CONTENTS ix 8.3. Digital Signatures 219 8.4. Hash Functions 221 8.5. Diffie–Hellman Key Exchange 225 8.6. Why RSA Works 228 8.7. Summary 230 8.8. Problems 231 Chapter 9. Error Detecting and Correcting Codes 239 9.1. Introduction 240 9.2. Error Detection and Correction Riddles 241 9.3. Definitions and Setup 247 9.4. Examples of Error Detecting Codes 249 9.5. Error Correcting Codes 252 9.6. More on the Hamming (7, 4) Code 255 9.7. From Parity to UPC Symbols 257 9.8. Summary and Further Topics 259 9.9. Problems 261 Chapter 10. Modern Cryptography 269 10.1. Steganography—Messages You Don’t Know Exist 269 10.2. Steganography in the Computer Age 273 10.3. Quantum Cryptography 278 10.4. Cryptography and Terrorists at Home and Abroad 282 10.5. Summary 285 10.6. Problems 285 Chapter 11. Primality Testing and Factorization 289 11.1. Introduction 289 11.2. Brute Force Factoring 291 11.3. Fermat’s Factoring Method 295 11.4. Monte Carlo Algorithms and F T Primality Test 299 11.5. Miller–Rabin Test 302 11.6. Agrawal–Kayal–Saxena Primality Test 305 11.7. Problems 310 Chapter 12. Solutions to Selected Problems 317 12.1. Chapter 1: Historical Introduction 317 12.2. Chapter 2: Classical Cryptography: Methods 317 12.3. Chapter 3: Enigma and Ultra 318 12.4. Chapter 4: Classical Cryptography: Attacks I 319 12.5. Chapter 5: Classical Cryptography: Attacks II 320 12.6. Chapter 6: Modern Symmetric Encryption 320 12.7. Chapter 7: Introduction to Public-Channel Cryptography 320 12.8. Chapter 8: Public-Channel Cryptography 321 12.9. Chapter 9: Error Detecting and Correcting Codes 321 12.10. Chapter 10: Modern Cryptography 322
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