Elliptische Kurven in der Kryptographie:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | German |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2002
|
| Schriftenreihe: | Springer-Lehrbuch
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | X, 142 S. graph. Darst. |
| ISBN: | 3540425187 9783540425182 |
Internformat
MARC
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Datensatz im Suchindex
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| adam_text | Inhaltsverzeichnis
1. Public-Key-Kryptographie.......................... 1
1.1
1.2 Diskreter Logarithmus............................. 4
1.2.1 Diffie-Hellman-Schlüsselaustausch.............. 5
1.2.2 ElGamal-Verschlüsselung..................... 6
1.2.3 ElGamal-Signatur........................... 7
1.3 Geeignete Gruppen................................ 8
2. Elliptische Kurven.................................. 11
2.1 Affine Kurven .................................... 12
2.2
2.3 Elliptische Kurven................................. 22
3. Elliptische Kurven über endlichen Körpern......... 55
3.1 Der Frobenius.................................... 55
3.2 Punkte zählen.................................... 57
3.3 Der
3.4 Supersinguläre elliptische Kurven ................... 66
4. Das Problem des diskreten Logarithmus für elliptische
Kurven ............................................. 75
4.1 Allgemeine Methoden.............................. 76
4.1.1 Enumerationsverfahren....................... 76
X
4.1.2 Babystep-Giantstep-Algorithmus (BSGS)....... 76
4.1.3 Pohlig-Hellman-Verfahren..................... 77
4.1.4 Pollard-^Methode........................... 79
4.1.5 Pollard-A-Methode........................... 82
4.2 Spezielle Methoden................................ 82
4.2.1 Der MOV-Algorithraus....................... 83
4.2.2 Anomale Kurven oder
5. Praktische Konsequenzen........................... 97
5.1 Geeignete elliptische Kurven........................ 97
5.2 Vergleich mit anderen Public Key-Verfahren.......... 98
5.2.1 RSA....................................... 98
5.2.2 DL-Verfahren in F*.......................... 102
5.3 ECDSA.......................................... 104
6. Anhang: Mathematische Grundlagen................ 111
6.1 Ganze Zahlen..................................... 111
6.2 Kongruenzen..................................... 114
6.3 Gruppen......................................... 117
6.4 Ringe und Körper................................. 122
6.5 Polynome ........................................ 125
6.6 Endliche Körper.................................. 128
6.7 Algebraisch abgeschlossene Körper.................. 130
6.8 Einheitswurzeln ................................... 131
6.9 p-adische Zahlen.................................. 131
6.10 Komplexität...................................... 134
Literaturverzeichnis .................................... 137
Sachverzeichnis......................................... 141
|
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| id | DE-604.BV014111770 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:57:51Z |
| institution | BVB |
| isbn | 3540425187 9783540425182 |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009668722 |
| oclc_num | 248309123 |
| open_access_boolean | |
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| physical | X, 142 S. graph. Darst. |
| publishDate | 2002 |
| publishDateSearch | 2002 |
| publishDateSort | 2002 |
| publisher | Springer |
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| series2 | Springer-Lehrbuch |
| spelling | Werner, Annette Verfasser aut Elliptische Kurven in der Kryptographie Annette Werner Berlin [u.a.] Springer 2002 X, 142 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Springer-Lehrbuch Public-Key-Kryptosystem - Elliptische Kurve Kryptologie (DE-588)4033329-2 gnd rswk-swf Elliptische Kurve (DE-588)4014487-2 gnd rswk-swf Public-Key-Kryptosystem (DE-588)4209133-0 gnd rswk-swf Elliptische Kurve (DE-588)4014487-2 s Kryptologie (DE-588)4033329-2 s DE-604 Public-Key-Kryptosystem (DE-588)4209133-0 s Digitalisierung UB Augsburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009668722&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Werner, Annette Elliptische Kurven in der Kryptographie Public-Key-Kryptosystem - Elliptische Kurve Kryptologie (DE-588)4033329-2 gnd Elliptische Kurve (DE-588)4014487-2 gnd Public-Key-Kryptosystem (DE-588)4209133-0 gnd |
| subject_GND | (DE-588)4033329-2 (DE-588)4014487-2 (DE-588)4209133-0 |
| title | Elliptische Kurven in der Kryptographie |
| title_auth | Elliptische Kurven in der Kryptographie |
| title_exact_search | Elliptische Kurven in der Kryptographie |
| title_full | Elliptische Kurven in der Kryptographie Annette Werner |
| title_fullStr | Elliptische Kurven in der Kryptographie Annette Werner |
| title_full_unstemmed | Elliptische Kurven in der Kryptographie Annette Werner |
| title_short | Elliptische Kurven in der Kryptographie |
| title_sort | elliptische kurven in der kryptographie |
| topic | Public-Key-Kryptosystem - Elliptische Kurve Kryptologie (DE-588)4033329-2 gnd Elliptische Kurve (DE-588)4014487-2 gnd Public-Key-Kryptosystem (DE-588)4209133-0 gnd |
| topic_facet | Public-Key-Kryptosystem - Elliptische Kurve Kryptologie Elliptische Kurve Public-Key-Kryptosystem |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009668722&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT wernerannette elliptischekurveninderkryptographie |