\babel@toc {ngerman}{}
\contentsline {chapter}{\numberline {1}Substitionsverfahren}{2}%
\contentsline {section}{\numberline {1.1}Skytale}{2}%
\contentsline {section}{\numberline {1.2}Monoalphabetische Substitionsverfahren}{2}%
\contentsline {subsection}{\numberline {1.2.1}Caesar-Verschlüsselung}{3}%
\contentsline {subsection}{\numberline {1.2.2}Häufigkeitsanalyse}{3}%
\contentsline {section}{\numberline {1.3}Polyalphabetische Substitutionsverfahren}{3}%
\contentsline {subsection}{\numberline {1.3.1}Vignère-Verfahren}{3}%
\contentsline {subsubsection}{\numberline {1.3.1.1}Verschlüsselung}{3}%
\contentsline {subsection}{\numberline {1.3.2}One-Time-Pad}{4}%
\contentsline {subsubsection}{\numberline {1.3.2.1}Verschlüsselung}{4}%
\contentsline {subsubsection}{\numberline {1.3.2.2}Perfekte Sicherheit}{4}%
\contentsline {section}{\numberline {1.4}algebraische Substitionsverfahren}{4}%
\contentsline {subsection}{\numberline {1.4.1}Hill-Verfahren}{4}%
\contentsline {subsubsection}{\numberline {1.4.1.1}Verschlüsselung}{4}%
\contentsline {subsubsection}{\numberline {1.4.1.2}Entschlüsselung}{4}%
\contentsline {chapter}{\numberline {2}Modulare Arithmetik}{5}%
\contentsline {section}{\numberline {2.1}Exkurs: Division mit Rest}{5}%
\contentsline {section}{\numberline {2.2}Der Ring $\mathbb {Z}_n$}{5}%
\contentsline {subsection}{\numberline {2.2.1}Addition und Multiplikation}{5}%
\contentsline {subsubsection}{\numberline {2.2.1.1}Inverse bezüglich der Addition}{5}%
\contentsline {subsubsection}{\numberline {2.2.1.2}Inverse bezüglich der Multiplikation}{5}%
\contentsline {subsection}{\numberline {2.2.2}Subtraktion}{6}%
\contentsline {subsection}{\numberline {2.2.3}Teiler, Vielfache}{6}%
\contentsline {subsubsection}{\numberline {2.2.3.1}Teilerregeln}{6}%
\contentsline {subsection}{\numberline {2.2.4}Kongruenz}{6}%
\contentsline {subsection}{\numberline {2.2.5}Matrizen}{6}%
\contentsline {subsubsection}{\numberline {2.2.5.1}Determinantenberechnung}{6}%
\contentsline {subsubsection}{\numberline {2.2.5.2}Inverse Matrix}{6}%
\contentsline {section}{\numberline {2.3}Der erweiterte Euklid'sche Algorithmus}{6}%
\contentsline {subsection}{\numberline {2.3.1}Euklid'scher Algorithmus}{7}%
\contentsline {subsection}{\numberline {2.3.2}erweiterter Euklid'scher Algorithmus}{7}%
\contentsline {subsubsection}{\numberline {2.3.2.1}Beispiel}{7}%
\contentsline {section}{\numberline {2.4}Euler'sche $\varphi $-Funktion}{8}%
\contentsline {subsection}{\numberline {2.4.1}$\varphi $-Funktion und Primzahlen}{8}%