The joy of factoring:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Providence, Rhode Island
American Mathematical Society
[2013]
|
| Schriftenreihe: | Student mathematical library
volume 68 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturverzeichnis: Seite 273 - 286 |
| Beschreibung: | xiv, 293 Seiten Illustrationen, Diagramme |
| ISBN: | 9781470410483 |
Internformat
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Datensatz im Suchindex
| _version_ | 1804151526298484736 |
|---|---|
| adam_text | Titel: The joy of factoring
Autor: Wagstaff, Samuel S
Jahr: 2013
Contents
Preface ix
Exercise xiv
Chapter 1. Why Factor Integers? 1
Introduction 1
§1.1. Public-Key Cryptography 2
§1.2. Repunits 5
§1.3. Repeating Decimal Fractions 6
§1.4. Perfect Numbers 8
§1.5. The Cunningham Project 9
Exercises 12
Chapter 2. Number Theory Review 13
Introduction 13
§2.1. Divisibility 17
§2.2. Prime Numbers 20
§2.3. Congruences 24
§2.4. Fermât and Euler 28
§2.5. Arithmetic Functions 33
V
VI
Contents
§2.6. Quadratic Congruences 36
Exercises 39
Chapter 3. Number Theory Relevant to Factoring 41
Introduction 41
§3.1. Smooth Numbers 42
§3.2. Finding Modular Square Roots 44
§3.3. Cyclotomic Polynomials 47
§3.4. Divisibility Sequences and bm — 1 49
§3.5. Factors of bm + 1 55
§3.6. Factors of Fibonacci and Lucas Numbers 56
§3.7. Primality Testing 59
Exercises 71
Chapter 4. How Are Factors Used? 75
Introduction 75
§4.1. Aurifeuillian Factorizations 76
§4.2. Perfect Numbers 83
§4.3. Harmonic Numbers 88
§4.4. Prime Proving 91
§4.5. Linear Feedback Shift Registers 93
§4.6. Testing Conjectures 97
§4.7. Bernoulli Numbers 101
§4.8. Cryptographic Applications 104
§4.9. Other Applications 113
Exercises 116
Chapter 5. Simple Factoring Algorithms 119
Introduction 119
§5.1. Trial Division 120
§5.2. Fermat s Difference of Squares Method 123
§5.3. Hart s One-Line Factoring Algorithm 127
§5.4. Lehman s Variation of Fermât 128
Contents
vii
§5.5. The Lehmers Factoring Method 132
§5.6. Pollard s Rho Method 135
§5.7. Pollard s p — 1 Method 138
Exercises 141
Chapter 6. Continued Fractions 143
Introduction 143
§6.1. Basic Facts about Continued Fractions 144
§6.2. McKee s Variation of Fermât 147
§6.3. Periodic Continued Fractions 149
§6.4. A General Plan for Factoring 153
§6.5. Lehmer and Powers 155
§6.6. Continued Fraction Factoring Algorithm 158
§6.7. SQUFOF—SQUare FOrms Factoring 163
§6.8. Pell s Equation 169
Exercises 170
Chapter 7. Elliptic Curves 173
Introduction 173
§7.1. Basic Properties of Elliptic Curves 174
§7.2. Factoring with Elliptic Curves 181
§7.3. Primality Proving with Elliptic Curves 187
§7.4. Applications of Factoring to Elliptic Curves 188
Exercises 190
Chapter 8. Sieve Algorithms 191
Introduction 191
§8.1. The Basic Sieve 192
§8.2. The Quadratic Sieve 195
§8.3. The Double Sieve 202
§8.4. Schroeppel s Linear Sieve 205
§8.5. The Number Field Sieve 207
Exercises 217
viii Contents
Chapter 9. Factoring Devices 219
Introduction 219
§9.1. Sieve Devices 219
§9.2. Special Computers 230
Exercise 237
Chapter 10. Theoretical and Practical Factoring 239
Introduction 239
§10.1. Theoretical Factoring 240
§10.2. Multiprecise Arithmetic 244
§10.3. Factoring—There s an App for That 246
§10.4. Dirty Tricks 248
§10.5. Dirty Tricks with Lattices 253
§10.6. The Future of Factoring 262
Exercises 267
Appendix. Answers and Hints for Exercises 269
Introduction 269
§A.l. Chapter 1 269
§A.2. Chapter 2 270
§A.3. Chapter 3 270
§A.4. Chapter 4 271
§A.5. Chapter 5 271
§A.6. Chapter 6 271
§A.7. Chapter 7 272
§A.8. Chapter 8 272
§A.9. Chapter 10 272
Bibliography 273
Index 287
|
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| discipline | Mathematik |
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| language | English |
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| spelling | Wagstaff, Samuel S. 1945- Verfasser (DE-588)117726672 aut The joy of factoring Samuel S. Wagstaff, Jr. Providence, Rhode Island American Mathematical Society [2013] © 2013 xiv, 293 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier Student mathematical library volume 68 Literaturverzeichnis: Seite 273 - 286 Number theory ... Computational number theory ... Factorization msc Number theory ... Elementary number theory ... Factorization; primality msc Factorization (Mathematics) Number theory Number theory ... Computational number theory ... Factorization Number theory ... Elementary number theory ... Factorization; primality Zahlentheorie (DE-588)4067277-3 gnd rswk-swf Faktorisierung (DE-588)4128927-4 gnd rswk-swf Zahlentheorie (DE-588)4067277-3 s Faktorisierung (DE-588)4128927-4 s DE-604 Erscheint auch als Online-Ausgabe 978-1-4704-1413-9 Student mathematical library volume 68 (DE-604)BV013184751 68 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026860792&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Wagstaff, Samuel S. 1945- The joy of factoring Student mathematical library Number theory ... Computational number theory ... Factorization msc Number theory ... Elementary number theory ... Factorization; primality msc Factorization (Mathematics) Number theory Number theory ... Computational number theory ... Factorization Number theory ... Elementary number theory ... Factorization; primality Zahlentheorie (DE-588)4067277-3 gnd Faktorisierung (DE-588)4128927-4 gnd |
| subject_GND | (DE-588)4067277-3 (DE-588)4128927-4 |
| title | The joy of factoring |
| title_auth | The joy of factoring |
| title_exact_search | The joy of factoring |
| title_full | The joy of factoring Samuel S. Wagstaff, Jr. |
| title_fullStr | The joy of factoring Samuel S. Wagstaff, Jr. |
| title_full_unstemmed | The joy of factoring Samuel S. Wagstaff, Jr. |
| title_short | The joy of factoring |
| title_sort | the joy of factoring |
| topic | Number theory ... Computational number theory ... Factorization msc Number theory ... Elementary number theory ... Factorization; primality msc Factorization (Mathematics) Number theory Number theory ... Computational number theory ... Factorization Number theory ... Elementary number theory ... Factorization; primality Zahlentheorie (DE-588)4067277-3 gnd Faktorisierung (DE-588)4128927-4 gnd |
| topic_facet | Number theory ... Computational number theory ... Factorization Number theory ... Elementary number theory ... Factorization; primality Factorization (Mathematics) Number theory Zahlentheorie Faktorisierung |
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