The mathematics of ciphers: number theory and RSA cryptography
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boca Raton ; London ; New York
CRC Press
1999
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | An AK Peters book |
| Beschreibung: | XV, 196 S. Ill. |
| ISBN: | 1568810822 |
Internformat
MARC
| LEADER | 00000nam a2200000 c 4500 | ||
|---|---|---|---|
| 001 | BV014305181 | ||
| 003 | DE-604 | ||
| 005 | 20181022 | ||
| 007 | t | ||
| 008 | 020521s1999 a||| |||| 00||| eng d | ||
| 020 | |a 1568810822 |9 1-56881-082-2 | ||
| 035 | |a (OCoLC)246130796 | ||
| 035 | |a (DE-599)BVBBV014305181 | ||
| 040 | |a DE-604 |b ger |e rakwb | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-355 |a DE-188 |a DE-706 | ||
| 050 | 0 | |a QA241 | |
| 082 | 0 | |a 512.7 | |
| 084 | |a SK 180 |0 (DE-625)143222: |2 rvk | ||
| 084 | |a 17,1 |2 ssgn | ||
| 100 | 1 | |a Coutinho, Severino Collier |e Verfasser |4 aut | |
| 240 | 1 | 0 | |a Números inteiros e criptografia RSA |
| 245 | 1 | 0 | |a The mathematics of ciphers |b number theory and RSA cryptography |c S. C. Coutinho |
| 264 | 1 | |a Boca Raton ; London ; New York |b CRC Press |c 1999 | |
| 300 | |a XV, 196 S. |b Ill. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a An AK Peters book | ||
| 650 | 4 | |a Kryptologie - Zahlentheorie | |
| 650 | 0 | 7 | |a Zahlentheorie |0 (DE-588)4067277-3 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Kryptologie |0 (DE-588)4033329-2 |2 gnd |9 rswk-swf |
| 655 | 4 | |a Lehrbuch - Elementare Zahlentheorie | |
| 689 | 0 | 0 | |a Kryptologie |0 (DE-588)4033329-2 |D s |
| 689 | 0 | 1 | |a Zahlentheorie |0 (DE-588)4067277-3 |D s |
| 689 | 0 | |5 DE-604 | |
| 856 | 4 | 2 | |m GBV Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009812655&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-009812655 | ||
Datensatz im Suchindex
| _version_ | 1804129201125588992 |
|---|---|
| adam_text | THE MATHEMATICS OF CIPHERS NUMBER THEORY AND RSA CRYPTOGRAPHY S. C.
COUTINHO DEPARTMENT OF COMPUTER SCIENCE FEDERAL UNIVERSITY OF RIO DE
JANEIRO RIO DE JANEIRO, BRAZIL A K PETERS NATICK, MASSACHUSETTS CONTENTS
PREFACE XIII 1 1 3 5 7 8 11 12 17 17 19 21 22 25 27 30 33 33 34 36 37 38
40 41 43 45 CHAPTER 3. PRIME NUMBERS 49 1. POLYNOMIAL FORMULAE 49 2.
EXPONENTIAL FORMULAE: MERSENNE NUMBERS 51 INTRODUCTION 1. 2. 3. 4. 5. 6.
7. CRYPTOGRAPHY THE RSA CRYPTOSYSTEM COMPUTER ALGEBRA THE GREEKS AND THE
INTEGERS FERMAT, EULER, AND GAUSS THE PROBLEMS OF NUMBER THEORY THEOREMS
AND PROOFS CHAPTER 1. FUNDAMENTAL ALGORITHMS 1. 2. 3. 4. 5. 6. I:
ALGORITHMS DIVISION ALGORITHM DIVISION THEOREM THE EUCLIDEAN ALGORITHM
PROOF OF THE EUCLIDEAN ALGORITHM EXTENDED EUCLIDEAN ALGORITHM EXERCISES
CHAPTER 2. UNIQUE FACTORIZATION 1. 2. 3. 4. 5. 6. 7. 8. 9. UNIQUE
FACTORIZATION THEOREM EXISTENCE OF THE FACTORIZATION EFFICIENCY OF THE
TRIAL DIVISION ALGORITHM FERMAT S FACTORIZATION ALGORITHM PROOF OF
FERMAT S ALGORITHM A FUNDAMENTAL PROPERTY OF PRIMES THE GREEKS AND THE
IRRATIONAL UNIQUENESS OF FACTORIZATION EXERCISES X CONTENTS 3.
