From 6bd94983a72cd4880341aaa807e5e4b08ac8f286 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Paul=20L=C3=B6dige?= Date: Tue, 15 Sep 2020 21:41:25 +0200 Subject: [PATCH] finished 3DES. Continue on Skript 2 Page 38(44) --- .vscode/settings.json | 6 ++ Zusammenfassung_DC.aux | 9 +++ Zusammenfassung_DC.fdb_latexmk | 76 +++++++++++--------- Zusammenfassung_DC.fls | 19 ++++- Zusammenfassung_DC.log | 63 +++++++++++----- Zusammenfassung_DC.pdf | Bin 2447532 -> 2512320 bytes Zusammenfassung_DC.synctex.gz | Bin 146919 -> 162900 bytes Zusammenfassung_DC.toc | 7 ++ chapters/Blockverschlüsselungsverfahren.tex | 71 ++++++++++++++++-- chapters/Stromverschlüsselungsverfahren.tex | 2 +- images/3DES.png | Bin 0 -> 21419 bytes images/CFB.png | Bin 0 -> 13020 bytes images/OFB.png | Bin 0 -> 13567 bytes 13 files changed, 193 insertions(+), 60 deletions(-) create mode 100644 .vscode/settings.json create mode 100644 images/3DES.png create mode 100644 images/CFB.png create mode 100644 images/OFB.png diff --git a/.vscode/settings.json b/.vscode/settings.json new file mode 100644 index 0000000..4f424c3 --- /dev/null +++ b/.vscode/settings.json @@ -0,0 +1,6 @@ +{ + "cSpell.words": [ + "Brute", + "parity" + ] +} \ No newline at end of file diff --git a/Zusammenfassung_DC.aux b/Zusammenfassung_DC.aux index 98679f3..aa0723f 100644 --- a/Zusammenfassung_DC.aux +++ b/Zusammenfassung_DC.aux @@ -89,6 +89,7 @@ \@writefile{lof}{\addvspace {10\p@ }} \@writefile{lot}{\addvspace {10\p@ }} \@writefile{toc}{\contentsline {section}{\numberline {5.1}Synchrone Stromverschlüsselungsverfahren}{16}\protected@file@percent } +\newlabel{synchrone Stromverschlüsselung}{{5.1}{16}} \@writefile{toc}{\contentsline {section}{\numberline {5.2}Zustandsabhängige Stromverschlüsselungsverfahren}{17}\protected@file@percent } \newlabel{zustandsabhängige Stromverschlüsselung}{{5.2}{17}} \@writefile{toc}{\contentsline {subsection}{\numberline {5.2.1}Additive zustandsabhängige Stromverschlüsselungsverfahren}{18}\protected@file@percent } @@ -111,3 +112,11 @@ \@writefile{toc}{\contentsline {subsubsection}{\numberline {6.2.3.2}CBC-CS2}{25}\protected@file@percent } \@writefile{toc}{\contentsline {subsubsection}{\numberline {6.2.3.3}CBC-CS3}{25}\protected@file@percent } \@writefile{toc}{\contentsline {subsection}{\numberline {6.2.4}CTR (Counter)}{25}\protected@file@percent } +\@writefile{toc}{\contentsline {subsection}{\numberline {6.2.5}OFB (Output Feedback)}{25}\protected@file@percent } +\newlabel{OFB}{{6.2.5}{25}} +\@writefile{toc}{\contentsline {subsubsection}{\numberline {6.2.5.1}OFB-8$n$}{26}\protected@file@percent } +\@writefile{toc}{\contentsline {subsection}{\numberline {6.2.6}CFB (Cipher-Feedback)}{26}\protected@file@percent } +\@writefile{toc}{\contentsline {subsubsection}{\numberline {6.2.6.1}CFB-8$n$}{26}\protected@file@percent } +\@writefile{toc}{\contentsline {section}{\numberline {6.3}Konstruktionsprinzipien von Blockverschlüsselungsverfahren}{27}\protected@file@percent } +\@writefile{toc}{\contentsline {section}{\numberline {6.4}DES und Tripple-DES}{27}\protected@file@percent } +\@writefile{toc}{\contentsline {subsection}{\numberline {6.4.1}Triple-DES (3DES)}{27}\protected@file@percent } diff --git a/Zusammenfassung_DC.fdb_latexmk b/Zusammenfassung_DC.fdb_latexmk index d531cfb..6258f50 100644 --- a/Zusammenfassung_DC.fdb_latexmk +++ b/Zusammenfassung_DC.fdb_latexmk @@ -1,33 +1,8 @@ # Fdb version 3 -["pdflatex"] 1600097658 "/home/paul/Documents/TH/Datensicherheit (DC)/Zusammenfassung/Zusammenfassung_DC.tex" "/home/paul/Documents/TH/Datensicherheit (DC)/Zusammenfassung/Zusammenfassung_DC.pdf" "Zusammenfassung_DC" 1600097698 - 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{subsection}{\numberline {6.2.5}OFB (Output Feedback)}{25}% +\contentsline {subsubsection}{\numberline {6.2.5.1}OFB-8$n$}{26}% +\contentsline {subsection}{\numberline {6.2.6}CFB (Cipher-Feedback)}{26}% +\contentsline {subsubsection}{\numberline {6.2.6.1}CFB-8$n$}{26}% +\contentsline {section}{\numberline {6.3}Konstruktionsprinzipien von Blockverschlüsselungsverfahren}{27}% +\contentsline {section}{\numberline {6.4}DES und Tripple-DES}{27}% +\contentsline {subsection}{\numberline {6.4.1}Triple-DES (3DES)}{27}% diff --git a/chapters/Blockverschlüsselungsverfahren.tex b/chapters/Blockverschlüsselungsverfahren.tex index c29573a..2a3d0c4 100644 --- a/chapters/Blockverschlüsselungsverfahren.tex +++ b/chapters/Blockverschlüsselungsverfahren.tex @@ -73,13 +73,72 @@ Dies geschieht ungeachtet davon, ob die Länge der Nachricht $m$ ein Vielfaches der Blocklänge $l$ ist. \subsection{CTR (Counter)} - Im CTR-Modus wird ein Blockverschlüsselungsverfahren $E$ mit einem Schlüssel $k$ und einem Nonce-Wert $Ctr\in\mathscr M$ wie folgt verwendet: + Im CTR-Modus wird ein Blockverschlüsselungsverfahren $E$ mit einem Schlüssel $k$ und einem Nonce-Wert $Ctr\in\mathscr M$ wie folgt verwendet: $$\begin{aligned} - c_i :=&m_i+E_k(Ctr\boxplus(i-1)) + c_i :=&m_i+E_k(Ctr\boxplus(i-1))\\ E-CTR_{k,Ctr}(m_1,...,m_r):=&(c_1,...,c_r) - \end{aligned}$$ - Der CTR-Modus definiert ein synchrones additives Stromverschlüsselungsverfahren (siehe \ref{synchron additive Stromverschlüsselung}). - Die Menge der $z_i=E_k(Ctr\boxplus(i-1))$ definiert hierbei den Schlüsselstrom.\\ + \end{aligned}$$ + Der CTR-Modus definiert ein synchrones additives Stromverschlüsselungsverfahren (siehe \ref{synchron additive Stromverschlüsselung}). + Die Menge der $z_i=E_k(Ctr\boxplus(i-1))$ definiert hierbei den Schlüsselstrom.\\ Aufgrund dessen ist die Entschlüsselungsfunktion $D$ gleich der Verschlüsselungsfunktion $E$: $$D-CTR_{k,Ctr}(c_1,...,c_r)=E-CTR_{k,Ctr}(c_1,...,c_r)$$ - \includegraphics{CTR.png} \ No newline at end of file + \includegraphics{CTR.png} + + \subsection{OFB (Output Feedback)}\label{OFB} + Bei der Konstruktion im OFB-Modus handelt es sich um ein synchrones Stromverschlüsselungsverfahren (siehe \ref{synchrone Stromverschlüsselung}) + Hierbei wird die Ausgabe der Verschlüsselungsfunktion jeweils als Eingabe für die nächste Verschlüsselungsfunktion genutzt:\\ + \includegraphics{OFB.png}\\ + + \subsubsection{OFB-8$n$} + bei dieser Variante des des OFB-Modus werden immer nur $n\in\mathbb{N}$ Bytes des verschlüsselten Blocks in der XOR-Verknüpfung genutzt. + Der Rest des Klartextblocks wird in den folgenden Schritten verschlüsselt. + $n$ darf hierbei maximal so groß wie die Blocklänge $l$ der Verschlüsselungsfunktion $E$ sein. + + \subsection{CFB (Cipher-Feedback)} + Der CFB-Modus hat viele Ähnlichkeiten mit dem OFB-Modus (siehe \ref{OFB}). + Allerdings wird hierbei immer der verschlüsselte Block als Eingabe für die jeweils nächste Verschlüsselungsfunktion genutzt. + Anders als beim OFB-Modus handelt es sich beim CFB-Modus aufgrund der Nutzung der Geheimtextblöcke nicht um eine synchrone Stromverschlüsselung.