137 lines
12 KiB
TeX
137 lines
12 KiB
TeX
\babel@toc {ngerman}{}
|
|
\contentsline {chapter}{\numberline {1}Substitionsverfahren}{4}{chapter.1}%
|
|
\contentsline {section}{\numberline {1.1}Skytale}{4}{section.1.1}%
|
|
\contentsline {section}{\numberline {1.2}Monoalphabetische Substitionsverfahren}{4}{section.1.2}%
|
|
\contentsline {subsection}{\numberline {1.2.1}Caesar-Verschlüsselung}{5}{subsection.1.2.1}%
|
|
\contentsline {subsection}{\numberline {1.2.2}Häufigkeitsanalyse}{5}{subsection.1.2.2}%
|
|
\contentsline {section}{\numberline {1.3}Polyalphabetische Substitutionsverfahren}{5}{section.1.3}%
|
|
\contentsline {subsection}{\numberline {1.3.1}Vignère-Verfahren}{5}{subsection.1.3.1}%
|
|
\contentsline {subsubsection}{\numberline {1.3.1.1}Verschlüsselung}{5}{subsubsection.1.3.1.1}%
|
|
\contentsline {subsection}{\numberline {1.3.2}One-Time-Pad}{6}{subsection.1.3.2}%
|
|
\contentsline {subsubsection}{\numberline {1.3.2.1}Verschlüsselung}{6}{subsubsection.1.3.2.1}%
|
|
\contentsline {subsubsection}{\numberline {1.3.2.2}Perfekte Sicherheit}{6}{subsubsection.1.3.2.2}%
|
|
\contentsline {section}{\numberline {1.4}algebraische Substitionsverfahren}{6}{section.1.4}%
|
|
\contentsline {subsection}{\numberline {1.4.1}Hill-Verfahren}{6}{subsection.1.4.1}%
|
|
\contentsline {subsubsection}{\numberline {1.4.1.1}Verschlüsselung}{6}{subsubsection.1.4.1.1}%
|
|
\contentsline {subsubsection}{\numberline {1.4.1.2}Entschlüsselung}{6}{subsubsection.1.4.1.2}%
|
|
\contentsline {chapter}{\numberline {2}Modulare Arithmetik}{7}{chapter.2}%
|
|
\contentsline {section}{\numberline {2.1}Exkurs: Division mit Rest}{7}{section.2.1}%
|
|
\contentsline {section}{\numberline {2.2}Der Ring $\mathbb {Z}_n$}{7}{section.2.2}%
|
|
\contentsline {subsection}{\numberline {2.2.1}Addition und Multiplikation}{7}{subsection.2.2.1}%
|
|
\contentsline {subsubsection}{\numberline {2.2.1.1}Inverse bezüglich der Addition}{7}{subsubsection.2.2.1.1}%
|
|
\contentsline {subsubsection}{\numberline {2.2.1.2}Inverse bezüglich der Multiplikation}{7}{subsubsection.2.2.1.2}%
|
|
\contentsline {subsection}{\numberline {2.2.2}Subtraktion}{8}{subsection.2.2.2}%
|
|
\contentsline {subsection}{\numberline {2.2.3}Teiler, Vielfache}{8}{subsection.2.2.3}%
|
|
\contentsline {subsubsection}{\numberline {2.2.3.1}Teilerregeln}{8}{subsubsection.2.2.3.1}%
|
|
\contentsline {subsection}{\numberline {2.2.4}Kongruenz}{8}{subsection.2.2.4}%
|
|
\contentsline {subsection}{\numberline {2.2.5}Matrizen}{8}{subsection.2.2.5}%
|
|
\contentsline {subsubsection}{\numberline {2.2.5.1}Determinantenberechnung}{8}{subsubsection.2.2.5.1}%
|
|
\contentsline {subsubsection}{\numberline {2.2.5.2}Inverse Matrix}{8}{subsubsection.2.2.5.2}%
|
|
\contentsline {subsection}{\numberline {2.2.6}Kartesisches Produkt von Ringen}{8}{subsection.2.2.6}%
|
|
\contentsline {subsection}{\numberline {2.2.7}Isomorphie von Ringen}{9}{subsection.2.2.7}%
|
|
\contentsline {section}{\numberline {2.3}Der erweiterte Euklid'sche Algorithmus}{9}{section.2.3}%
|
|
\contentsline {subsection}{\numberline {2.3.1}Euklid'scher Algorithmus}{9}{subsection.2.3.1}%
|
|
\contentsline {subsection}{\numberline {2.3.2}erweiterter Euklid'scher Algorithmus}{9}{subsection.2.3.2}%
|
|
\contentsline {subsubsection}{\numberline {2.3.2.1}Beispiel}{9}{subsubsection.2.3.2.1}%
|
|