EXPONENTIAL FORMULAE: FERMAT NUMBERS 53 4. THE PRIMORIAL FORMULA 54 5.
INFINITY OF PRIMES . 55 6. THE SIEVE OF ERATHOSTENES 57 7. EXERCISES 61
CHAPTER 4. MODULAR ARITHMETIC 63 1. EQUIVALENCE RELATIONS 63 2. THE
CONGRUENCE RELATION 66 3. MODULAR ARITHMETIC 68 4. DIVISIBILITY CRITERIA
71 5. POWERS 72 6. DIOPHANTINE EQUATIONS 73 7. DIVISION MODULO N 75 8.
EXERCISES 77 CHAPTER 5. INDUCTION AND FERMAT 79 1. HANOI! HANOI! 79 2.
FINITE INDUCTION 83 3. FERMAT S THEOREM 86 4. COUNTING ROOTS 88 5.
EXERCISES 92 CHAPTER 6. PSEUDOPRIMES 95 1. PSEUDOPRIMES 95 2. CARMICHAEL
NUMBERS 97 3. MILLER S TEST 100 4. PRIMALITY TESTING AND COMPUTER
ALGEBRA 103 5. EXERCISES 104 CHAPTER 7. SYSTEMS OF CONGRUENCES 107 1.
LINEAR EQUATIONS 107 2. AN ASTRONOMICAL EXAMPLE 108 3. THE CHINESE
REMAINDER ALGORITHM: CO-PRIME MODULI 110 4. THE CHINESE REMAINDER
ALGORITHM: GENERAL CASE 113 5. POWERS, AGAIN 114 6. ON SHARING SECRETS
116 7. EXERCISES 118 CHAPTER 8. GROUPS 121 1. DEFINITIONS AND EXAMPLES
121 2. SYMMETRIES 122 3. INTERLUDE 126 4. ARITHMETIC GROUPS 129 5.
SUBGROUPS 132 6. CYCLIC SUBGROUPS 133 7. 8. 9. FINDING SUBGROUPS
LAGRANGE S THEOREM EXERCISES CHAPTER 9. MERSENNE AND FERMAT 1. 2. 3. 4.
5. MERSENNE NUMBERS ** FERMAT NUMBERS FERMAT, AGAIN THE LUCAS-LEHMER
TEST EXERCISES CHAPTER 10. PRIMALITY TESTS AND PRIMITIVE ROOTS 1. 2. 3.
4. 5. 6. 7. LUCAS S TEST ANOTHER PRIMALITY TEST CARMICHAEL NUMBERS
PRELIMINARIES PRIMITIVE ROOTS COMPUTING ORDERS EXERCISES CONTENTS XI 134
136 138 141 141 143 145 146 149 151 151 154 155 156 157 158 160 CHAPTER
11. THE RSA CRYPTOSYSTEM 163 1. ON FIRST AND LAST THINGS 163 2.
ENCRYPTION AND DECRYPTION 164 3. WHY DOES IT WORK? 166 4. WHY IS IT
SECURE? 167 5. CHOOSING THE PRIMES 168 6. SIGNATURES 170 7. EXERCISES
171 CODA 175 APPENDIX. ROOTS AND POWERS 179 1. SQUARE ROOTS 179 2. POWER
ALGORITHM 180 BIBLIOGRAPHY 183 INDEX OF THE MAIN ALGORITHMS 189 INDEX OF
THE MAIN RESULTS 191 INDEX 192
|
| any_adam_object | 1 |
| author | Coutinho, Severino Collier |
| author_facet | Coutinho, Severino Collier |
| author_role | aut |
| author_sort | Coutinho, Severino Collier |
| author_variant | s c c sc scc |
| building | Verbundindex |
| bvnumber | BV014305181 |
| callnumber-first | Q - Science |
| callnumber-label | QA241 |
| callnumber-raw | QA241 |
| callnumber-search | QA241 |
| callnumber-sort | QA 3241 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 180 |
| ctrlnum | (OCoLC)246130796 (DE-599)BVBBV014305181 |
| dewey-full | 512.7 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.7 |
| dewey-search | 512.7 |
| dewey-sort | 3512.7 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01567nam a2200421 c 4500</leader><controlfield tag="001">BV014305181</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20181022 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">020521s1999 a||| |||| 00||| eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">1568810822</subfield><subfield code="9">1-56881-082-2</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)246130796</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV014305181</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-355</subfield><subfield code="a">DE-188</subfield><subfield code="a">DE-706</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QA241</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">512.7</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 180</subfield><subfield code="0">(DE-625)143222:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">17,1</subfield><subfield code="2">ssgn</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Coutinho, Severino Collier</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="240" ind1="1" ind2="0"><subfield code="a">Números inteiros e criptografia RSA</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">The mathematics of ciphers</subfield><subfield code="b">number theory and RSA cryptography</subfield><subfield code="c">S. C. Coutinho</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Boca Raton ; London ; New York</subfield><subfield code="b">CRC Press</subfield><subfield code="c">1999</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">XV, 196 S.