Elementary number theory: primes, congruences, and secrets ; a computational approach
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Springer
2009
|
| Schriftenreihe: | Undergraduate texts in mathematics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | X, 166 S. Illustrationen |
| ISBN: | 9780387855240 |
Internformat
MARC
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| 100 | 1 | |a Stein, William |d 1974- |e Verfasser |0 (DE-588)137841973 |4 aut | |
| 245 | 1 | 0 | |a Elementary number theory |b primes, congruences, and secrets ; a computational approach |c William Stein |
| 264 | 1 | |a New York, NY |b Springer |c 2009 | |
| 300 | |a X, 166 S. |b Illustrationen | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Undergraduate texts in mathematics | |
| 650 | 0 | 7 | |a Zahlentheorie |0 (DE-588)4067277-3 |2 gnd |9 rswk-swf |
| 655 | 7 | |0 (DE-588)4123623-3 |a Lehrbuch |2 gnd-content | |
| 689 | 0 | 0 | |a Zahlentheorie |0 (DE-588)4067277-3 |D s |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-017029195 | ||
Datensatz im Suchindex
| _version_ | 1804138488677793794 |
|---|---|
| adam_text | Contents
Preface
їх
Prime Numbers
1
1.1
Prime Factorization
...................... 2
1.2
The Sequence of Prime Numbers
............... 10
1.3
Exercises
............................ 19
The Ring of Integers Modulo
η
21
2.1
Congruences Modulo
η
..................... 22
2.2
The Chinese Remainder Theorem
............... 29
2.3
Quickly Computing Inverses and Huge Powers
........ 31
2.4
Primality Testing
........................ 36
2.5
The Structure of (Z/pZ)*
.................., 39
2.6
Exercises
............................ 44
Public-key Cryptography
49
3.1
Playing with Fire
........................ 49
3.2
The Diffie-Hellman Key Exchange
.............. 51
3.3
The RSA Cryptosystem
.................... 56
3.4
Attacking RSA
......................... 61
3.5
Exercises
............................ 67
Quadratic Reciprocity
69
4.1
Statement of the Quadratic Reciprocity Law
........ 70
ι
Contents
4.2 Euler s
Criterion
........................ 73
4.3 First
Proof of Quadratic Reciprocity
............. 75
4.4
A Proof of Quadratic Reciprocity Using Gauss Sums
.... 81
4.5
Finding Square Roots
..................... 86
4.6
Exercises
............................ 89
Continued Fractions
93
5.1
The Definition
......................... 94
5.2
Finite Continued Fractions
.................. 95
5.3
Infinite Continued Fractions
.................. 101
5.4
The Continued Fraction of
e
.................. 107
5.5
Quadratic Irrationals
...................... 110
5.6
Recognizing Rational Numbers
................ 115
5.7
Sums of Two Squares
..................... 117
5.8
Exercises
............................ 121
Elliptic Curves
123
6.1
The Definition
......................... 124
6.2
The Group Structure on an Elliptic Curve
.......... 125
6.3
Integer Factorization Using Elliptic Curves
......... 129
6.4
Elliptic Curve Cryptography
................. 135
6.5
Elliptic Curves Over the Rational Numbers
......... 140
6.6
Exercises
............................ 146
Answers and Hints
149
References
155
Index
161
|
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| indexdate | 2024-07-09T21:28:58Z |
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| isbn | 9780387855240 |
| language | English |
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| physical | X, 166 S. Illustrationen |
| publishDate | 2009 |
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| spelling | Stein, William 1974- Verfasser (DE-588)137841973 aut Elementary number theory primes, congruences, and secrets ; a computational approach William Stein New York, NY Springer 2009 X, 166 S. Illustrationen txt rdacontent n rdamedia nc rdacarrier Undergraduate texts in mathematics Zahlentheorie (DE-588)4067277-3 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Zahlentheorie (DE-588)4067277-3 s DE-604 Erscheint auch als Online-Ausgabe 978-0-387-85525-7 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017029195&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Stein, William 1974- Elementary number theory primes, congruences, and secrets ; a computational approach Zahlentheorie (DE-588)4067277-3 gnd |
| subject_GND | (DE-588)4067277-3 (DE-588)4123623-3 |
| title | Elementary number theory primes, congruences, and secrets ; a computational approach |
| title_auth | Elementary number theory primes, congruences, and secrets ; a computational approach |
| title_exact_search | Elementary number theory primes, congruences, and secrets ; a computational approach |
| title_full | Elementary number theory primes, congruences, and secrets ; a computational approach William Stein |
| title_fullStr | Elementary number theory primes, congruences, and secrets ; a computational approach William Stein |
| title_full_unstemmed | Elementary number theory primes, congruences, and secrets ; a computational approach William Stein |
| title_short | Elementary number theory |
| title_sort | elementary number theory primes congruences and secrets a computational approach |
| title_sub | primes, congruences, and secrets ; a computational approach |
| topic | Zahlentheorie (DE-588)4067277-3 gnd |
| topic_facet | Zahlentheorie Lehrbuch |
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