||||
A & f \\
|
||||
B & ä \\
|
||||
C & g \\
|
||||
D & j \\
|
||||
E & ö \\
|
||||
F & x \\
|
||||
G & n \\
|
||||
J & i \\
|
||||
K & m \\
|
||||
L & c \\
|
||||
M & ß \\
|
||||
N & v \\
|
||||
O & d \\
|
||||
P & r \\
|
||||
Q & a \\
|
||||
R & l \\
|
||||
S & e \\
|
||||
T & ü \\
|
||||
U & h \\
|
||||
V & z \\
|
||||
W & t \\
|
||||
X & w \\
|
||||
Y & p \\
|
||||
Z & s \\
|
||||
Ä & o \\
|
||||
Ö & b \\
|
||||
Ü & u \\
|
||||
ß & k \\
|
||||
? & q \\
|
||||
? & y \\
|
||||
2
school/intro-crypto/uebung/01/u01/.gitignore
vendored
Normal file
2
school/intro-crypto/uebung/01/u01/.gitignore
vendored
Normal file
@ -0,0 +1,2 @@
|
||||
/target
|
||||
**/*.rs.bk
|
||||
32
school/intro-crypto/uebung/01/u01/Cargo.lock
generated
Normal file
32
school/intro-crypto/uebung/01/u01/Cargo.lock
generated
Normal file
@ -0,0 +1,32 @@
|
||||
[[package]]
|
||||
name = "countmap"
|
||||
version = "0.2.0"
|
||||
source = "registry+https://github.com/rust-lang/crates.io-index"
|
||||
dependencies = [
|
||||
"num-traits 0.1.43 (registry+https://github.com/rust-lang/crates.io-index)",
|
||||
]
|
||||
|
||||
[[package]]
|
||||
name = "num-traits"
|
||||
version = "0.1.43"
|
||||
source = "registry+https://github.com/rust-lang/crates.io-index"
|
||||
dependencies = [
|
||||
"num-traits 0.2.6 (registry+https://github.com/rust-lang/crates.io-index)",
|
||||
]
|
||||
|
||||
[[package]]
|
||||
name = "num-traits"
|
||||
version = "0.2.6"
|
||||
source = "registry+https://github.com/rust-lang/crates.io-index"
|
||||
|
||||
[[package]]
|
||||
name = "u01"
|
||||
version = "0.1.0"
|
||||
dependencies = [
|
||||
"countmap 0.2.0 (registry+https://github.com/rust-lang/crates.io-index)",
|
||||
]
|
||||
|
||||
[metadata]
|
||||
"checksum countmap 0.2.0 (registry+https://github.com/rust-lang/crates.io-index)" = "1ef2a403c4af585607826502480ab6e453f320c230ef67255eee21f0cc72c0a6"
|
||||
"checksum num-traits 0.1.43 (registry+https://github.com/rust-lang/crates.io-index)" = "92e5113e9fd4cc14ded8e499429f396a20f98c772a47cc8622a736e1ec843c31"
|
||||
"checksum num-traits 0.2.6 (registry+https://github.com/rust-lang/crates.io-index)" = "0b3a5d7cc97d6d30d8b9bc8fa19bf45349ffe46241e8816f50f62f6d6aaabee1"
|
||||
7
school/intro-crypto/uebung/01/u01/Cargo.toml
Normal file
7
school/intro-crypto/uebung/01/u01/Cargo.toml
Normal file
@ -0,0 +1,7 @@
|
||||
[package]
|
||||
name = "u01"
|
||||
version = "0.1.0"
|
||||
authors = ["Valentin Brandl <vbrandl@riseup.net>"]
|
||||
|
||||
[dependencies]
|
||||
countmap = "0.2.0"
|
||||
81
school/intro-crypto/uebung/01/u01/src/main.rs
Normal file
81
school/intro-crypto/uebung/01/u01/src/main.rs
Normal file
@ -0,0 +1,81 @@
|
||||
extern crate countmap;
|
||||
|
||||
use countmap::CountMap;
|
||||
use std::{
|
||||
fs::File,
|
||||
io::{BufRead, BufReader},
|
||||
};
|
||||
|
||||
fn count() {
|
||||
let args: Vec<_> = std::env::args().collect();
|
||||
let file = args.get(1).unwrap();
|
||||
let mut map: CountMap<char, u32> = CountMap::new();
|
||||
let read = BufReader::new(File::open(file).unwrap());
|
||||
for line in read.lines() {
|
||||
if let Ok(line) = line {
|
||||
line.chars().filter(|c| c.is_alphabetic()).for_each(|c| {
|
||||
map.insert_or_increment(c);
|
||||
});
|
||||
}
|
||||
}
|
||||
let sum: u32 = map
|
||||
.iter()
|
||||
.filter(|(k, _)| k.is_alphabetic())
|
||||
.map(|(_, v)| v)
|
||||
.sum();
|
||||
let mut vec: Vec<_> = map.into_iter().collect();
|
||||
vec.sort_unstable();
|
||||
vec.into_iter().for_each(|(k, v)| {
