Chinese remainder theorem: applications in computing, coding, cryptography
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Singapore [u.a.]
World Scientific
1996
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | VIII, 213 S. graph. Darst. |
| ISBN: | 9810228279 |
Internformat
MARC
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| 300 | |a VIII, 213 S. |b graph. Darst. | ||
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| 650 | 4 | |a Cryptography | |
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Datensatz im Suchindex
| _version_ | 1804126994229624832 |
|---|---|
| adam_text | Contents
Preface V
1 Introduction and Philosophy 1
1.1 A Historical Overview 1
1.2 Pars pro toto 3
1.3 Chinese Remainder Theorem: A First Formulation 5
1.4 CRT in the Hands of Old Mathematicians 8
1.5 CRT in Applications: the Three C s 10
2 Chinese Remainder Algorithm 13
2.1 Historical Development 13
2.2 Chinese Remainder Algorithms 22
2.3 Chinese Remainder Theorem 24
2.4 A Generalized CRA 25
2.5 Another Generalized CRT 29
3 In Modular Computations 33
3.1 Modular Computation Based on CRA 33
3.2 A Modular Approach to Multiplication 38
3.3 Computing Exact Polynomial Resultants 47
3.4 Other Applications in Symbolic Computations 58
3.5 CRA and Homomorphic Image Computing 59
3.6 Information and CRT 62
4 In Algorithmics 65
4.1 Divide and Conquer Techniques 66
4.2 Polynomial Interpolation over Fields 68
4.3 Polynomial Interpolation over Z/(m) 71
4.4 Shift Register Synthesis over Z/(m) 74
4.5 Common Primitive Roots 80
4.6 From One to Multi dimension 82
VII
VIII CONTENTS
4.7 A Modular Algorithm for Cyclic Convolution 85
4.8 A Fast Algorithm for Cyclic Convolution 87
4.9 Fast Fourier Transform and CRT 90
5 In Bridging Computations 95
5.1 A Main Bridge 95
5.2 Solving Equations over Z/(m) 97
5.3 Number of Roots of Equations over Z/(m) 99
5.4 Computing Fixed Points 101
5.5 Bridging Divisions of Polynomials 105
5.6 Permutation Polynomials of Z/(m) 106
6 In Coding Theory 113
6.1 Basics of Block Codes 114
6.2 Redundant Residue Codes 120
6.3 Reed Solomon Codes 122
6.4 Redundant Residue Codes of Degree 2 128
6.5 Bossen Yau Codes 131
6.6 Generalized Redundant Residue Codes 141
6.7 Restricted GRR Codes 146
6.8 A Class of Arithmetic Residue Codes 147
7 In Cryptography 157
7.1 Secret Sharing and CRT 157
7.2 Secret Sharing and Codes 165
7.3 CRT and Stream Ciphering 171
7.4 CRA and Knapsack Problems 175
7.5 Public Key Systems via CRT 179
A Tutorial in Information Theory 185
B Tutorial in Algebra 193
C List of Mathematical Symbols 201
Bibliography 203
Index 211
|
| any_adam_object | 1 |
| author | Ding, Cunsheng 1962- Pei, Dingyi Salomaa, Arto 1934- |
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| discipline | Informatik Mathematik |
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| id | DE-604.BV012365306 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:26:17Z |
| institution | BVB |
| isbn | 9810228279 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008385330 |
| oclc_num | 36413556 |
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| physical | VIII, 213 S. graph. Darst. |
| publishDate | 1996 |
| publishDateSearch | 1996 |
| publishDateSort | 1996 |
| publisher | World Scientific |
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| spelling | Ding, Cunsheng 1962- Verfasser (DE-588)121230457 aut Chinese remainder theorem applications in computing, coding, cryptography C. Ding ; D. Pei ; A. Salomaa Singapore [u.a.] World Scientific 1996 VIII, 213 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Coding theory Cryptography Chinesischer Restsatz (DE-588)4470755-1 gnd rswk-swf Chinesischer Restsatz (DE-588)4470755-1 s DE-604 Pei, Dingyi Verfasser aut Salomaa, Arto 1934- Verfasser (DE-588)121031764 aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008385330&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Ding, Cunsheng 1962- Pei, Dingyi Salomaa, Arto 1934- Chinese remainder theorem applications in computing, coding, cryptography Coding theory Cryptography Chinesischer Restsatz (DE-588)4470755-1 gnd |
| subject_GND | (DE-588)4470755-1 |
| title | Chinese remainder theorem applications in computing, coding, cryptography |
| title_auth | Chinese remainder theorem applications in computing, coding, cryptography |
| title_exact_search | Chinese remainder theorem applications in computing, coding, cryptography |
| title_full | Chinese remainder theorem applications in computing, coding, cryptography C. Ding ; D. Pei ; A. Salomaa |
| title_fullStr | Chinese remainder theorem applications in computing, coding, cryptography C. Ding ; D. Pei ; A. Salomaa |
| title_full_unstemmed | Chinese remainder theorem applications in computing, coding, cryptography C. Ding ; D. Pei ; A. Salomaa |
| title_short | Chinese remainder theorem |
| title_sort | chinese remainder theorem applications in computing coding cryptography |
| title_sub | applications in computing, coding, cryptography |
| topic | Coding theory Cryptography Chinesischer Restsatz (DE-588)4470755-1 gnd |
| topic_facet | Coding theory Cryptography Chinesischer Restsatz |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008385330&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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