Cryptography, Information Theory, and Error-Correction A Handbook for the 21st Century

by Bruen, Aiden A.; Forcinito, Mario A.

Edition: 1st

ISBN13: 9780471653172

ISBN10: 0471653179

Format: Hardcover

Pub. Date: 2004-12-31

Publisher(s): Wiley-Interscience

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Summary

Stressing the interconnections of the areas of study,Cryptography, Information Theory, and Error-Correction offers a complete yet accessible account of the technologies shaping the twenty-first century. This title contains the most up-to-date, detailed, and balanced treatment available on these subjects. The authors draw on their experience both in the classroom and in industry, giving the books material and presentation a unique real-world orientation. Features include over 300 example problems and their solutions; the latest and most exciting new algorithms in use; discussion of cutting-edge cell biology applications; and a tiered approach to topics facilitating understanding by a wider group of readers. With its reader-friendly style and interdisciplinary emphasis,Cryptography, Information Theory, and Error-Correction serves as both an admirable teaching text and a tool for self-learning.

Author Biography

AIDEN A. BRUEN, PHD, is a Professor of Mathematics and Statistics at the University of Calgary in Calgary, Alberta, Canada. He has over 100 published articles in refereed journals and has served for many years on the Editorial Board of Designs, Codes and Cryptography. His research interests include error-correcting codes, number theory, algebraic geometry, algebra finite geometries, information theory, and cryptography. <p>MARIO A. FORCINITO, PHD, is a professional engineer with over ten years' experience as an industrial consultant. He is President of SUR Consultants in Engineering Science Inc., a member of the IEEE Computer Society, and has published extensively in peer-reviewed journals. Dr. Forcinito has experience lecturing on cryptography and numerical methods at several technical meetings.

Preface

xiii

I Cryptography

(158)

1 History and Claude E. Shannon

(14)

1.1 Historical Background

(5)

1.2 Brief Biography of Claude E. Shannon

(1)

1.3 Career

(1)

1.4 Personal Professional

(1)

1.5 Scientific Legacy

(3)

1.6 Modern Developments

(3)

2 Classical Ciphers and Their Cryptanalysis

(22)

2.1 Introduction

(1)

2.2 The Caesar Cipher

(2)

2.3 The Scytale Cipher

(1)

2.4 The Vigenère Cipher

(1)

2.5 The Enigma Machine and Its Mathematics

(4)

2.6 Frequency Analysis

(1)

2.7 Breaking the Vigenere Cipher, Babbage-Kasiski

(5)

2.8 Modern Enciphering Systems

(1)

2.9 Problems

(1)

2.10 Solutions

(6)

3 RSA, Key Searches, SSL, and Encrypting Email

(30)

3.1 Background

(1)

3.2 The Basic Idea of Cryptography

(4)

3.3 Public Key Cryptography and RSA on a Calculator

(3)

3.4 The General RSA Algorithm

(3)

3.5 Public Key Versus Symmetric Key

(3)

3.6 Attacks, Security of DES, Key-spaces

(2)

3.7 Summary of Encryption

(1)

3.8 SSL (Secure Socket Layer)

(2)

3.9 PGP and GPG

(1)

3.10 RSA Challenge

(1)

3.11 Problems

(3)

3.12 Solutions

(5)

4 The Fundamentals of Modern Cryptography

(90)

4.1 Encryption Revisited

(2)

4.2 Block Ciphers, Shannon's Confusion and Diffusion

(2)

4.3 Perfect Secrecy, Stream Ciphers, One-Time Pad

(3)

4.4 Hash Functions

(3)

4.5 Message Integrity Using Symmetric Cryptography

(1)

4.6 General Public Key Cryptosystems

(2)

4.7 Electronic Signatures

(2)

4.8 The Diffie-Hellman Key Exchange

(3)

4.9 Quantum Encryption

(2)

4.10 Key Management and Kerberos

(2)

4.11 DES

(1)

4.12 Problems

(1)

4.13 Solutions

(3)

5 DES, AES and Operating Modes

(18)

5.1 The Data Encryption Standard Code

(6)

5.2 Triple DES

101

(1)

5.3 DES and Unix

102

(1)

5.4 The Advanced Encryption Standard Code

102

(7)

