Holdings: The development of the number field sieve

The development of the number field sieve:

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Bibliographic Details
Format:	Book
Language:	English
Published:	Berlin [u.a.] Springer 1993
Series:	Lecture notes in mathematics 1554
Subjects:	Cribles (Mathématiques) Getaltheorie Teoria Dos Numeros Sieves (Mathematics) Faktorisierung Zahlentheorie Primzahlzerlegung Algebraischer Zahlkörper Siebmethode Algorithmus Aufsatzsammlung
Online Access:	Inhaltsverzeichnis
Physical Description:	VIII, 131 S. graph. Darst.
ISBN:	3540570136 0387570136

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MARC


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Record in the Search Index

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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
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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
subject_GND	(DE-588)4128927-4 (DE-588)4067277-3 (DE-588)4175717-8 (DE-588)4068537-8 (DE-588)4181206-2 (DE-588)4001183-5 (DE-588)4143413-4
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
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