Foundations of Coding (eBook)

JEAN-GUILLAUME DUMAS is Professor at the University of Grenoble, where he teaches security, programming languages, cryptology, and computer algebra. JEAN-LOUIS ROCH is Associate Professor at the National Polytechnique Institute of Grenoble (INPG), and teaches security, coding theory, cryptology, parallelism, and algorithms. ÉRIC TANNIER is Research Associate at the National French Institute for Computer Science (INRIA). He works in computational biology in the Biometry and Evolutionary Biology Laboratory (LBBE) of the University of Lyon. SÉBASTIEN VARRETTE is Research Associate at the University of Luxembourg. He works in the High Performance Computing (HPC) area, in particular as regards the security of distributed and/or parallel executions.

List of Figures, Tables, Algorithms and Acronyms ix

Foreword xv

Introduction xvii

1 Foundations of Coding 1

1.1 From Julius Caesar to telecopy 2

1.2 Stream ciphers and probabilities 10

1.3 Block ciphers, algebra and arithmetic 21

1.4 Decoding, decryption, attacks 59

2 Information theory and compression 89

2.1 Information theory 90

2.2 Statistical encoding 93

2.3 Heuristics of entropy reduction 106

2.4 Common compression codes 111

2.5 Lossy Compression 116

3 Cryptology 125

3.1 General principles 126

3.2 Secret key cryptography 129

3.3 Key exchange 148

3.4 Public key cryptography 154

3.5 Authentication, Integrity, Nonrepudiation, Signatures 162

3.6 Key management 177

4 Error detection and correction 193

4.1 Principle of error detection and error correction 195

4.2 Error detection by parity CRC codes 201

4.3 Distance of a code 207

4.4 Linear codes and cyclic codes 215

4.5 Bursts of errors and interleaving 242

4.6 Convolutional codes and turbocodes 248

Compression, encryption, correction: as a conclusion 257

Problem Solutions 261

Solutions for chapter 1 261

Solutions for chapter 2 274

Solutions for chapter 3 281

Solutions for chapter 4 299

Solution for the "Casino" exercise 315

References 317

Index 319