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Brute-Force}{section.4.5}% 54 -\BOOKMARK [1][-]{section.4.6}{W\366rterbuchangriffe}{chapter.4}% 55 -\BOOKMARK [2][-]{subsection.4.6.1}{Schutz vor W\366rterbuchangriffen}{section.4.6}% 56 -\BOOKMARK [0][-]{chapter.5}{Stromverschl\374sselungsverfahren}{}% 57 -\BOOKMARK [1][-]{section.5.1}{Synchrone Stromverschl\374sselungsverfahren}{chapter.5}% 58 -\BOOKMARK [1][-]{section.5.2}{Zustandsabh\344ngige Stromverschl\374sselungsverfahren}{chapter.5}% 59 -\BOOKMARK [2][-]{subsection.5.2.1}{Additive zustandsabh\344ngige Stromverschl\374sselungsverfahren}{section.5.2}% 60 -\BOOKMARK [1][-]{section.5.3}{Schl\374sselstrom vs. One-Time-Pad}{chapter.5}% 61 -\BOOKMARK [1][-]{section.5.4}{Nonces zur Initialisierung eines Schl\374sselstromgenerators}{chapter.5}% 62 -\BOOKMARK [1][-]{section.5.5}{ChaCha20}{chapter.5}% 63 -\BOOKMARK [1][-]{section.5.6}{Cipher-Instanzen: Verschl\374sselungsalgorithmen in Java-Laufzeitumgebungen}{chapter.5}% 64 -\BOOKMARK [0][-]{chapter.6}{Blockverschl\374sselungsverfahren}{}% 65 -\BOOKMARK [1][-]{section.6.1}{Padding-Verfahren}{chapter.6}% 66 -\BOOKMARK [1][-]{section.6.2}{Betriebsmodi}{chapter.6}% 67 -\BOOKMARK [2][-]{subsection.6.2.1}{ECB \(Electronic Code Book\)}{section.6.2}% 68 -\BOOKMARK [2][-]{subsection.6.2.2}{CBC \(Cipher Block Chaining\)}{section.6.2}% 69 -\BOOKMARK [2][-]{subsection.6.2.3}{CBC-CS \(Chiphertext Stealing for CBC Mode\)}{section.6.2}% 70 -\BOOKMARK [2][-]{subsection.6.2.4}{CTR \(Counter\)}{section.6.2}% 71 -\BOOKMARK [2][-]{subsection.6.2.5}{OFB \(Output Feedback\)}{section.6.2}% 72 -\BOOKMARK [2][-]{subsection.6.2.6}{CFB \(Cipher-Feedback\)}{section.6.2}% 73 -\BOOKMARK [1][-]{section.6.3}{Konstruktionsprinzipien von Blockverschl\374sselungsverfahren}{chapter.6}% 74 -\BOOKMARK [1][-]{section.6.4}{DES}{chapter.6}% 75 -\BOOKMARK [2][-]{subsection.6.4.1}{Triple-DES \(3DES\)}{section.6.4}% 76 -\BOOKMARK [1][-]{section.6.5}{Meet-in-the-Middle-Angriff}{chapter.6}% 77 -\BOOKMARK [1][-]{section.6.6}{AES \(Advanced Encryption Standard\)}{chapter.6}% 78 -\BOOKMARK [2][-]{subsection.6.6.1}{AES-128}{section.6.6}% 79 -\BOOKMARK [0][-]{chapter.7}{Hashfunktionen}{}% 80 -\BOOKMARK [1][-]{section.7.1}{schwache Kollisionsfreiheit}{chapter.7}% 81 -\BOOKMARK [1][-]{section.7.2}{MessageDigest-Instanzen: Hashfunktionen in Java}{chapter.7}% 82 -\BOOKMARK [1][-]{section.7.3}{Anwendungsbeispiele}{chapter.7}% 83 -\BOOKMARK [2][-]{subsection.7.3.1}{Anwendungsbeispiel: Passwortdatei}{section.7.3}% 84 -\BOOKMARK [2][-]{subsection.7.3.2}{Anwendungsbeispiel: Integrit\344tsschutz von Dateien}{section.7.3}% 85 -\BOOKMARK [2][-]{subsection.7.3.3}{Anwendungsbeispiel: Integrit\344tsschutz bei einem Dateidownload}{section.7.3}% 86 -\BOOKMARK [1][-]{section.7.4}{Brute-Force-Angriffe auf Hashfunktionen}{chapter.7}% 87 -\BOOKMARK [2][-]{subsection.7.4.1}{Brute-Force-Urbildsuche}{section.7.4}% 88 -\BOOKMARK [2][-]{subsection.7.4.2}{Brute-Force-Kollisionssuche}{section.7.4}% 89 -\BOOKMARK [1][-]{section.7.5}{Konstruktionsverfahren von Hashfunktionen}{chapter.7}% 90 -\BOOKMARK [0][-]{chapter.8}{MAC-Verfahren}{}% 91 -\BOOKMARK [1][-]{section.8.1}{HMAC}{chapter.8}% 92 -\BOOKMARK [1][-]{section.8.2}{CMAC, CBC-MAC}{chapter.8}% 93 -\BOOKMARK [2][-]{subsection.8.2.1}{CMAC}{section.8.2}% 94 -\BOOKMARK [2][-]{subsection.8.2.2}{CBC-MAC}{section.8.2}% 95 -\BOOKMARK [0][-]{chapter.9}{Modulare Arithmetik - Teil 2}{}% 96 -\BOOKMARK [1][-]{section.9.1}{Potenzen}{chapter.9}% 97 -\BOOKMARK [2][-]{subsection.9.1.1}{Erzeugnis und Ordnung eines invertierbaren Elements}{section.9.1}% 98 -\BOOKMARK [2][-]{subsection.9.1.2}{Faktorenzerlegung}{section.9.1}% 99 -\BOOKMARK [2][-]{subsection.9.1.3}{Kleiner Satz von Fermat}{section.9.1}% 