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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