5.5 Problems

109

(1)

5.6 Solutions

110

(3)

6 Elliptic Curve Cryptography (ECC)

113

(18)

6.1 Abelian Integrals, Fields, Groups

113

(2)

6.2 Curves, Cryptography

115

(2)

6.3 Nonsingularity

117

(1)

6.4 The Hasse Theorem, and an Example

117

(1)

6.5 More Examples

118

(1)

6.6 The Group Law on Elliptic Curves

119

(3)

6.7 Key Exchange with Elliptic Curves

122

(1)

6.8 Elliptic Curves mod n

122

(1)

6.9 Encoding Plain Text

122

(1)

6.10 Security of ECC

123

(1)

6.11 More Geometry of Cubic Curves

123

(1)

6.12 Cubic Curves and Arcs

124

(1)

6.13 Homogeneous Coordinates

124

(1)

6.14 Fermat's Last Theorem, Elliptic Curves, Gerhard Frey

125

(1)

6.15 Problems

126

(1)

6.16 Solutions

126

(5)

7 Attacks in Cryptography

131

(14)

7.1 Cryptanalysis

131

(1)

7.2 Soft Attacks

132

(1)

7.3 Brute Force Attacks

133

(1)

7.4 Man-In-The-Middle Attacks

134

(1)

7.5 Known Plain Text Attacks

135

(1)

7.6 Known Cipher Text Attacks

135

(1)

7.7 Chosen Plain Text Attacks

136

(1)

7.8 Chosen Cipher Text Attacks, Digital Signatures

136

(1)

7.9 Replay Attacks

137

(1)

7.10 Birthday Attacks

137

(1)

7.11 Birthday Attack on Digital Signatures

138

(1)

7.12 Birthday Attack on the Discrete Log Problem

139

(1)

7.13 Attacks on RSA

139

(1)

7.14 Attacks on RSA using Low-Exponents

140

(1)

7.15 Timing Attack

141

(1)

7.16 Dfferential Cryptanalysis

142

(1)

7.17 Implementation Errors and Unforeseen States

143

(2)

8 Practical Issus

145

(16)

8.1 Introduction

145

(1)

8.2 Hot Issues

146

(1)

8.3 Authentication

147

(4)

8.4 E-Commerce

151

(1)

8.5 E-Government

152

(1)

8.6 Key Lengths

153

(1)

8.7 Digital Rights

154

(1)

8.8 Wireless Networks

154

(2)

8.9 Communication Protocols

156

(3)

II Information Theory

159

(158)

9 Information Theory and Its Applications

161

(14)

9.1 Axioms, Physics, Computation

161

(1)

9.2 Entropy

162

(2)

9.3 Information Gained, Cryptography

164

(2)

9.4 Practical Applications of Information Theory

166

(1)

9.5 Information Theory and Physics

167

(1)

9.6 Axiomatics of Information Theory

168

(1)

9.7 Number Bases, Erdos, and the Hand of God

169

(2)

9.8 Weighing Problems and Your MBA

171

(2)

9.9 Shannon Bits, the Big Picture

173

(2)

10 Random Variables and Entropy

175

(28)

10.1 Random Variables

175

(3)

10.2 Mathematics of Entropy

178

(1)

10.3 Calculating Entropy

179

(1)

10.4 Conditional Probability

180

(4)

10.5 Bernoulli Trials

184

(1)

10.6 Typical Sequences

185

(1)

10.7 Law of Large Numbers

186

(1)

10.8 Joint and Conditional Entropy

187

(5)

10.9 Applications of Entropy

192

(1)

10.10 Calculation of Mutual Information

193

(1)

10.11 Mutual Information and Channels

194

(1)

10.12 The Entropy of X + Y

195

(1)

10.13 Subadditivity of the Function -x log x

196

(1)

10.14 Entropy and Cryptography

196

(1)

10.15 Problems

196

(2)

10.16 Solutions

198

(5)

11 Source Coding, Data Compression, Redundancy

203

(22)

11.1 Introduction, Source Extensions

204

(1)

11.2 Encodings, Kraft, McMillan

205

(6)

11.3 Block Coding, The Oracle, Yes-No Questions

211

(1)