\\ + \includegraphics{CFB.png} + + \subsubsection{CFB-8$n$} + Diese Sonderfunktion des CFB-Modus stellt das Pendant zum OFB-8$n$-Modus im OFB-Modus (siehe \ref{OFB}) dar. + \section{Konstruktionsprinzipien von Blockverschlüsselungsverfahren} + Alle Blockverschlüsselungsverfahren führen innerhalb des jeweiligen Blocks Permutationen aus. + Diese Permutationen werden in Schleifen (Runden) angewandt. + Die Permutationen können in folgende elementare Operationen zusammengefasst werden: + \begin{itemize} + \item \textit{Transpositionen} von Bitwerten innerhalb eines Blocks + \item \textit{Substitution} von Werten innerhalb kleinerer Teilblöcke. + Hierbei handelt es sich um eine Abbildung, welche durch eine Rechenvorschrift oder eine Wertetabelle gegeben werden kann. + Wertetabellen werden in diesem Zusammenhang auch als \textit{S-Boxen} bezeichnet. + \end{itemize} + Zudem findet der Schlüssel $k$ ebenfalls eine Berücksichtigung. + Aus ihm werden Rundenschlüssel $k_i$ mit $i\in\{1,...,r\}$ abgeleitet, welche bei jeder Runde mit in die Berechnung einfließen. + Bei einer Entschlüsselung wird das durch die Runden beschriebene Verfahren einfach rückwärts angewandt. + + \section{DES und Tripple-DES} + Das einfach DES wurde 1977 veröffentlicht und 2005 zurückgezogen. + Sowohl die Blöcke als auch die Schlüssel setzten sich jeweils aus 8 Bytes zusammen: + $$\begin{aligned} + \mathscr M=&({\mathbb{Z}_2}^8)^8=\{(m_1,...m_8)\mid m_i\in{\mathbb{Z}_2}^8\}\\ + \mathscr K=&\{(k_1,...k_8)\mid k_i\in{\mathbb{Z}_2}^8,\text{parity}(k_i)=1\}\subseteq ({\mathbb{Z}_2}^8)^8 + \end{aligned}$$ + Die Parität ist definiert durch: + $${\mathbb{Z}_2}^8\rightarrow\mathbb{Z}_2 \hspace{5mm} \text{parity}\left(\sum_{i=0}^7 b_i\cdot 2^i\right)=\left(\sum_{i=0}^7 b_i\right)\mod 2$$ + Mit anderen Worten: \say{Die Anzahl der 1-Bits im Byte muss ungerade sein}\\ + Durch die Parität ist der Wert des achten Bits schon festgelegt. + Aufgrund dessen ist hat der Schlüsselraum eine Bitlänge von $8\cdot 7=56$. + Da dies für moderne PCs mithilfe eines Brute-Force-Angriffs (siehe \ref{brute-force}) in trivialer Zeit zu knacken ist sollte DES nicht mehr verwendet werden. + + \subsection{Triple-DES (3DES)} + Beim Triple-DES wird das DES verfahren 3mal hintereinander ausgeführt. + Üblicherweise im EDE-Modus (Encrypt-Decrypt-Encrypt) mit 16Byte langen Schlüsseln. + Dadurch ergibt sich für den Schlüsselraum eine effektive Länge von 112 Bits. + Die Menge der 8-Byte-langen Blöcke und der Schlüsselraum definieren sich wie folgt: + $$\begin{aligned} + \mathscr M=&({\mathbb{Z}_2}^8)^8=\{(m_1,...m_8)\mid m_i\in{\mathbb{Z}_2}^8\}\\ + \mathscr K=&\{(k_1,...k_8)\mid k_i\in{\mathbb{Z}_2}^8,\text{parity}(k_i)=1\}^{\color{red}{\mathbf{2}}} + \end{aligned}$$ + Die 3-DES Entschlüsselungsfunktion definiert sich durch: + $$E((k^{(1)},k^{(2)},m)) := E_{DES}\left(k^{(1)},D_{DES}\left(k^{(2)},E_{DES}\left(k^{(1)},m \right)\right)\right)$$ + \includegraphics[scale=0.8]{3DES.png} \ No newline at end of file diff --git a/chapters/Stromverschlüsselungsverfahren.tex b/chapters/Stromverschlüsselungsverfahren.tex index 096c075..b51bffd 100644 --- a/chapters/Stromverschlüsselungsverfahren.tex +++ b/chapters/Stromverschlüsselungsverfahren.tex @@ -10,7 +10,7 @@ \includegraphics{Stromverschlüsselung.png} - \section{Synchrone Stromverschlüsselungsverfahren} + \section{Synchrone Stromverschlüsselungsverfahren}\label{synchrone Stromverschlüsselung} Bei synchronen Stromverschlüsselungsverfahren hängen die Zeichen einer Geheimtextnachricht nicht von den vorherigen ab. So ist es möglich die einzelnen Zeichen des Klartextes gleichzeitig (synchron) zu verschlüsseln. 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