100 -\BOOKMARK [2][-]{subsection.9.1.4}{Berechnung modularer Potenzen}{section.9.1}% 101 -\BOOKMARK [1][-]{section.9.2}{Exkurs: Einheitengruppe Zpe*}{chapter.9}% 102 -\BOOKMARK [2][-]{subsection.9.2.1}{Z2e*}{section.9.2}% 103 -\BOOKMARK [1][-]{section.9.3}{Der chinesische Restsatz}{chapter.9}% 104 -\BOOKMARK [2][-]{subsection.9.3.1}{Beispiel}{section.9.3}% 105 -\BOOKMARK [1][-]{section.9.4}{Elemente gerader und ungerader Ordnung in Zn**}{chapter.9}% 106 -\BOOKMARK [0][-]{chapter.10}{Das Diffie-Hellman-Schl\374sselaustauschverfahren}{}% 107 -\BOOKMARK [1][-]{section.10.1}{Das DH-Verfahren in Einzelschritten}{chapter.10}% 108 -\BOOKMARK [1][-]{section.10.2}{Das Diskrete-Logarithmus-Problem \(DL-Problem\)}{chapter.10}% 109 -\BOOKMARK [2][-]{subsection.10.2.1}{Das Diffie-Hellman-Problem \(DH-Problem\)}{section.10.2}% 110 -\BOOKMARK [1][-]{section.10.3}{Beispielanwendung des DH-Verfahrens}{chapter.10}% 111 -\BOOKMARK [1][-]{section.10.4}{Angriffe auf das DH-Verfahren}{chapter.10}% 112 -\BOOKMARK [2][-]{subsection.10.4.1}{Pohlig-Hellman-Reduktion}{section.10.4}% 113 -\BOOKMARK [2][-]{subsection.10.4.2}{Shanks' \214Baby Steps Giant Steps\215-Verfahren \(BSGS-Verfahren\)}{section.10.4}% 114 -\BOOKMARK [2][-]{subsection.10.4.3}{Pollard's Rho-Methode}{section.10.4}% 115 -\BOOKMARK [2][-]{subsection.10.4.4}{Zahlk\366rpersieb}{section.10.4}% 116 -\BOOKMARK [0][-]{chapter.11}{Das RSA-Verfahren}{}% 117 -\BOOKMARK [1][-]{section.11.1}{RSA-Schl\374sselpaare}{chapter.11}% 118 -\BOOKMARK [2][-]{subsection.11.1.1}{Beispiel f\374r die Schl\374sselpaarerstellung}{section.11.1}% 119 -\BOOKMARK [1][-]{section.11.2}{RSA-Verschl\374sselungsverfahren}{chapter.11}% 120 -\BOOKMARK [2][-]{subsection.11.2.1}{Beispiel f\374r die Verschl\374sselung}{section.11.2}% 121 -\BOOKMARK [1][-]{section.11.3}{Padding}{chapter.11}% 122 -\BOOKMARK [2][-]{subsection.11.3.1}{Padding nach PKCS\0431}{section.11.3}% 123 -\BOOKMARK [2][-]{subsection.11.3.2}{Optimal Asymmetric Encryption Padding\(OAEP\)}{section.11.3}% 124 -\BOOKMARK [1][-]{section.11.4}{Das RSA-Signaturverfahren}{chapter.11}% 125 -\BOOKMARK [2][-]{subsection.11.4.1}{Beispiel f\374r ein RSA-Signaturverfahren}{section.11.4}% 126 diff --git a/Zusammenfassung_DC.pdf b/Zusammenfassung_DC.pdf deleted file mode 100644 index 0663403..0000000 Binary files a/Zusammenfassung_DC.pdf and /dev/null differ diff --git a/Zusammenfassung_DC.synctex.gz b/Zusammenfassung_DC.synctex.gz deleted file mode 100644 index a1abc20..0000000 Binary files a/Zusammenfassung_DC.synctex.gz and /dev/null differ diff --git a/Zusammenfassung_DC.toc b/Zusammenfassung_DC.toc deleted file mode 100644 index 35e8c2c..0000000 --- a/Zusammenfassung_DC.toc +++ /dev/null @@ -1,146 +0,0 @@ -\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}% -\contentsline {chapter}{\numberline {11}Das RSA-Verfahren}{46}{chapter.11}% -\contentsline {section}{\numberline {11.1}RSA-Schlüsselpaare}{46}{section.11.1}% -\contentsline {subsection}{\numberline {11.1.1}Beispiel für die Schlüsselpaarerstellung}{47}{subsection.11.1.1}% -\contentsline {section}{\numberline {11.2}RSA-Verschlüsselungsverfahren}{47}{section.11.2}% -\contentsline {subsection}{\numberline {11.2.1}Beispiel für die Verschlüsselung}{48}{subsection.11.2.1}% -\contentsline {section}{\numberline {11.3}Padding}{48}{section.11.3}% -\contentsline {subsection}{\numberline {11.3.1}Padding nach PKCS\#1}{49}{subsection.11.3.1}% -\contentsline {subsection}{\numberline {11.3.2}Optimal Asymmetric Encryption Padding(OAEP)}{49}{subsection.11.3.2}% -\contentsline {section}{\numberline {11.4}Das RSA-Signaturverfahren}{49}{section.11.4}% -\contentsline {subsection}{\numberline {11.4.1}Beispiel für ein RSA-Signaturverfahren}{50}{subsection.11.4.1}%