11.4 Optimal Codes

212

(1)

11.5 Huffman Coding

213

(5)

11.6 Optimality of Huffman Coding

218

(1)

11.7 Data Compression, Lempel-Ziv Coding, Redundancy

219

(3)

11.8 Problems

222

(1)

11.9 Solutions

223

(2)

12 Channels, Capacity, the Fundamental Theorem

225

(28)

12.1 Abstract Channels

226

(1)

12.2 More Specific Channels

227

(1)

12.3 New Channels from Old, Cascades

228

(3)

12.4 Input Probability, Channel Capacity

231

(3)

12.5 Capacity for General Binary Channels, Entropy

234

(2)

12.6 Hamming Distance

236

(1)

12.7 Improving Reliability of a Binary Symmetric Channel

237

(1)

12.8 Error Correction, Error Reduction, Good Redundancy

238

(3)

12.9 The Fundamental Theorem of Information Theory

241

(7)

12.10 Summary, the Big Picture

248

(1)

12.11 Problems

248

(1)

12.12 Solutions

249

(4)

13 Signals, Sampling, SNR, Coding Gain

253

(8)

13.1 Continuous Signals, Shannon's Sampling Theorem

253

(3)

13.2 The Band-Limited Capacity Theorem, an Example

256

(3)

13.3 The Coding Gain

259

(2)

14 Ergodic and Markov Sources, Language Entropy

261

(16)

14.1 General and Stationary Sources

261

(3)

14.2 Ergodic Sources

264

(1)

14.3 Markov Chains and Markov Sources

265

(4)

14.4 Irreducible Markov Sources, Adjoint Source

269

(1)

14.5 Cascades and the Data Processing Theorem

270

(1)

14.6 The Redundancy of Languages

271

(3)

14.7 Problems

274

(1)

14.8 Solutions

275

(2)

15 Perfect Secrecy: the New Paradigm

277

(12)

15.1 Symmetric Key Cryptosystems

277

(2)

15.2 Perfect Secrecy and Equiprobable Keys

279

(1)

15.3 Perfect Secrecy and Latin Squares

280

(2)

15.4 The Abstract Approach to Perfect Secrecy

282

(1)

15.5 Cryptography, Information Theory, Shannon

283

(1)

15.6 Unique Message from Ciphertext, Unicity

283

(1)

15.7 Problems

284

(2)

15.8 Solutions

286

(3)

16 Shift Registers (LFSR) and Stream Ciphers

289

(18)

16.1 Vernam Cipher, Psuedo-Random Key

290

(1)

16.2 Construction of Feedback Shift Registers

290

(3)

16.3 Periodicity

293

(3)

16.4 Maximal Periods, Pseudo-Random Sequences

296

(1)

16.5 Determining the Output from 2m Bits

297

(3)

16.6 The Tap Polynomial and the Period

300

(1)

16.7 Berlekamp-Massey Algorithm

301

(3)

16.8 Problems

304

(1)

16.9 Solutions

305

(2)

17 The Genetic Code

307

(10)

17.1 Biology and Information Theory

308

(1)

17.2 History of Genetics

308

(1)

17.3 Structure of DNA

309

(1)

17.4 DNA as an Information Channel

309

(1)

17.5 The Double Helix, Replication

310

(1)

17.6 Protein Synthesis and the Genetic code

310

(2)

17.7 Viruses

312

(1)

17.8 Entropy and Compression in Genetics

313

(1)

17.9 Channel Capacity of the Genetic Code

314

(3)

III Error-Correction

317

(128)

18 Error-Correction, Haddamard, Block Designs

319

(16)

18.1 General Ideas of Error Correction

319

(1)

18.2 Error Detection, Error Correction

320

(1)

18.3 A Formula for Correction and Detection

321

(1)

18.4 Hadamard Matrices

322

(3)

18.5 Mariner, Hadamard and Reed-Muller

325

(1)

18.6 Reed-Muller Codes

325

(1)

18.7 Block Designs

326

(2)

18.8 A Problem of Lander, the Bruen-Ott Theorem

328

(1)

18.9 The Main Coding Theory Problem, Bounds

328

(5)

18.10 Problems

333

(1)

18.11 Solutions

333

(2)

