Algebraic geometry in coding theory and cryptography:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Princeton [u.a.]
Princeton Univ. Press
2009
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Includes bibliographical references and index |
| Beschreibung: | VIII, 260 S. |
| ISBN: | 9780691102887 |
Internformat
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| 245 | 1 | 0 | |a Algebraic geometry in coding theory and cryptography |c Harald Niederreiter and Chaoping Xing |
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| 650 | 4 | |a Geometry, Algebraic | |
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Datensatz im Suchindex
| _version_ | 1804140719027257344 |
|---|---|
| adam_text | Titel: Algebraic geometry in coding theory and cryptography
Autor: Niederreiter, Harald
Jahr: 2009
Contents
Preface ix
Finit 1.1 te Fields and Function Fields Structure of Finite Fields 1 1
1.2 Algebraic Closure of Finite Fields 4
1.3 Irreducible Polynomials 7
1.4 Trace and Norm 9
1.5 Function Fields of One Variable 12
1.6 Extensions of Valuations 25
1.7 Constant Field Extensions 27
Algebraic Varieties 30
2.1 Affine and Projective Spaces 30
2.2 Algebraic Sets 37
2.3 Varieties 44
2.4 Function Fields of Varieties 50
2.5 Morphisms and Rational Maps 56
Algebraic Curves 68
3.1 Nonsingular Curves 68
3.2 Maps Between Curves 76
3.3 Divisors 80
3.4 Riemann-Roch Spaces 84
3.5 Riemann s Theorem and Genus 87
3.6 The Riemann-Roch Theorem 89
3.7 Elliptic Curves 95
3.8 Summary: Curves and Function Fields 104
Rational Places 105
4.1 Zeta Functions 105
4.2 The Hasse-Weil Theorem 115
4.3 Further Bounds and Asymptotic Results 122
4.4 Character Sums 127
Contents
Applications to Coding Theory 147
5.1 Background on Codes 147
5.2 Algebraic-Geometry Codes 151
5.3 Asymptotic Results 155
5.4 NXL and XNL Codes 174
5.5 Function-Field Codes 181
5.6 Applications of Character Sums 187
5.7 Digital Nets 192
Applications to Cryptography 206
6.1 Background on Cryptography 206
6.2 Elliptic-Curve Cryptosystems 210
6.3 Hyperelliptic-Curve Cryptography 214
6.4 Code-Based Public-Key Cryptosystems 218
6.5 Frameproof Codes 223
6.6 Fast Arithmetic in Finite Fields 233
Appendix 241
A.1 Topological Spaces 241
A.2 Krull Dimension 244
A.3 Discrete Valuation Rings 245
Bibliography 249
Index 257
|
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| discipline | Informatik Mathematik |
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| indexdate | 2024-07-09T22:04:26Z |
| institution | BVB |
| isbn | 9780691102887 |
| language | English |
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| physical | VIII, 260 S. |
| publishDate | 2009 |
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| publisher | Princeton Univ. Press |
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| spelling | Niederreiter, Harald 1944- Verfasser (DE-588)117716979 aut Algebraic geometry in coding theory and cryptography Harald Niederreiter and Chaoping Xing Princeton [u.a.] Princeton Univ. Press 2009 VIII, 260 S. txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references and index Coding theory Cryptography Geometry, Algebraic Codierungstheorie (DE-588)4139405-7 gnd rswk-swf Kryptologie (DE-588)4033329-2 gnd rswk-swf Algebraische Geometrie (DE-588)4001161-6 gnd rswk-swf Algebraische Geometrie (DE-588)4001161-6 s Codierungstheorie (DE-588)4139405-7 s Kryptologie (DE-588)4033329-2 s DE-604 Xing, Chaoping 1963- Sonstige (DE-588)138740844 oth HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018642246&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Niederreiter, Harald 1944- Algebraic geometry in coding theory and cryptography Coding theory Cryptography Geometry, Algebraic Codierungstheorie (DE-588)4139405-7 gnd Kryptologie (DE-588)4033329-2 gnd Algebraische Geometrie (DE-588)4001161-6 gnd |
| subject_GND | (DE-588)4139405-7 (DE-588)4033329-2 (DE-588)4001161-6 |
| title | Algebraic geometry in coding theory and cryptography |
| title_auth | Algebraic geometry in coding theory and cryptography |
| title_exact_search | Algebraic geometry in coding theory and cryptography |
| title_full | Algebraic geometry in coding theory and cryptography Harald Niederreiter and Chaoping Xing |
| title_fullStr | Algebraic geometry in coding theory and cryptography Harald Niederreiter and Chaoping Xing |
| title_full_unstemmed | Algebraic geometry in coding theory and cryptography Harald Niederreiter and Chaoping Xing |
| title_short | Algebraic geometry in coding theory and cryptography |
| title_sort | algebraic geometry in coding theory and cryptography |
| topic | Coding theory Cryptography Geometry, Algebraic Codierungstheorie (DE-588)4139405-7 gnd Kryptologie (DE-588)4033329-2 gnd Algebraische Geometrie (DE-588)4001161-6 gnd |
| topic_facet | Coding theory Cryptography Geometry, Algebraic Codierungstheorie Kryptologie Algebraische Geometrie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018642246&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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