\contentsline {section}{\numberline {2.4}Euler'sche $\varphi $-Funktion}{10}{section.2.4}%
|
|
\contentsline {subsection}{\numberline {2.4.1}$\varphi $-Funktion und Primzahlen}{10}{subsection.2.4.1}%
|
|
\contentsline {chapter}{\numberline {3}IT-Sicherheit: Gefährdungen und Maßnahmen}{11}{chapter.3}%
|
|
\contentsline {section}{\numberline {3.1}Vertraulichkeit}{11}{section.3.1}%
|
|
\contentsline {subsection}{\numberline {3.1.1}Schutzmaßnahmen: Verschlüsselungsverfahren}{11}{subsection.3.1.1}%
|
|
\contentsline {section}{\numberline {3.2}Integrität}{11}{section.3.2}%
|
|
\contentsline {subsection}{\numberline {3.2.1}Schutzmaßnahme: Hashfunktionen, Whitelists}{12}{subsection.3.2.1}%
|
|
\contentsline {section}{\numberline {3.3}Authenzität der Daten}{12}{section.3.3}%
|
|
\contentsline {subsection}{\numberline {3.3.1}Schutzmaßnahme: Signaturen}{12}{subsection.3.3.1}%
|
|
\contentsline {subsection}{\numberline {3.3.2}Schutz vor Replay-Angriffen}{12}{subsection.3.3.2}%
|
|
\contentsline {section}{\numberline {3.4}Authenzität von Nutzern}{12}{section.3.4}%
|
|
\contentsline {subsection}{\numberline {3.4.1}Schutzmaßnahmen}{12}{subsection.3.4.1}%
|
|
\contentsline {section}{\numberline {3.5}Zugriffskontrolle}{12}{section.3.5}%
|
|
\contentsline {subsection}{\numberline {3.5.1}Schutzmaßname: Zugriffskontrollsystem}{13}{subsection.3.5.1}%
|
|
\contentsline {section}{\numberline {3.6}Nichtabstreitbarkeit, Verbindlichkeit}{13}{section.3.6}%
|
|
\contentsline {subsection}{\numberline {3.6.1}Schutzmaßname: Signaturen und PKI}{13}{subsection.3.6.1}%
|
|
\contentsline {section}{\numberline {3.7}Verfügbarkeit}{13}{section.3.7}%
|
|
\contentsline {subsection}{\numberline {3.7.1}Schutzmaßnahmen}{13}{subsection.3.7.1}%
|
|
\contentsline {section}{\numberline {3.8}Anonymität}{13}{section.3.8}%
|
|
\contentsline {chapter}{\numberline {4}Verschlüsselungsverfahren}{14}{chapter.4}%
|
|
\contentsline {section}{\numberline {4.1}Das Kerckhoffs'sche Prinzip}{14}{section.4.1}%
|
|
\contentsline {section}{\numberline {4.2}Mathematische Modelierung von Verschlüsselungsverfahren}{14}{section.4.2}%
|
|
\contentsline {section}{\numberline {4.3}Schlüsselaustausch}{14}{section.4.3}%
|
|
\contentsline {section}{\numberline {4.4}Angriffsszenarien}{15}{section.4.4}%
|
|
\contentsline {subsection}{\numberline {4.4.1}Ciphertext-only Angriffe}{15}{subsection.4.4.1}%
|
|
\contentsline {subsection}{\numberline {4.4.2}Known-plaintext Angriffe}{15}{subsection.4.4.2}%
|
|
\contentsline {subsection}{\numberline {4.4.3}Chosen-plaintext Angriffe}{15}{subsection.4.4.3}%
|
|
\contentsline {section}{\numberline {4.5}Brute-Force Angriffe}{15}{section.4.5}%
|
|
\contentsline {subsection}{\numberline {4.5.1}Beispiel: Brute-Force Angriff auf $k$}{15}{subsection.4.5.1}%
|
|
\contentsline {subsection}{\numberline {4.5.2}Beispiel: Brute-Force Angriff auf $m$}{15}{subsection.4.5.2}%
|
|
\contentsline {subsection}{\numberline {4.5.3}Anforderungen zum Schutz vor Brute-Force}{15}{subsection.4.5.3}%
|
|
\contentsline {section}{\numberline {4.6}Wörterbuchangriffe}{16}{section.4.6}%
|
|
\contentsline {subsection}{\numberline {4.6.1}Schutz vor Wörterbuchangriffen}{16}{subsection.4.6.1}%
|
|
\contentsline {subsubsection}{\numberline {4.6.1.1}Nonce-Verschlüsselung}{16}{subsubsection.4.6.1.1}%
|
|
\contentsline {chapter}{\numberline {5}Stromverschlüsselungsverfahren}{17}{chapter.5}%
