Coding theory and cryptography: the essentials
Gespeichert in:
| Vorheriger Titel: | Coding theory |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Dekker
2000
|
| Ausgabe: | 2. ed., rev. and expanded |
| Schriftenreihe: | Pure and applied mathematics
234 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | X, 350 S. Illustrationen, Diagramme |
| ISBN: | 0824704657 |
Internformat
MARC
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| 245 | 1 | 0 | |a Coding theory and cryptography |b the essentials |c D. R. Hankerson ... |
| 250 | |a 2. ed., rev. and expanded | ||
| 264 | 1 | |a New York [u.a.] |b Dekker |c 2000 | |
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| 650 | 4 | |a Teoría de la codificación | |
| 650 | 4 | |a Coding theory | |
| 650 | 4 | |a Cryptography | |
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Datensatz im Suchindex
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Contents v Preface Part I: Coding Theory Introduction to Coding Theory 1.1 Introduction. 1.2 Basic assumptions. 1.3 Correcting and detecting error patterns. 1.4 Information rate. 1.5 The effects of error correction and detection. 1.6 Finding the most likely codeword transmitted. 1.7 Some basic algebra. 1.8 Weight and distance. 1.9 Maximum likelihood decoding. 1.10 Reliability of MLD. 1.11 Error-detecting codes. 1.12 Error-correcting codes . 1 1 2 4 6 7 8 10 11 12 16 18 22 2 Linear Codes 2.1 Linear codes. 2.2 Two important subspaces. 2.3 Independence, basis, dimension . 2.4 Matrices. 2.5
Bases for C = (S) and C1 . 2.6 Generating matrices and encoding. 2.7 Parity-check matrices. 2.8 Equivalent codes. 2.9 Distance of a linear code. 2.10 Cosets. 2.11 MLD for linear codes. 2.12 Reliability of IMLD for linear codes. 27 27 28 30 35 37 41 45 48 52 53 57 62 1 vii
Contents viii 3 Perfect and Related Codes 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 Some bounds for codes. Perfect codes. Hamming codes. Extended codes. The extended Golay code. Decoding the extended Golay code. The Golay code. Reed-Muller codes. Fast decoding for RM(1, m). 65 65 70 72 75 77 79 82 84 88 4 Cyclic Linear Codes 4.1 4.2 4.3 4.4 4.5 91 Polynomials and words. 91 Introduction to cyclic codes. 96 Generating and parity check matrices for cyclic codes. 101 Finding cyclic codes . 104 Dual cyclic codes. 109 111 5.1 Finite fields. Ill 5.2 Minimal
polynomials. 115 5.3 Cyclic Hamming codes. 118 5.4 BCH codes. 120 5.5 Decoding 2 error-correcting BCH code. 122 5 BCH Codes 127 Codes over GF(2r). 127 Reed-Solomon codes. 129 Decoding Reed-Solomon codes. 135 Transform approach to Reed-Solomon codes. 141 Berlekamp-Massey algorithm. 148 Erasures. 153 6 Reed-Solomon Codes 6.1 6.2 6.3 6.4 6.5 6.6 7 Burst Error-Correcting Codes 7.1 7.2 7.3 159 Introduction. 159 Interleaving. 163 Application to compact discs. 170 173 Shift registers and polynomials. 173 Encoding convolutional codes. 179 Decoding convolutional codes. 186
Truncated Viterbi decoding. 193 8 Convolutional Codes 8.1 8.2 8.3 8.4
Contents ix 9 Reed-Muller and Preparata Codes 205 9.1 Reed-Muller codes. 205 9.2 Decoding Reed-Muller codes. 208 9.3 Extended Preparata codes. 213 9.4 Encoding extended Preparata codes . 219 9.5 Decoding extended Preparata codes . 222 Part II: Cryptography 10 Classical Cryptography 227 10.1 Encryption schemes. 228 10.2 Symmetric-key encryption. 230 10.3 Feistel ciphers and DES. 238 10.3.1 The New Data Seal. 240 10.3.2 The Data Encryption Standard. 243 10.4 Notes. 249 11 Topics in Algebra and Number Theory 253 11.1 Algorithms, complexity, and modular arithmetic. 253 11.2 Quadratic residues . 260 11.3 Primality testing. 264 11.4 Factoring and square roots. 267 11.4.1
Pollard’s rho. 267 11.4.2 Random squares. 269 11.4.3 Square roots . 271 11.5 Discrete logarithms. 274 11.5.1 Baby-step giant-step. 274 11.5.2 Index calculus . 275 11.6 Notes. 277 12 Public-key Cryptography 279 12.1 One-way and hash functions. 280 12.2 RS A. 284 12.3 Provable security. '. 290 12.4 ElGamal. 293 12.5 Cryptographic protocols . 297 12.5.1 Diffie-Hellman key agreement. 298 12.5.2 Zero-knowledge proofs. 299 12.5.3 Coin-tossing and mental poker. 301 12.6 Notes. 305 A The
Euclidean Algorithm 307
x Contents B Factorization ofl +xn 311 C Example of Compact Disc Encoding 313 D Solutions to Selected Exercises 317 Bibliography 335 Index 343 |
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| illustrated | Illustrated |
| indexdate | 2024-09-10T00:55:30Z |
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| isbn | 0824704657 |
| language | English |
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| physical | X, 350 S. Illustrationen, Diagramme |
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| series | Pure and applied mathematics |
| series2 | Pure and applied mathematics |
| spelling | Coding theory and cryptography the essentials D. R. Hankerson ... 2. ed., rev. and expanded New York [u.a.] Dekker 2000 X, 350 S. Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier Pure and applied mathematics 234 Codage Cryptographie Teoría de la codificación Coding theory Cryptography Codierungstheorie (DE-588)4139405-7 gnd rswk-swf Kryptologie (DE-588)4033329-2 gnd rswk-swf Codierungstheorie (DE-588)4139405-7 s DE-604 Kryptologie (DE-588)4033329-2 s Hankerson, Darrel R. Sonstige (DE-588)128640642 oth 1. Auflage Coding theory Pure and applied mathematics 234 (DE-604)BV000001885 234 Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009440156&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Coding theory and cryptography the essentials Pure and applied mathematics Codage Cryptographie Teoría de la codificación Coding theory Cryptography Codierungstheorie (DE-588)4139405-7 gnd Kryptologie (DE-588)4033329-2 gnd |
| subject_GND | (DE-588)4139405-7 (DE-588)4033329-2 |
| title | Coding theory and cryptography the essentials |
| title_auth | Coding theory and cryptography the essentials |
| title_exact_search | Coding theory and cryptography the essentials |
| title_full | Coding theory and cryptography the essentials D. R. Hankerson ... |
| title_fullStr | Coding theory and cryptography the essentials D. R. Hankerson ... |
| title_full_unstemmed | Coding theory and cryptography the essentials D. R. Hankerson ... |
| title_old | Coding theory |
| title_short | Coding theory and cryptography |
| title_sort | coding theory and cryptography the essentials |
| title_sub | the essentials |
| topic | Codage Cryptographie Teoría de la codificación Coding theory Cryptography Codierungstheorie (DE-588)4139405-7 gnd Kryptologie (DE-588)4033329-2 gnd |
| topic_facet | Codage Cryptographie Teoría de la codificación Coding theory Cryptography Codierungstheorie Kryptologie |
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