Primality Testing and Integer Factorization in Public-Key Cryptography:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York, NY
Springer
2009
|
| Edition: | 2. ed. |
| Series: | Advances in Information Security
11 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVIII, 371 S. graph. Darst. 235 mm x 155 mm |
| ISBN: | 9780387772677 0387772677 |
Staff View
MARC
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Record in the Search Index
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| adam_text | Table of Contents
Preface to the Second Edition................................ ix
Preface to the First Edition .................................. xi
1. Number-Theoretic Preliminaries......................... 1
1.1 Problems in Number Theory ................................ 1
1.2 Groups. Rings and Fields.................................... 13
1.3 Divisibility Properties....................................... 23
1.4 Euclid s Algorithm and Continued Fractions................... 34
1.5 Arithmetic Functions ó{ç).ô{ç). o(n). (ç).ì(ç) ............... 50
1.6 Linear Congruences......................................... 63
1.7 Quadratic Congruences...................................... 85
1.8 Primitive Roots and Power Residues.......................... 103
1.9 Arithmetic of Elliptic Curves................................. 113
1.10 Chapter Notes and Further Reading.......................... 124
2. Primality Testing and Prime Generation.................127
2.1 Computing with Numbers and Curves.........................127
2.2 Riemann æ and Dirichlet L Functions.........................139
2.3 Rigorous Primality Tests....................................149
2.4 Compositeness and Pseudoprimality Tests.....................157
2.5 Lucas Pseudoprimality Test..................................108
2.6 Elliptic Curve Primality Tests................................172
2.7 Superpolynomial-Time Tests.................................177
2.8 Polynomial-Time Tests......................................182
2.9 Comparison of General Purpose Primality Tests................188
2.10 Primality Tests for Special Numbers..........................192
2.11 Prime Number Generation ..................................201
2.12 Chapter Notes and Further Reading ..........................207
3. Integer Factorization and Discrete Logarithms...........209
3.1 Introduction...............................................209
3.2 Simple Factoring Methods...................................212
3.3 Elliptic Curve Method (ECM) ...............................221
Table of Contents
3.4 General Factoring Congruence ...............................226
3.5 Continued FRACtion Method (CFRAC) ......................230
3.6 Quadratic Sieve (QS) .......................................234
3.7 Number Field Sieve (NFS)...................................239
3.8 Quantum Factoring Algorithm...............................251
3.9 Discrete Logarithms........................................257
3.10 itth Roots.................................................270
3.11 Elliptic Curve Discrete Logarithms ...........................278
3.12 Chapter Notes and Further Reading..........................285
4. Number-Theoretic Cryptography ........................287
4.1 Public-Key Cryptography ...................................287
4.2 RSA Cryptosystem.........................................292
4.3 Security and Cryptanalysis of RSA...........................301
4.4 Rabin Cryptography........................................314
4.5 Quadratic Residuosity Cryptography..........................320
4.6 Discrete Logarithm Cryptography............................326
4.7 Elliptic Curve Cryptography.................................331
4.8 Zero-Knowledge Techniques..................................338
4.9 Deniable Authentication.....................................341
4.10 Non-Factoring Based Cryptography...........................346
4.11 Chapter Notes and Further Reading..........................351
Bibliography..................................................353
Index.........................................................367
About the Author............................................373
|
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| id | DE-604.BV035337997 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T21:31:36Z |
| institution | BVB |
| isbn | 9780387772677 0387772677 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-017142341 |
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| owner | DE-29T DE-91G DE-BY-TUM |
| owner_facet | DE-29T DE-91G DE-BY-TUM |
| physical | XVIII, 371 S. graph. Darst. 235 mm x 155 mm |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | Springer |
| record_format | marc |
| series | Advances in Information Security |
| series2 | Advances in Information Security |
| spelling | Yan, Song Y. 1954- Verfasser (DE-588)121556034 aut Primality Testing and Integer Factorization in Public-Key Cryptography Song Y. Yan 2. ed. New York, NY Springer 2009 XVIII, 371 S. graph. Darst. 235 mm x 155 mm txt rdacontent n rdamedia nc rdacarrier Advances in Information Security 11 Computer security Cryptography Public-Key-Kryptosystem (DE-588)4209133-0 gnd rswk-swf Primzahltest (DE-588)4704538-3 gnd rswk-swf Faktorisierung (DE-588)4128927-4 gnd rswk-swf Faktorisierung (DE-588)4128927-4 s Public-Key-Kryptosystem (DE-588)4209133-0 s Primzahltest (DE-588)4704538-3 s DE-604 Advances in Information Security 11 (DE-604)BV014168308 11 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017142341&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Yan, Song Y. 1954- Primality Testing and Integer Factorization in Public-Key Cryptography Advances in Information Security Computer security Cryptography Public-Key-Kryptosystem (DE-588)4209133-0 gnd Primzahltest (DE-588)4704538-3 gnd Faktorisierung (DE-588)4128927-4 gnd |
| subject_GND | (DE-588)4209133-0 (DE-588)4704538-3 (DE-588)4128927-4 |
| title | Primality Testing and Integer Factorization in Public-Key Cryptography |
| title_auth | Primality Testing and Integer Factorization in Public-Key Cryptography |
| title_exact_search | Primality Testing and Integer Factorization in Public-Key Cryptography |
| title_full | Primality Testing and Integer Factorization in Public-Key Cryptography Song Y. Yan |
| title_fullStr | Primality Testing and Integer Factorization in Public-Key Cryptography Song Y. Yan |
| title_full_unstemmed | Primality Testing and Integer Factorization in Public-Key Cryptography Song Y. Yan |
| title_short | Primality Testing and Integer Factorization in Public-Key Cryptography |
| title_sort | primality testing and integer factorization in public key cryptography |
| topic | Computer security Cryptography Public-Key-Kryptosystem (DE-588)4209133-0 gnd Primzahltest (DE-588)4704538-3 gnd Faktorisierung (DE-588)4128927-4 gnd |
| topic_facet | Computer security Cryptography Public-Key-Kryptosystem Primzahltest Faktorisierung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017142341&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV014168308 |
| work_keys_str_mv | AT yansongy primalitytestingandintegerfactorizationinpublickeycryptography |