The mathematics of encryption : an elementary introduction / Margaret Cozzens, Steven J. Miller.
Record details
- ISBN: 9780821883211
- Physical Description: xvii, 332 páginas : ilustraciones a color ; 26 cm.
- Publisher: Providence, Rhode Island : American Mathematical Society, [2013] .
Content descriptions
| Bibliography, etc. Note: | Incluye bibliografía e índice. |
| Immediate Source of Acquisition Note: | Compra/R.1615-2014. |
| Language Note: | En inglés |
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| Subject: | Teoría de la codificación > Libros de texto. Criptografía > Libros de texto. Criptografía > Matemáticas > Libros de texto. Criptografía > Historia > Libros de texto. |
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- 1 of 1 copy available at IPICYT.
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| Location | Call Number / Copy Notes | Barcode | Shelving Location | Status | Due Date |
|---|---|---|---|---|---|
| Biblioteca Ipicyt | QA268C6 M3 2013 v. 29 | APL01344 | Coleccion General | Available | - |
| Preface | xi | |
| Acknowledgments | xvii | |
| Chapter 1. | Historical Introduction | 1 |
| 1.1. | Ancient Times | 2 |
| 1.2. | Cryptography During the Two World Wars | 8 |
| 1.3. | Postwar Cryptography, Computers, and Security | 12 |
| 1.4. | Summary | 14 |
| 1.5. | Problems | 15 |
| Chapter 2. | Classical Cryptology: Methods | 19 |
| 2.1. | Ancient Cryptography | 20 |
| 2.2. | Substitution Alphabet Ciphers | 22 |
| 2.3. | The Caesar Cipher | 24 |
| 2.4. | Modular Arithmetic | 26 |
| 2.5. | Number Theory Notation | 28 |
| 2.6. | The Affine Cipher | 30 |
| 2.7. | The Vigenère Cipher | 33 |
| 2.8. | The Permutation Cipher | 36 |
| 2.9. | The Hill Cipher | 39 |
| 2.10. | Summary | 42 |
| 2.11. | Problems | 42 |
| Chapter 3. | Enigma and Ultra | 51 |
| 3.1. | Setting the Stage | 51 |
| 3.2. | Some Counting | 54 |
| 3.3. | Enigma's Security | 60 |
| 3.4. | Cracking the Enigma | 67 |
| 3.5. | Codes in World War II | 70 |
| 3.6. | Summary | 72 |
| 3.7. | Appendix: Proofs by Induction | 73 |
| 3.8. | Problems | 75 |
| Chapter 4. | Classical Cryptography: Attacks I | 81 |
| 4.1. | Breaking the Caesar Cipher | 81 |
| 4.2. | Function Preliminaries | 84 |
| 4.3. | Modular Arithmetic and the Affine Cipher | 86 |
| 4.4. | Breaking the Affine Cipher | 91 |
| 4.5. | The Substitution Alphabet Cipher | 94 |
| 4.6. | Frequency Analysis and the Vigenère Cipher | 99 |
| 4.7. | The Kasiski Test | 102 |
| 4.8. | Summary | 106 |
| 4.9. | Problems | 107 |
| Chapter 5. | Classical Cryptography: Attacks II | 113 |
| 5.1. | Breaking the Permutation Cipher | 114 |
| 5.2. | Breaking the Hill Cipher | 115 |
| 5.3. | Running Key Ciphers | 120 |
| 5.4. | One-Time Pads | 122 |
| 5.5. | Summary | 127 |
| 5.6. | Problems | 128 |
| Chapter 6. | Modern Symmetric Encryption | 133 |
| 6.1. | Binary Numbers and Message Streams | 133 |
| 6.2. | Linear Feedback Shift Registers | 138 |
| 6.3. | Known-Plaintext Attack on LFSR Stream Ciphers | 142 |
| 6.4. | LFSRsum | 145 |
| 6.5. | BabyCSS | 150 |
| 6.6. | Breaking BabyCSS | 152 |
| 6.7. | BabyBlock | 158 |
| 6.8. | Security of BabyBlock | 161 |
| 6.9. | Meet-in-the-Middle Attacks | 162 |
| 6.10. | Summary | 164 |
| 6.11. | Problems | 164 |
| Chapter 7. | Introduction to Public-Channel Cryptography | 171 |
| 7.1. | The Perfect Code Cryptography System | 173 |
| 7.2. | KidRSA | 180 |
| 7.3. | The Euclidean Algorithm | 182 |
| 7.4. | Binary Expansion and Fast Modular Exponentiation | 188 |
| 7.5. | Prime Numbers | 192 |
| 7.6. | Fermat's Little Theorem | 198 |
| 7.7. | Summary | 203 |
| 7.8. | Problems | 203 |
| Chapter 8. | Public-Channel Cryptography | 213 |
| 8.1. | RSA | 214 |
| 8.2. | RSA and Symmetric Encryption | 218 |
| 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 â 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 the Fermat 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 |
| 12.11. | Chapter 11: Primality Testing and Factorization | 322 |
| Bibliography | 325 | |
| Index | 329 |