|
|
\contentsline {section}{\numberline {5.1}Synchrone Stromverschlüsselungsverfahren}{17}{section.5.1}%
|
|
\contentsline {section}{\numberline {5.2}Zustandsabhängige Stromverschlüsselungsverfahren}{18}{section.5.2}%
|
|
\contentsline {subsection}{\numberline {5.2.1}Additive zustandsabhängige Stromverschlüsselungsverfahren}{19}{subsection.5.2.1}%
|
|
\contentsline {subsubsection}{\numberline {5.2.1.1}Synchrone additive Stromverschlüsselungsverfahren}{19}{subsubsection.5.2.1.1}%
|
|
\contentsline {section}{\numberline {5.3}Schlüsselstrom vs. One-Time-Pad}{20}{section.5.3}%
|
|
\contentsline {section}{\numberline {5.4}Nonces zur Initialisierung eines Schlüsselstromgenerators}{20}{section.5.4}%
|
|
\contentsline {section}{\numberline {5.5}ChaCha20}{21}{section.5.5}%
|
|
\contentsline {section}{\numberline {5.6}Cipher-Instanzen: Verschlüsselungsalgorithmen in Java-Laufzeitumgebungen}{22}{section.5.6}%
|
|
\contentsline {chapter}{\numberline {6}Blockverschlüsselungsverfahren}{23}{chapter.6}%
|
|
\contentsline {section}{\numberline {6.1}Padding-Verfahren}{23}{section.6.1}%
|
|
\contentsline {section}{\numberline {6.2}Betriebsmodi}{23}{section.6.2}%
|
|
\contentsline {subsection}{\numberline {6.2.1}ECB (Electronic Code Book)}{23}{subsection.6.2.1}%
|
|
\contentsline {subsection}{\numberline {6.2.2}CBC (Cipher Block Chaining)}{24}{subsection.6.2.2}%
|
|
\contentsline {subsection}{\numberline {6.2.3}CBC-CS (Chiphertext Stealing for CBC Mode)}{25}{subsection.6.2.3}%
|
|
\contentsline {subsubsection}{\numberline {6.2.3.1}CBC-CS1}{25}{subsubsection.6.2.3.1}%
|
|
\contentsline {subsubsection}{\numberline {6.2.3.2}CBC-CS2}{26}{subsubsection.6.2.3.2}%
|
|
\contentsline {subsubsection}{\numberline {6.2.3.3}CBC-CS3}{26}{subsubsection.6.2.3.3}%
|
|
\contentsline {subsection}{\numberline {6.2.4}CTR (Counter)}{26}{subsection.6.2.4}%
|
|
\contentsline {subsection}{\numberline {6.2.5}OFB (Output Feedback)}{26}{subsection.6.2.5}%
|
|
\contentsline {subsubsection}{\numberline {6.2.5.1}OFB-8$n$}{27}{subsubsection.6.2.5.1}%
|
|
\contentsline {subsection}{\numberline {6.2.6}CFB (Cipher-Feedback)}{27}{subsection.6.2.6}%
|
|
\contentsline {subsubsection}{\numberline {6.2.6.1}CFB-8$n$}{27}{subsubsection.6.2.6.1}%
|
|
\contentsline {section}{\numberline {6.3}Konstruktionsprinzipien von Blockverschlüsselungsverfahren}{28}{section.6.3}%
|
|
\contentsline {section}{\numberline {6.4}DES}{28}{section.6.4}%
|
|
\contentsline {subsection}{\numberline {6.4.1}Triple-DES (3DES)}{28}{subsection.6.4.1}%
|
|
\contentsline {section}{\numberline {6.5}Meet-in-the-Middle-Angriff}{29}{section.6.5}%
|
|
\contentsline {section}{\numberline {6.6}AES (Advanced Encryption Standard)}{30}{section.6.6}%
|
|
\contentsline {subsection}{\numberline {6.6.1}AES-128}{30}{subsection.6.6.1}%
|
|
\contentsline {chapter}{\numberline {7}Hashfunktionen}{32}{chapter.7}%
|
|
\contentsline {section}{\numberline {7.1}schwache Kollisionsfreiheit}{32}{section.7.1}%
|
|
\contentsline {section}{\numberline {7.2}\texttt {MessageDigest}-Instanzen: Hashfunktionen in Java}{32}{section.7.2}%
|
|
\contentsline {section}{\numberline {7.3}Anwendungsbeispiele}{33}{section.7.3}%
|
|
\contentsline {subsection}{\numberline {7.3.1}Anwendungsbeispiel: Passwortdatei}{33}{subsection.7.3.1}%
|
|