19 Finite Fields, Linear Algebra, and Number Theory

335

(24)

19.1 Modular Arithmetic

335

(4)

19.2 A Little Linear Algebra

339

(2)

19.3 Applications to RSA

341

(1)

19.4 Primitive Roots for Primes and Diffie-Hellman

342

(3)

19.5 The Extended Euclidean Algorithm

345

(1)

19.6 Proof that the RSA Algorithm Works

346

(1)

19.7 Constructing Finite Fields

346

(4)

19.8 Pollard's p - 1 Factoring Algorithm

350

(1)

19.9 Turing Machines, Complexity, P and NP

351

(3)

19.10 Problems

354

(1)

19.11 Solutions

355

(4)

20 Introduction to Linear Codes

359

(20)

20.1 Repetition Codes and Parity Checks

359

(2)

20.2 Details of Linear Codes

361

(3)

20.3 Parity Checks, the Syndrome, Weights

364

(2)

20.4 Hamming Codes, an Inequality

366

(1)

20.5 Perfect Codes, Errors and the BSC

367

(1)

20.6 Generalizations of Binary Hamming Codes

368

(1)

20.7 The Football Pools Problem, Extended Hamming Codes

369

(1)

20.8 Golay Codes

370

(1)

20.9 McEliece Cryptosystem

371

(1)

20.10 Historical Remarks

372

(1)

20.11 Problems

373

(2)

20.12 Solutions

375

(4)

21 Linear Cyclic Codes, Shift Registers and CRC

379

(14)

21.1 Cyclic Linear Codes

379

(2)

21.2 Generators for Cyclic Codes

381

(2)

21.3 The Dual Code and The Two Methods

383

(1)

21.4 Linear Feedback Shift Registers and Codes

384

(2)

21.5 Finding the Period of an LFSR

386

(1)

21.6 Cyclic Redundancy Check (CRC)

387

(1)

21.7 Problems

388

(2)

21.8 Solutions

390

(3)

22 Reed Solomon, MDS Codes, Bruen-Thas-Blokhuis

393

(18)

22.1 Cyclic Linear Codes and Vandermonde

394

(2)

22.2 The Singleton Bound

396

(1)

22.3 Reed-Solomon Codes

397

(1)

22.4 Reed-Solomon Codes and the Fourier Transform Approach

398

(1)

22.5 Correcting Burst Errors, Interleaving

399

(1)

22.6 Decoding Reed-Solomon Codes

400

(3)

22.7 An Algorithm for Decoding and an Example

403

(2)

22.8 MDS Codes and a Solution of a Fifty Year-Old Problem

405

(3)

22.9 Problems

408

(1)

22.10 Solutions

408

(3)

23 MDS Codes, Secret Sharing, Invariant Theory

411

(12)

23.1 General MDS Codes

411

(1)

23.2 The Case k = 2, Bruck Nets

412

(2)

23.3 Upper Bounds on MDS Codes, Bruck-Ryser

414

(2)

23.4 MDS Codes and Secret Sharing Schemes

416

(1)

23.5 MacWilliams Identities, Invariant Theory

417

(1)

23.6 Codes, Planes, Blocking Sets

418

(4)

23.7 Binary Linear Codes of Minimum Distance 4

422

(1)

24 Key Reconciliation, New Algorithms

423

(22)

24.1 Symmetirc and Public Key Cryptography

423

(1)

24.2 General Background

424

(2)

24.3 The Secret Key and the Reconciliation Algorithm

426

(3)

24.4 Equality of Remnant Keys: the Halting Criterion

429

(2)

24.5 Linear Codes: the Checking Hash Function

431

(2)

24.6 Convergence and Length of Keys

433

(5)

24.7 Main Results

438

(1)

24.8 Some Details on the Random Permutation

439

(2)

24.9 The Case Where Eve Has Non-zero Initial Information

441

(1)

24.10 Hash Functions Using Block Designs

442

(1)

24.11 Concluding Remarks

443

(2)

ASCII

445

(2)

Shannon's Entropy Table

447

(2)

Glossary

449

(5)

Bibliography

454

(8)

Index

462

Cryptography, Information Theory, and Error-Correction A Handbook for the 21st Century

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