Blockverschlüsselung finished until CTS (Skript 2 Seite 29)
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\graphicspath{ {./images/} }
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%mathsymbols
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\usepackage{amsmath}
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\usepackage{amssymb}
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\usepackage{amsfonts}
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\usepackage{mathrsfs}
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%for code highlighting
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@ -52,4 +53,6 @@ rightsub = \grq%
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\input{chapters/Stromverschlüsselungsverfahren.tex}
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\input{chapters/Blockverschlüsselungsverfahren.tex}
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\end{document}
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@ -74,3 +74,8 @@
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\contentsline {section}{\numberline {5.4}Nonces zur Initialisierung eines Schlüsselstromgenerators}{19}%
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\contentsline {section}{\numberline {5.5}ChaCha20}{20}%
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\contentsline {section}{\numberline {5.6}Cipher-Instanzen: Verschlüsselungsalgorithmen in Java-Laufzeitumgebungen}{21}%
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\contentsline {chapter}{\numberline {6}Blockverschlüsselungsverfahren}{22}%
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\contentsline {section}{\numberline {6.1}Padding-Verfahren}{22}%
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\contentsline {section}{\numberline {6.2}Betriebsmodi}{22}%
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\contentsline {subsection}{\numberline {6.2.1}ECB (Electronic Code Book)}{22}%
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\contentsline {subsection}{\numberline {6.2.2}CBC (Cipher Block Chaining)}{23}%
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chapters/Blockverschlüsselungsverfahren.tex
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chapters/Blockverschlüsselungsverfahren.tex
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\chapter{Blockverschlüsselungsverfahren}
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Ein Verschlüsselungsverfahren wird als Blockverschlüsselungsverfahren bezeichnet,
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wenn die Menge der Nachrichten $\mathscr M$ durch die Menge der Blöcker einer festen Länge $n\in \mathbb{N}$ gegeben ist:
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$$\mathscr M := ({\mathbb{Z}_2}^8)^n = \{(z_1,z_2,...,z_n)\mid z_i\in{\mathbb{Z}_2}^8\}$$
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\textbf{Wichtig}\\
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\begin{itemize}
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\item Häufig wird für Blöcke die aus $n$ Bytewerten die Blocklänge in Bits (Blocklänge$=n\cdot 8$) angegeben
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\item Die Menge der Blöcke $\mathscr M$ kann als Vektorraum über $\mathbb{Z}_2$ aufgefasst werden.
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Hierbei wird die Summe von zwei Blöcken $m_1,m_2\in\mathscr M$ durch eine bitweise Addition definiert, welcher einer Bitweisen XOR-Verknüpfung ($\oplus$) entspricht.
|
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\item Da sich die Vektoren aus ${\mathbb{Z}_2}^{8\cdot n}$ in Zahlen aus $\mathbb{Z}_{2^{8\cdot n}}$ umrechnen lassen könnte man sie auch auf diese Art addieren.
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Hierbei erhält man allerdings ein deutlich anderes Ergebnis als bei XOR-Addition.
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Aus diesem Grund wird in diesem Fall das Symbol $\boxplus$ verwendet.
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\end{itemize}
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\section{Padding-Verfahren}
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Damit Daten beliebiger Länge mit einem Blockverschlüsselungsverfahren verschlüsselt werden können muss die Nachricht auf ein Vielfaches der Blocklänge aufgestockt werden.
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Man spricht von Padding.
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Um dem Empfänger mitzuteilen, welche übertragenen Daten zum Padding und nicht zur Nachricht gehören gibt es mehrere Möglichkeiten:
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||||
\begin{itemize}
|
||||
\item Die Anzahl der Padding-Bytes wird mit übertragen
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\item Als Paddingbytes werden Zeichen verwendet, die nicht in die Kodierung passen (z.B. 0x00 bei ASCII)
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||||
\item Es findet immer Padding statt (bei passender Nachrichtenlänge ist der ganze letzte Block Padding), wobei im Padding die Paddinglänge kodiert ist.
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||||
\end{itemize}
|
||||
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\section{Betriebsmodi}
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Es gibt eine Vielzahl von Betriebsmodi, die für die Blockverschlüsselung verwendet werden.
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||||
Auf diese wird im Folgenden eingegangen
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||||
\subsection{ECB (Electronic Code Book)}
|
||||
Im ECB-Modus wir mit dem Verschlüsselungsverfahren $E$ jedes Tupel von Blöcken blockweise verschlüsselt:
|
||||
$$E_k((m_1,...,m_r)) := (E_k(m_1),...,E_k(m_r))$$
|
||||
eine auf diese Weise verschlüsselte Nachricht kann ebenfalls Blockweise entschlüsselt werden:
|
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$$D_k((c_1,...,c_r)) := (D_k(c_1),...,D_k(c_r))$$
|
||||
\includegraphics{ECB.png}\\
|
||||
Da diese Modus anfällig für Wörterbuchangriffe ist wird häufig ein Nonce-Wert verwendet, der jeweils mit dem Klartextblock addiert ($\oplus$) wird:\\
|
||||
\includegraphics{ECB_Nonce.png}
|
||||
|
||||
\subsection{CBC (Cipher Block Chaining)}
|
||||
Der CBC-Modus ist eine spezielle Form des ECB-Modus, bei dem der errechnete Geheimtextblock als Nonce-Wert für die Verschlüsselung des nächsten Blocks verwendet wird.
|
||||
Hierbei wird der erste Nonce-Wert $c_0$ durch einen Initialisierungsvektor $IV\in\mathscr M$ gegeben.
|
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$$\begin{aligned}
|
||||
c_i:=&E_k(m_i+c_{i-1})\\
|
||||
E_{k,IV}(m_1,...,m_r) :=&(c_1,...,c_r)
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||||
\end{aligned}$$
|
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\includegraphics{CBC_enc.png}\\
|
||||
Bei der Entschlüsselung wird wie folgt vorgegangen:
|
||||
$$\begin{aligned}
|
||||
m_i :=&D_k(c_i)+c_{i-1}\\
|
||||
D_{k,IV}(c_1,...,c_r):=&(m_1,...,m_r)
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\end{aligned}$$
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\includegraphics{CBC_dec.png}
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