</subfield><subfield code="b">Ill.</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">An AK Peters book</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Kryptologie - Zahlentheorie</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Zahlentheorie</subfield><subfield code="0">(DE-588)4067277-3</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Kryptologie</subfield><subfield code="0">(DE-588)4033329-2</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="655" ind1=" " ind2="4"><subfield code="a">Lehrbuch - Elementare Zahlentheorie</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Kryptologie</subfield><subfield code="0">(DE-588)4033329-2</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Zahlentheorie</subfield><subfield code="0">(DE-588)4067277-3</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">GBV Datenaustausch</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009812655&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-009812655</subfield></datafield></record></collection> |
| genre | Lehrbuch - Elementare Zahlentheorie |
| genre_facet | Lehrbuch - Elementare Zahlentheorie |
| id | DE-604.BV014305181 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T19:01:22Z |
| institution | BVB |
| isbn | 1568810822 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009812655 |
| oclc_num | 246130796 |
| open_access_boolean | |
| owner | DE-355 DE-BY-UBR DE-188 DE-706 |
| owner_facet | DE-355 DE-BY-UBR DE-188 DE-706 |
| physical | XV, 196 S. Ill. |
| publishDate | 1999 |
| publishDateSearch | 1999 |
| publishDateSort | 1999 |
| publisher | CRC Press |
| record_format | marc |
| spelling | Coutinho, Severino Collier Verfasser aut Números inteiros e criptografia RSA The mathematics of ciphers number theory and RSA cryptography S. C. Coutinho Boca Raton ; London ; New York CRC Press 1999 XV, 196 S. Ill. txt rdacontent n rdamedia nc rdacarrier An AK Peters book Kryptologie - Zahlentheorie Zahlentheorie (DE-588)4067277-3 gnd rswk-swf Kryptologie (DE-588)4033329-2 gnd rswk-swf Lehrbuch - Elementare Zahlentheorie Kryptologie (DE-588)4033329-2 s Zahlentheorie (DE-588)4067277-3 s DE-604 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009812655&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Coutinho, Severino Collier The mathematics of ciphers number theory and RSA cryptography Kryptologie - Zahlentheorie Zahlentheorie (DE-588)4067277-3 gnd Kryptologie (DE-588)4033329-2 gnd |
| subject_GND | (DE-588)4067277-3 (DE-588)4033329-2 |
| title | The mathematics of ciphers number theory and RSA cryptography |
| title_alt | Números inteiros e criptografia RSA |
| title_auth | The mathematics of ciphers number theory and RSA cryptography |
| title_exact_search | The mathematics of ciphers number theory and RSA cryptography |
| title_full | The mathematics of ciphers number theory and RSA cryptography S. C. Coutinho |
| title_fullStr | The mathematics of ciphers number theory and RSA cryptography S. C. Coutinho |
| title_full_unstemmed | The mathematics of ciphers number theory and RSA cryptography S. C. Coutinho |
| title_short | The mathematics of ciphers |
| title_sort | the mathematics of ciphers number theory and rsa cryptography |
| title_sub | number theory and RSA cryptography |
| topic | Kryptologie - Zahlentheorie Zahlentheorie (DE-588)4067277-3 gnd Kryptologie (DE-588)4033329-2 gnd |
| topic_facet | Kryptologie - Zahlentheorie Zahlentheorie Kryptologie Lehrbuch - Elementare Zahlentheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009812655&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT coutinhoseverinocollier numerosinteirosecriptografiarsa AT coutinhoseverinocollier themathematicsofciphersnumbertheoryandrsacryptography |