\contentsline {subsubsection}{\numberline {7.3.1.1}Anwendungsbeispiel: Passwortdatei mit Salt und Iteration Count}{33}{subsubsection.7.3.1.1}%
|
|
\contentsline {subsection}{\numberline {7.3.2}Anwendungsbeispiel: Integritätsschutz von Dateien}{33}{subsection.7.3.2}%
|
|
\contentsline {subsection}{\numberline {7.3.3}Anwendungsbeispiel: Integritätsschutz bei einem Dateidownload}{33}{subsection.7.3.3}%
|
|
\contentsline {section}{\numberline {7.4}Brute-Force-Angriffe auf Hashfunktionen}{33}{section.7.4}%
|
|
\contentsline {subsection}{\numberline {7.4.1}Brute-Force-Urbildsuche}{33}{subsection.7.4.1}%
|
|
\contentsline {subsection}{\numberline {7.4.2}Brute-Force-Kollisionssuche}{34}{subsection.7.4.2}%
|
|
\contentsline {section}{\numberline {7.5}Konstruktionsverfahren von Hashfunktionen}{34}{section.7.5}%
|
|
\contentsline {chapter}{\numberline {8}MAC-Verfahren}{36}{chapter.8}%
|
|
\contentsline {section}{\numberline {8.1}HMAC}{36}{section.8.1}%
|
|
\contentsline {section}{\numberline {8.2}CMAC, CBC-MAC}{36}{section.8.2}%
|
|
\contentsline {subsection}{\numberline {8.2.1}CMAC}{36}{subsection.8.2.1}%
|
|
\contentsline {subsection}{\numberline {8.2.2}CBC-MAC}{37}{subsection.8.2.2}%
|
|
\contentsline {chapter}{\numberline {9}Modulare Arithmetik - Teil 2}{38}{chapter.9}%
|
|
\contentsline {section}{\numberline {9.1}Potenzen}{38}{section.9.1}%
|
|
\contentsline {subsection}{\numberline {9.1.1}Erzeugnis und Ordnung eines invertierbaren Elements}{38}{subsection.9.1.1}%
|
|
\contentsline {subsection}{\numberline {9.1.2}Faktorenzerlegung}{39}{subsection.9.1.2}%
|
|
\contentsline {subsection}{\numberline {9.1.3}Kleiner Satz von Fermat}{39}{subsection.9.1.3}%
|
|
\contentsline {subsection}{\numberline {9.1.4}Berechnung modularer Potenzen}{39}{subsection.9.1.4}%
|
|
\contentsline {section}{\numberline {9.2}Exkurs: Einheitengruppe $\mathbb {Z}_{p^e}^*$}{40}{section.9.2}%
|
|
\contentsline {subsection}{\numberline {9.2.1}$\mathbb {Z}_{2^e}^*$}{40}{subsection.9.2.1}%
|
|
\contentsline {section}{\numberline {9.3}Der chinesische Restsatz}{40}{section.9.3}%
|
|
\contentsline {subsection}{\numberline {9.3.1}Beispiel}{41}{subsection.9.3.1}%
|
|
\contentsline {section}{\numberline {9.4}Elemente gerader und ungerader Ordnung in $\mathbb {Z}_n$**}{41}{section.9.4}%
|
|
\contentsline {chapter}{\numberline {10}Das Diffie-Hellman-Schlüsselaustauschverfahren}{42}{chapter.10}%
|
|
\contentsline {section}{\numberline {10.1}Das DH-Verfahren in Einzelschritten}{42}{section.10.1}%
|
|
\contentsline {section}{\numberline {10.2}Das Diskrete-Logarithmus-Problem (DL-Problem)}{43}{section.10.2}%
|
|
\contentsline {subsection}{\numberline {10.2.1}Das Diffie-Hellman-Problem (DH-Problem)}{43}{subsection.10.2.1}%
|
|
\contentsline {section}{\numberline {10.3}Beispielanwendung des DH-Verfahrens}{44}{section.10.3}%
|
|
\contentsline {section}{\numberline {10.4}Angriffe auf das DH-Verfahren}{44}{section.10.4}%
|
|
\contentsline {subsection}{\numberline {10.4.1}Pohlig-Hellman-Reduktion}{44}{subsection.10.4.1}%
|
|
\contentsline {subsection}{\numberline {10.4.2}Shanks' \glqq Baby Steps Giant Steps\grqq -Verfahren (BSGS-Verfahren)}{44}{subsection.10.4.2}%
|
|
\contentsline {subsection}{\numberline {10.4.3}Pollard's Rho-Methode}{45}{subsection.10.4.3}%
|
|
\contentsline {subsection}{\numberline {10.4.4}Zahlkörpersieb}{45}{subsection.10.4.4}%
|