From b2070128449490cb7c9af8ee7c71246d565872f4 Mon Sep 17 00:00:00 2001 From: Paul Date: Mon, 14 Sep 2020 17:35:52 +0200 Subject: [PATCH] =?UTF-8?q?finished=20the=20basic=20Blockverschl=C3=BCssel?= =?UTF-8?q?ungs-Betriebs-Modi=20(weiter=20in=20Skrip=202=20Seite=2032(38))?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- Zusammenfassung_DC.aux | 7 +++ Zusammenfassung_DC.fdb_latexmk | 15 ++++--- Zusammenfassung_DC.fls | 3 ++ Zusammenfassung_DC.log | 45 +++++++++++++++----- Zusammenfassung_DC.pdf | Bin 2429659 -> 2447532 bytes Zusammenfassung_DC.synctex.gz | Bin 137519 -> 146919 bytes Zusammenfassung_DC.toc | 5 +++ chapters/Blockverschlüsselungsverfahren.tex | 38 ++++++++++++++++- chapters/Stromverschlüsselungsverfahren.tex | 2 +- images/CTR.png | Bin 0 -> 13658 bytes 10 files changed, 95 insertions(+), 20 deletions(-) create mode 100644 images/CTR.png diff --git a/Zusammenfassung_DC.aux b/Zusammenfassung_DC.aux index 708da57..98679f3 100644 --- a/Zusammenfassung_DC.aux +++ b/Zusammenfassung_DC.aux @@ -93,6 +93,7 @@ \newlabel{zustandsabhängige Stromverschlüsselung}{{5.2}{17}} \@writefile{toc}{\contentsline {subsection}{\numberline {5.2.1}Additive zustandsabhängige Stromverschlüsselungsverfahren}{18}\protected@file@percent } \@writefile{toc}{\contentsline {subsubsection}{\numberline {5.2.1.1}Synchrone additive Stromverschlüsselungsverfahren}{18}\protected@file@percent } +\newlabel{synchron additive Stromverschlüsselung}{{5.2.1.1}{18}} \@writefile{toc}{\contentsline {section}{\numberline {5.3}Schlüsselstrom vs. One-Time-Pad}{19}\protected@file@percent } \@writefile{toc}{\contentsline {section}{\numberline {5.4}Nonces zur Initialisierung eines Schlüsselstromgenerators}{19}\protected@file@percent } \@writefile{toc}{\contentsline {section}{\numberline {5.5}ChaCha20}{20}\protected@file@percent } @@ -104,3 +105,9 @@ \@writefile{toc}{\contentsline {section}{\numberline {6.2}Betriebsmodi}{22}\protected@file@percent } 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z>u=xu!5aU~|MicbfBE6>|M%a1eEsI%|MBZjzaUJaPv88(6$bs=&wu&+*MI)<>)&6$ O`TqdNUc>ymY6<`g&pM6( diff --git a/Zusammenfassung_DC.toc b/Zusammenfassung_DC.toc index 49dafae..85066ad 100644 --- a/Zusammenfassung_DC.toc +++ b/Zusammenfassung_DC.toc @@ -79,3 +79,8 @@ \contentsline {section}{\numberline {6.2}Betriebsmodi}{22}% \contentsline {subsection}{\numberline {6.2.1}ECB (Electronic Code Book)}{22}% \contentsline {subsection}{\numberline {6.2.2}CBC (Cipher Block Chaining)}{23}% +\contentsline {subsection}{\numberline {6.2.3}CBC-CS (Chiphertext Stealing for CBC Mode)}{24}% +\contentsline {subsubsection}{\numberline {6.2.3.1}CBC-CS1}{24}% +\contentsline {subsubsection}{\numberline {6.2.3.2}CBC-CS2}{25}% +\contentsline {subsubsection}{\numberline {6.2.3.3}CBC-CS3}{25}% +\contentsline {subsection}{\numberline {6.2.4}CTR (Counter)}{25}% diff --git a/chapters/Blockverschlüsselungsverfahren.tex b/chapters/Blockverschlüsselungsverfahren.tex index 2ba6a6f..c29573a 100644 --- a/chapters/Blockverschlüsselungsverfahren.tex +++ b/chapters/Blockverschlüsselungsverfahren.tex @@ -35,7 +35,7 @@ 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)} + \subsection{CBC (Cipher Block Chaining)}\label{CBC} 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. $$\begin{aligned} @@ -48,4 +48,38 @@ m_i :=&D_k(c_i)+c_{i-1}\\ D_{k,IV}(c_1,...,c_r):=&(m_1,...,m_r) \end{aligned}$$ - \includegraphics{CBC_dec.png} \ No newline at end of file + \includegraphics{CBC_dec.png} + + \subsection{CBC-CS (Chiphertext Stealing for CBC Mode)} + Der CBC-CS-Modus wird auch als CTS-Modus (Chiphertext Stealing Mode) bezeichnet. + Dieser Modus basiert auf dem CBC-Modus (siehe \ref{CBC}), erlaubt aber eine Verschlüsselung von Nachrichten mit beliebiger Länge (ohne Padding). + Um das Padding zu umgehen gibt es mehrere Varianten: + + \subsubsection{CBC-CS1} + Bei der Variante 1 der CBC-CS-Verschlüsselung wird der letzte Block $m^*_r$ der Nachricht mit 00-Bytes auf die Blocklänge aufgefüllt (00-Padding). + Anschließend wird die Nachricht inkl. dem gepaddeten Block $m_r$ mit dem CBC-Verfahren (siehe \ref{CBC}) verschlüsselt. + Um wieder auf die ursprüngliche Länge der Nachricht zu kommen werden aus dem vorletzten Block $c_{r-1}$ des Geheimtextes die gleiche Anzahl Bytes entfernt, die zu $m^*_r$ hinzugefügt wurden. + Hierdurch ergibt sich die Geheimtextnachricht $c_1,...,c_{r-2},c^*_{r-1},c_r$, die die gleiche Länge wie $m$ hat.\\ + Wenn die Länge der Nachricht $m$ ein Vielfaches des Blocklänge $l$ ist wird das normale CBC-Verschlüsselungsverfahren angewandt. + + \subsubsection{CBC-CS2} + Bei der Variante 2 der CBC-CS-Verschlüsselung wird auf die gleiche Weise vorgegangen, wie bei Variante 1. + Allerdings werden, \textbf{falls} ein Padding notwendig ist nach der Verschlüsselung und dem Stealing die letzten beiden Blöcke vertauscht. + $$E-CBC-CS2_{k,IV}(m_1,...,m_{r-1},m^*_r) := (c_1,...,c_r,c^*_{r-1})$$ + Wenn die Länge der Nachricht $m$ ein Vielfaches des Blocklänge $l$ ist wird das normale CBC-Verschlüsselungsverfahren angewandt. + + \subsubsection{CBC-CS3} + Die Variante 3 der CBC-CS-Verschlüsselung unterscheidet sich nur darin von der Variante 2, dass immer die letzten beiden Blöcke vertauscht werden. + 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: + $$\begin{aligned} + c_i :=&m_i+E_k(Ctr\boxplus(i-1)) + E-CTR_{k,Ctr}(m_1,...,m_r):=&(c_1,...,c_r) + \end{aligned}$$ + 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.\\ + 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 diff --git a/chapters/Stromverschlüsselungsverfahren.tex b/chapters/Stromverschlüsselungsverfahren.tex index 06723a4..096c075 100644 --- a/chapters/Stromverschlüsselungsverfahren.tex +++ b/chapters/Stromverschlüsselungsverfahren.tex @@ -45,7 +45,7 @@ \includegraphics{additive zustandsabhängige Stromverschlüsselung.png} - \subsubsection{Synchrone additive Stromverschlüsselungsverfahren} + \subsubsection{Synchrone additive Stromverschlüsselungsverfahren}\label{synchron additive Stromverschlüsselung} eine additive Stromverschlüsselung lässt sich synchron durchführen, falls die Übergangsfunktion $s$ nicht von den Zeichen des Klartextes abhängt. $$\sigma_{i+1}=s(\sigma_i) \text{ mit } s:\mathscr{S}\rightarrow\mathscr{S}$$ Hierdurch definiert sich der Schlüsselstrom: diff --git a/images/CTR.png b/images/CTR.png new file mode 100644 index 0000000000000000000000000000000000000000..aea86519e7ba51167d0ac077d48a2053e9348103 GIT binary patch literal 13658 zcmd6ObySsKw>65Of+!7=ij=fUBOq{S1i>RHEiKaBsGyX9lqe}B4blxFCEeZSp}X^2 z$KM^}z2Erm`~Le~#xTx#p0m%h_g;Igx#pbsJyDd#!=b>zz`($hl|iUrU|clAz_@Vx 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