|
||||
println!(
|
||||
"{} &\\text{{:}}& {:3} \\to{{}} {:.2} \\\\",
|
||||
k,
|
||||
v,
|
||||
v as f64 / sum as f64
|
||||
)
|
||||
});
|
||||
println!("sum &\\text{{:}}& {}", sum);
|
||||
}
|
||||
|
||||
fn main() {
|
||||
let args: Vec<_> = std::env::args().collect();
|
||||
let file = args.get(1).unwrap();
|
||||
let read = BufReader::new(File::open(file).unwrap());
|
||||
for line in read.lines() {
|
||||
if let Ok(line) = line {
|
||||
let s: String = line
|
||||
.chars()
|
||||
.map(|c| match c {
|
||||
'A' => 'f',
|
||||
'B' => 'ä',
|
||||
'C' => 'g',
|
||||
'D' => 'j',
|
||||
'E' => 'ö',
|
||||
'F' => 'x',
|
||||
'G' => 'n',
|
||||
'J' => 'i',
|
||||
'K' => 'm',
|
||||
'L' => 'c',
|
||||
'M' => 'ß',
|
||||
'N' => 'v',
|
||||
'O' => 'd',
|
||||
'P' => 'r',
|
||||
'Q' => 'a',
|
||||
'R' => 'l',
|
||||
'S' => 'e',
|
||||
'T' => 'ü',
|
||||
'U' => 'h',
|
||||
'V' => 'z',
|
||||
'W' => 't',
|
||||
'X' => 'w',
|
||||
'Y' => 'p',
|
||||
'Z' => 's',
|
||||
'Ä' => 'o',
|
||||
'Ö' => 'b',
|
||||
'Ü' => 'u',
|
||||
'ß' => 'k',
|
||||
c => c,
|
||||
}).collect();
|
||||
println!("{}", s);
|
||||
}
|
||||
}
|
||||
}
|
||||
BIN
school/intro-crypto/uebung/01/Übung_1_EK1_WS1819.pdf
Normal file
BIN
school/intro-crypto/uebung/01/Übung_1_EK1_WS1819.pdf
Normal file
Binary file not shown.
67
school/intro-crypto/uebung/template.tex
Normal file
67
school/intro-crypto/uebung/template.tex
Normal file
@ -0,0 +1,67 @@
|
||||
\documentclass[12pt,a4paper,german]{article}
|
||||
\usepackage{url}
|
||||
%\usepackage{graphics}
|
||||
\usepackage{times}
|
||||
\usepackage[T1]{fontenc}
|
||||
\usepackage{ngerman}
|
||||
\usepackage[latin1]{inputenc}
|
||||
\usepackage{geometry}
|
||||
\usepackage{amsfonts}
|
||||
\usepackage{graphicx}
|
||||
\usepackage{epsfig}
|
||||
\usepackage{paralist}
|
||||
\geometry{left=2.0cm,textwidth=17cm,top=3.5cm,textheight=23cm}
|
||||
|
||||
%%%%%%%%%% Fill out the the definitions %%%%%%%%%
|
||||
\def \name {Vorname1 Nachname1} %
|
||||
\def \matrikel {Matrikelnummer1} %
|
||||
\def \pname {Vorname2 Nachname2} %
|
||||
\def \pmatrikel {Matrikelnummer2} %
|
||||
\def \gruppe {Gruppenkuerzel} %
|
||||
\def \uebung {1} %
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
|
||||
% 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}
|
||||
}
|
||||
|
||||
\begin{document}
|
||||
%Import header
|
||||
\hwsol
|
||||
|
||||
|
||||
\section*{Aufgabe 1}
|
||||
\begin{enumerate}[(a)]
|
||||
\item Beispielantwort
|
||||
\item Hier k\"onnte deine Antwort auf diese Teilaufgabe stehen.
|
||||
\item F<>r das Beispiel gilt $b_1=2^4+1=17=(10001)_2$ und $b_2=2^4-1=15=(1111)_2$.
|
||||
\end{enumerate}
|
||||
|
||||
\section*{Aufgabe 2}
|
||||
Notation von mathematischen L\"osungen:
|
||||
\begin{eqnarray*}
|
||||
r_{0} &=& \beta^{K_{X}} \bmod n\\
|
||||
r_{1} &=& \alpha^{K_{X}+1} = \alpha \cdot \alpha^{K_{n}} = \alpha \cdot r_{1} \bmod p\\
|
||||
r_{2} &=& (a_{1}-d \cdot q_{1}) \cdot z_{E}^{-1} \bmod p-1 \Leftrightarrow d = (x_{1}-s_{1} \cdot o_{E}) \cdot r_{1}^{-1} \bmod p-1\\
|
||||
\end{eqnarray*}
|
||||
|
||||
\section*{Aufgabe 3}
|
||||
\begin{center}
|
||||
\begin{tabular}{|c|c|c|c|}
|
||||
\hline
|
||||
Tabellenzeile & Tabellenzeile & Tabellenzeile & Tabellenzeile \\
|
||||
\hline
|
||||
e & f & g & h \\
|
||||
\hline
|
||||
i & j & k & l \\
|
||||
\hline
|
||||
m & n & o & p \\
|
||||
\hline
|
||||
\end{tabular}
|
||||
\end{center}
|
||||
\end{document}
|
||||
|
||||
Reference in New Issue
Block a user