\babel@toc {ngerman}{}
\contentsline {chapter}{\numberline {1}Substitionsverfahren}{3}%
\contentsline {section}{\numberline {1.1}Skytale}{3}%
\contentsline {section}{\numberline {1.2}Monoalphabetische Substitionsverfahren}{3}%
\contentsline {subsection}{\numberline {1.2.1}Caesar-Verschlüsselung}{4}%
\contentsline {subsection}{\numberline {1.2.2}Häufigkeitsanalyse}{4}%
\contentsline {section}{\numberline {1.3}Polyalphabetische Substitutionsverfahren}{4}%
\contentsline {subsection}{\numberline {1.3.1}Vignère-Verfahren}{4}%
\contentsline {subsubsection}{\numberline {1.3.1.1}Verschlüsselung}{4}%
\contentsline {subsection}{\numberline {1.3.2}One-Time-Pad}{5}%
\contentsline {subsubsection}{\numberline {1.3.2.1}Verschlüsselung}{5}%
\contentsline {subsubsection}{\numberline {1.3.2.2}Perfekte Sicherheit}{5}%
\contentsline {section}{\numberline {1.4}algebraische Substitionsverfahren}{5}%
\contentsline {subsection}{\numberline {1.4.1}Hill-Verfahren}{5}%
\contentsline {subsubsection}{\numberline {1.4.1.1}Verschlüsselung}{5}%
\contentsline {subsubsection}{\numberline {1.4.1.2}Entschlüsselung}{5}%
\contentsline {chapter}{\numberline {2}Modulare Arithmetik}{6}%
\contentsline {section}{\numberline {2.1}Exkurs: Division mit Rest}{6}%
\contentsline {section}{\numberline {2.2}Der Ring $\mathbb {Z}_n$}{6}%
\contentsline {subsection}{\numberline {2.2.1}Addition und Multiplikation}{6}%
\contentsline {subsubsection}{\numberline {2.2.1.1}Inverse bezüglich der Addition}{6}%
\contentsline {subsubsection}{\numberline {2.2.1.2}Inverse bezüglich der Multiplikation}{6}%
\contentsline {subsection}{\numberline {2.2.2}Subtraktion}{7}%
\contentsline {subsection}{\numberline {2.2.3}Teiler, Vielfache}{7}%
\contentsline {subsubsection}{\numberline {2.2.3.1}Teilerregeln}{7}%
\contentsline {subsection}{\numberline {2.2.4}Kongruenz}{7}%
\contentsline {subsection}{\numberline {2.2.5}Matrizen}{7}%
\contentsline {subsubsection}{\numberline {2.2.5.1}Determinantenberechnung}{7}%
\contentsline {subsubsection}{\numberline {2.2.5.2}Inverse Matrix}{7}%
\contentsline {section}{\numberline {2.3}Der erweiterte Euklid'sche Algorithmus}{7}%
\contentsline {subsection}{\numberline {2.3.1}Euklid'scher Algorithmus}{8}%
\contentsline {subsection}{\numberline {2.3.2}erweiterter Euklid'scher Algorithmus}{8}%
\contentsline {subsubsection}{\numberline {2.3.2.1}Beispiel}{8}%
\contentsline {section}{\numberline {2.4}Euler'sche $\varphi $-Funktion}{9}%
\contentsline {subsection}{\numberline {2.4.1}$\varphi $-Funktion und Primzahlen}{9}%
\contentsline {chapter}{\numberline {3}IT-Sicherheit: Gefährdungen und Maßnahmen}{10}%
\contentsline {section}{\numberline {3.1}Vertraulichkeit}{10}%
\contentsline {subsection}{\numberline {3.1.1}Schutzmaßnahmen: Verschlüsselungsverfahren}{10}%
\contentsline {section}{\numberline {3.2}Integrität}{10}%
\contentsline {subsection}{\numberline {3.2.1}Schutzmaßnahme: Hashfunktionen, Whitelists}{11}%
\contentsline {section}{\numberline {3.3}Authenzität der Daten}{11}%
\contentsline {subsection}{\numberline {3.3.1}Schutzmaßnahme: Signaturen}{11}%
\contentsline {subsection}{\numberline {3.3.2}Schutz vor Replay-Angriffen}{11}%
\contentsline {section}{\numberline {3.4}Authenzität von Nutzern}{11}%
\contentsline {subsection}{\numberline {3.4.1}Schutzmaßnahmen}{11}%
\contentsline {section}{\numberline {3.5}Zugriffskontrolle}{11}%
\contentsline {subsection}{\numberline {3.5.1}Schutzmaßname: Zugriffskontrollsystem}{12}%
\contentsline {section}{\numberline {3.6}Nichtabstreitbarkeit, Verbindlichkeit}{12}%
\contentsline {subsection}{\numberline {3.6.1}Schutzmaßname: Signaturen und PKI}{12}%
\contentsline {section}{\numberline {3.7}Verfügbarkeit}{12}%
\contentsline {subsection}{\numberline {3.7.1}Schutzmaßnahmen}{12}%
\contentsline {section}{\numberline {3.8}Anonymität}{12}%
\contentsline {chapter}{\numberline {4}Verschlüsselungsverfahren}{13}%
\contentsline {section}{\numberline {4.1}Das Kerckhoffs'sche Prinzip}{13}%
\contentsline {section}{\numberline {4.2}Mathematische Modelierung von Verschlüsselungsverfahren}{13}%
\contentsline {section}{\numberline {4.3}Schlüsselaustausch}{13}%
\contentsline {section}{\numberline {4.4}Angriffsszenarien}{14}%
\contentsline {subsection}{\numberline {4.4.1}Ciphertext-only Angriffe}{14}%
\contentsline {subsection}{\numberline {4.4.2}Known-plaintext Angriffe}{14}%
\contentsline {subsection}{\numberline {4.4.3}Chosen-plaintext Angriffe}{14}%
\contentsline {section}{\numberline {4.5}Brute-Force Angriffe}{14}%
\contentsline {subsection}{\numberline {4.5.1}Beispiel: Brute-Force Angriff auf $k$}{14}%
\contentsline {subsection}{\numberline {4.5.2}Beispiel: Brute-Force Angriff auf $m$}{14}%
\contentsline {subsection}{\numberline {4.5.3}Anforderungen zum Schutz vor Brute-Force}{14}%
\contentsline {section}{\numberline {4.6}Wörterbuchangriffe}{15}%
\contentsline {subsection}{\numberline {4.6.1}Schutz vor Wörterbuchangriffen}{15}%
\contentsline {subsubsection}{\numberline {4.6.1.1}Nonce-Verschlüsselung}{15}%