Primality testing for beginners:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Providence, RI
American Math. Soc.
2014
|
| Schriftenreihe: | Student mathematical library
70 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturverz. S. 233 - 236 |
| Beschreibung: | XII, 244 S. |
| ISBN: | 9780821898833 |
Internformat
MARC
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Datensatz im Suchindex
| _version_ | 1804151779836821504 |
|---|---|
| adam_text | Titel: Primality testing for beginners
Autor: Rempe-Gillen, Lasse
Jahr: 2014
Contents
Preface xi
Introduction 1
Part 1. Foundations
Chapter 1. Natural numbers and primes 13
§1.1. The natural numbers 13
§1.2. Divisibility and primes 26
§1.3. Prime factor decomposition 31
§1.4. The Euclidean algorithm 35
§1.5. The Sieve of Eratosthenes 39
§1.6. There are infimtely many primes 41
Further reading 42
Chapter 2. Algorithms and complexity 43
§2.1. Algorithms 43
§2.2. Decidable and undecidable problems 52
§2.3. Complexity of algorithms and the class P 57
§2.4. The class NP 68
viii Contents
§2.5. Randomized algorithms 73
Further reading 81
Chapter 3. Foundations of number theory 83
§3.1. Modular arithmetic 84
§3.2. Fermat s Little Theorem 94
§3.3. A first primality test 104
§3.4. Polynomials 107
§3.5. Polynomials and modular arithmetic 120
Further reading 127
Chapter 4. Prime numbers and cryptography 129
§4.1. Cryptography 129
§4.2. RSA 132
§4.3. Distribution of primes 136
§4.4. Proof of the weak prime number theorem 139
§4.5. Randomized primality tests 143
Further reading 150
Part 2. The AKS Algorithm
Chapter 5. The starting point: Fermat for polynomials 153
§5.1. A generalization of Fermat s Theorem 153
§5.2. The idea of the AKS algorithm 159
§5.3. The Agrawal-Biswas test 163
Chapter 6. The theorem of Agrawal, Kayal, and Saxena 169
§6.1. Statement of the theorem 170
§6.2. The idea of the proof 171
§6.3. The number of polynomials in V 173
§6.4. Cyclotomic polynomials 178
Contents ix
Chapter 7. The algorithm 183
§7.1. How quickly does the order of n modulo r grow? 183
§7.2. The algorithm of Agrawal, Kayal, and Saxena 186
§7.3. Further comments 189
Further reading 192
Appendix A. Open questions 193
Further reading 205
Appendix B. Solutions and comments to important exercises 207
Bibliography 233
List of Symbols 237
Index 239
|
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| spelling | Rempe-Gillen, Lasse 1978- Verfasser (DE-588)124924131 aut Primzahltests für Einsteiger Primality testing for beginners Lasse Rempe-Gillen ; Rebecca Waldecker Providence, RI American Math. Soc. 2014 XII, 244 S. txt rdacontent n rdamedia nc rdacarrier Student mathematical library 70 Literaturverz. S. 233 - 236 Number theory ... Instructional exposition (textbooks, tutorial papers, etc.) msc Number theory ... Research exposition (monographs, survey articles) msc Number theory ... Elementary number theory ... Elementary number theory msc Number theory ... Computational number theory ... Primality msc Number theory ... Computational number theory ... Algorithms; complexity msc Number theory Number theory ... Instructional exposition (textbooks, tutorial papers, etc.) Number theory ... Research exposition (monographs, survey articles) Number theory ... Elementary number theory ... Elementary number theory Number theory ... Computational number theory ... Primality Number theory ... Computational number theory ... Algorithms; complexity Algorithmus (DE-588)4001183-5 gnd rswk-swf Kryptologie (DE-588)4033329-2 gnd rswk-swf Primzahltest (DE-588)4704538-3 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Primzahltest (DE-588)4704538-3 s Algorithmus (DE-588)4001183-5 s Kryptologie (DE-588)4033329-2 s DE-604 Waldecker, Rebecca 1979- Verfasser (DE-588)132966824 aut Student mathematical library 70 (DE-604)BV013184751 70 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027032861&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Rempe-Gillen, Lasse 1978- Waldecker, Rebecca 1979- Primality testing for beginners Student mathematical library Number theory ... Instructional exposition (textbooks, tutorial papers, etc.) msc Number theory ... Research exposition (monographs, survey articles) msc Number theory ... Elementary number theory ... Elementary number theory msc Number theory ... Computational number theory ... Primality msc Number theory ... Computational number theory ... Algorithms; complexity msc Number theory Number theory ... Instructional exposition (textbooks, tutorial papers, etc.) Number theory ... Research exposition (monographs, survey articles) Number theory ... Elementary number theory ... Elementary number theory Number theory ... Computational number theory ... Primality Number theory ... Computational number theory ... Algorithms; complexity Algorithmus (DE-588)4001183-5 gnd Kryptologie (DE-588)4033329-2 gnd Primzahltest (DE-588)4704538-3 gnd |
| subject_GND | (DE-588)4001183-5 (DE-588)4033329-2 (DE-588)4704538-3 (DE-588)4123623-3 |
| title | Primality testing for beginners |
| title_alt | Primzahltests für Einsteiger |
| title_auth | Primality testing for beginners |
| title_exact_search | Primality testing for beginners |
| title_full | Primality testing for beginners Lasse Rempe-Gillen ; Rebecca Waldecker |
| title_fullStr | Primality testing for beginners Lasse Rempe-Gillen ; Rebecca Waldecker |
| title_full_unstemmed | Primality testing for beginners Lasse Rempe-Gillen ; Rebecca Waldecker |
| title_short | Primality testing for beginners |
| title_sort | primality testing for beginners |
| topic | Number theory ... Instructional exposition (textbooks, tutorial papers, etc.) msc Number theory ... Research exposition (monographs, survey articles) msc Number theory ... Elementary number theory ... Elementary number theory msc Number theory ... Computational number theory ... Primality msc Number theory ... Computational number theory ... Algorithms; complexity msc Number theory Number theory ... Instructional exposition (textbooks, tutorial papers, etc.) Number theory ... Research exposition (monographs, survey articles) Number theory ... Elementary number theory ... Elementary number theory Number theory ... Computational number theory ... Primality Number theory ... Computational number theory ... Algorithms; complexity Algorithmus (DE-588)4001183-5 gnd Kryptologie (DE-588)4033329-2 gnd Primzahltest (DE-588)4704538-3 gnd |
| topic_facet | Number theory ... Instructional exposition (textbooks, tutorial papers, etc.) Number theory ... Research exposition (monographs, survey articles) Number theory ... Elementary number theory ... Elementary number theory Number theory ... Computational number theory ... Primality Number theory ... Computational number theory ... Algorithms; complexity Number theory Algorithmus Kryptologie Primzahltest Lehrbuch |
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