Preface ............................................................ ix
Chapter 1: Origins, Computer Arithmetic, and Complexity......1
1.1 What is Cryptography and Why Study it - A History................ 1
1.2 A History of Factoring and Primality Testing.................... 181.3 Computer Arithmetic............................................. 32
1.4 Complexity...................................................... 47
Chapter 2: Symmetric-Key Cryptosystems...............................57
2.1 An Introduction to Congruences.................................. 572.2 Block Ciphers................................................... 76
2.3 DES Cryptanalysis and Successors (optional).....................102
2.4 Stream Ciphers..................................................113
Chapter 3: Public-Key Cryptosystems..............................127
3.1 Exponentiation, Discrete Logs, and Protocols....................1273.2 Public-Key Cryptography.........................................137
3.3 Authentication .................................................146
3.4 Knapsack........................................................153
Chapter 4: Primality Testing....................................... 161
4.1 An Introduction to Primitive Roots............................. 1614.2 True Primality Tests........................................... 180
4.3 Probabilistic Primality Tests.................................. 188
Chapter 5: Factoring (optional).................................... 195
5.1 Three Algorithms............................................... 1955.2 The Number Field Sieve......................................... 207
Chapter 6: Advanced Topics (optional)...............................221
6.1 Elliptic Curves and Cryptography................................2216.2 Zero-Knowledge..................................................252
6.3 Quantum Cryptography............................................262
Appendix A: Fundamental Facts...................................... 271
Solutions to Odd Numbered Exercises.................................303
Bibliography........................................................331
List of Symbols.....................................................346
Index...............................................................347
About the Author....................................................373
Last updated: April 9, 2000
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