The development of the number field sieve:
Gespeichert in:
| Format: | Buch |
|---|---|
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
1993
|
| Schriftenreihe: | Lecture notes in mathematics
1554 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | VIII, 131 S. graph. Darst. |
| ISBN: | 3540570136 0387570136 |
Internformat
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| 245 | 1 | 0 | |a The development of the number field sieve |c A. K. Lenstra ... (eds.) |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 1993 | |
| 300 | |a VIII, 131 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
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Datensatz im Suchindex
| _version_ | 1805082756804247552 |
|---|---|
| adam_text |
CONTENTS
The number field sieve: an annotated bibliography 1
H. W. Lenstra, Jr.
Factoring with cubic integers 4
3. M. Pollard
Introduction 4
Properties of the set 5 5
Operations on the integers of S 6
Factorisation of F j 7
Computer and program details 9
Example of an j4 solution 10
References 10
The number field sieve 11
A. K. Lenstra, H. W. Lenstra, Jr., M. S. Manasse, J. M. Pollard
1. Introduction 11
2. The algorithm 14
3. Finding generators 20
4. Sieving 25
5. Finding the unit contribution 29
6. Run time analysis 30
7. Additional remarks 33
8. Examples 34
9. Generalization 38
References 40
The lattice sieve 43
J. M. Pollard
Object of the lattice sieve 43
Operation of the sieve 45
More factorisations of F7! 46
Some programming notes 48
Numerical example from the factorisation of F7 49
References 49
Factoring integers with the number field sieve 50
J.P. Buhler, H. W. Lenstra, Jr., Carl Pomerance
1. Introduction 50
2. The idea of the number field sieve 52
3. Finding a polynomial 54
4. The rational sieve 55
5. The algebraic sieve 57
6. Four obstructions 60
viii CONTENTS
7. Algebraic interlude 63
8. Quadratic characters 67
9. Finding square roots 70
10. Analytic interlude 76
11. Summary of the number field sieve and a heuristic analysis 80
12. Homogeneous polynomials 84
References 92
Computing a square root for the number field sieve 95
Jean Marc Couveignes
1. Introduction 95
2. Description and analysis of the method 98
References 102
A general number field sieve implementation 103
Daniel J. Bernstein, A. K. Lenstra
1. Introduction 103
2. Outline of the implementation 104
3. Choosing the polynomial 104
4. Searching for a polynomial 107
5. Computing bases 108
6. Sieving 108
7. Trial dividing 114
8. Constructing the matrix 115
9. Reducing the matrix 116
10. Computing the square root 116
11. Proof that the square root works 118
12. Examples 120
13. Future directions 124
References 125
The illustration on the front cover 127
Index 129 |
| any_adam_object | 1 |
| author_GND | (DE-588)1089560745 |
| building | Verbundindex |
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| dewey-full | 510 512/.72 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 510 - Mathematics 512 - Algebra |
| dewey-raw | 510 512/.72 |
| dewey-search | 510 512/.72 |
| dewey-sort | 3510 |
| dewey-tens | 510 - Mathematics |
| discipline | Informatik Mathematik |
| format | Book |
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| indexdate | 2024-07-20T07:37:43Z |
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| isbn | 3540570136 0387570136 |
| language | English |
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| publishDate | 1993 |
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| spelling | The development of the number field sieve A. K. Lenstra ... (eds.) Berlin [u.a.] Springer 1993 VIII, 131 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 1554 Cribles (Mathématiques) Getaltheorie gtt Teoria Dos Numeros larpcal Sieves (Mathematics) Faktorisierung (DE-588)4128927-4 gnd rswk-swf Zahlentheorie (DE-588)4067277-3 gnd rswk-swf Primzahlzerlegung (DE-588)4175717-8 gnd rswk-swf Algebraischer Zahlkörper (DE-588)4068537-8 gnd rswk-swf Siebmethode (DE-588)4181206-2 gnd rswk-swf Algorithmus (DE-588)4001183-5 gnd rswk-swf (DE-588)4143413-4 Aufsatzsammlung gnd-content Zahlentheorie (DE-588)4067277-3 s DE-604 Faktorisierung (DE-588)4128927-4 s Algorithmus (DE-588)4001183-5 s Siebmethode (DE-588)4181206-2 s Algebraischer Zahlkörper (DE-588)4068537-8 s DE-188 Primzahlzerlegung (DE-588)4175717-8 s Lenstra, Arjen K. 1956- Sonstige (DE-588)1089560745 oth Lecture notes in mathematics 1554 (DE-604)BV000676446 1554 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005336271&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | The development of the number field sieve Lecture notes in mathematics Cribles (Mathématiques) Getaltheorie gtt Teoria Dos Numeros larpcal Sieves (Mathematics) Faktorisierung (DE-588)4128927-4 gnd Zahlentheorie (DE-588)4067277-3 gnd Primzahlzerlegung (DE-588)4175717-8 gnd Algebraischer Zahlkörper (DE-588)4068537-8 gnd Siebmethode (DE-588)4181206-2 gnd Algorithmus (DE-588)4001183-5 gnd |
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| title | The development of the number field sieve |
| title_auth | The development of the number field sieve |
| title_exact_search | The development of the number field sieve |
| title_full | The development of the number field sieve A. K. Lenstra ... (eds.) |
| title_fullStr | The development of the number field sieve A. K. Lenstra ... (eds.) |
| title_full_unstemmed | The development of the number field sieve A. K. Lenstra ... (eds.) |
| title_short | The development of the number field sieve |
| title_sort | the development of the number field sieve |
| topic | Cribles (Mathématiques) Getaltheorie gtt Teoria Dos Numeros larpcal Sieves (Mathematics) Faktorisierung (DE-588)4128927-4 gnd Zahlentheorie (DE-588)4067277-3 gnd Primzahlzerlegung (DE-588)4175717-8 gnd Algebraischer Zahlkörper (DE-588)4068537-8 gnd Siebmethode (DE-588)4181206-2 gnd Algorithmus (DE-588)4001183-5 gnd |
| topic_facet | Cribles (Mathématiques) Getaltheorie Teoria Dos Numeros Sieves (Mathematics) Faktorisierung Zahlentheorie Primzahlzerlegung Algebraischer Zahlkörper Siebmethode Algorithmus Aufsatzsammlung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005336271&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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