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| Preface | |
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| Overview of Cryptography and Its Applications | |
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| Secure Communications | |
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| Cryptographic Applications | |
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| Classical Cryptosystems | |
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| Shift Ciphers | |
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| Affine Ciphers | |
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| The Vigenere Cipher | |
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| Substitution Ciphers | |
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| Sherlock Holmes | |
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| The Playfair and ADFGX Ciphers | |
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| Block Ciphers | |
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| Binary Numbers and ASCII | |
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| One-Time Pads | |
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| Pseudo-random Bit Generation | |
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| LFSR Sequences | |
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| Enigma | |
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| Exercises | |
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| Computer Problems | |
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| Basic Number Theory | |
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| Basic Notions | |
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| Solving ax + by = d | |
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| Congruences | |
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| The Chinese Remainder Theorem | |
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| Modular Exponentiation | |
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| Fermat and Euler | |
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| Primitive Roots | |
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| Inverting Matrices Mod n | |
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| Square Roots Mod n | |
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| Legendre and Jacobi Symbols | |
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| Finite Fields | |
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| Continued Fractions | |
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| Exercises | |
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| Computer Problems | |
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| The Data Encryption Standard | |
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| Introduction | |
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| A Simplified DES-Type Algorithm | |
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| Differential Cryptanalysis | |
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| DES | |
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| Modes of Operation | |
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| Breaking DES | |
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| Meet-in-the-Middle Attacks | |
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| Password Security | |
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| Exercises | |
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| Computer Problems | |
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| The Advanced Encryption Standard: Rijndael | |
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| The Basic Algorithm | |
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| The Layers | |
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| Decryption | |
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| Design Considerations | |
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| Exercises | |
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| The RSA Algorithm | |
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| The RSA Algorithm | |
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| Attacks on RSA | |
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| Primality Testing | |
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| Factoring | |
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| The RSA Challenge | |
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| An Application to Treaty Verification | |
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| The Public Key Concept | |
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| Exercises | |
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| Computer Problems | |
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| Discrete Logarithms | |
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| Discrete Logarithms | |
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| Computing Discrete Logs | |
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| Bit Commitment | |
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| Diffie-Hellman Key Exchange | |
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| The ElGamal Public Key Cryptosystem | |
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| Exercises | |
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| Computer Problems | |
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| Hash Functions | |
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| Hash Functions | |
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| A Simple Hash Example | |
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| The Secure Hash Algorithm | |
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| Birthday Attacks | |
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| Multicollisions | |
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| The Random Oracle Model | |
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| Using Hash Functions to Encrypt | |
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| Exercises | |
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| Computer Problems | |
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| Digital Signatures | |
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| RSA Signatures | |
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| The ElGamal Signature Scheme | |
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| Hashing and Signing | |
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| Birthday Attacks on Signatures | |
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| The Digital Signature Algorithm | |
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| Exercises | |
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| Computer Problems | |
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| Security Protocols | |
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| Intruders-in-the-Middle and Impostors | |
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| Key Distribution | |
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| Kerberos | |
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| Public Key Infrastructures (PKI) | |
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| X.509 Certificates | |
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| Pretty Good Privacy | |
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| SSL and TLS | |
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| Secure Electronic Transaction | |
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| Exercises | |
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| Digital Cash | |
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| Digital Cash | |
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| Exercises | |
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| Secret Sharing Schemes | |
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| Secret Splitting | |
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| Threshold Schemes | |
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| Exercises | |
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| Computer Problems | |
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| Games | |
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| Flipping Coins over the Telephone | |
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| Poker over the Telephone | |
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| Exercises | |
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| Zero-Knowledge Techniques | |
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| The Basic Setup | |
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| The Feige-Fiat-Shamir Identification Scheme | |
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| Exercises | |
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| Information Theory | |
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| Probability Review | |
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| Entropy | |
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| Huffman Codes | |
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| Perfect Secrecy | |
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| The Entropy of English | |
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| Exercises | |
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| Elliptic Curves | |
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| The Addition Law | |
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| Elliptic Curves Mod p | |
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| Factoring with Elliptic Curves | |
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| Elliptic Curves in Characteristic 2 | |
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| Elliptic Curve Cryptosystems | |
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| Identity-Based Encryption | |
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| Exercises | |
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| Computer Problems | |
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| Lattice Methods | |
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| Lattices | |
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| Lattice Reduction | |
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| An Attack on RSA | |
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| NTRU | |
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| Exercises | |
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| Error Correcting Codes | |
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| Introduction | |
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| Error Correcting Codes | |
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| Bounds on General Codes | |
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| Linear Codes | |
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| Hamming Codes | |
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| Golay Codes | |
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| Cyclic Codes | |
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| BCH Codes | |
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| Reed-Solomon Codes | |
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| The McEliece Cryptosystem | |
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| Other Topics | |
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| Exercises | |
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| Computer Problems | |
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| Quantum Techniques in Cryptography | |
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| A Quantum Experiment | |
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| Quantum Key Distribution | |
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| Shor's Algorithm | |
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| Exercises | |
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| Mathematica Examples | |
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| Getting Started with Mathematica | |
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| Some Commands | |
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| Examples for Chapter 2 | |
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| Examples for Chapter 3 | |
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| Examples for Chapter 6 | |
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| Examples for Chapter 8 | |
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| Examples for Chapter 12 | |
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| Examples for Chapter 13 | |
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| Examples for Chapter 16 | |
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| Maple Examples | |
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| Getting Started with Maple | |
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| Some Commands | |
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| Examples for Chapter 2 | |
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| Examples for Chapter 3 | |
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| Examples for Chapter 6 | |
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| Examples for Chapter 8 | |
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| Examples for Chapter 12 | |
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| Examples for Chapter 13 | |
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| Examples for Chapter 16 | |
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| Matlab Examples | |
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| Getting Started with Matlab | |
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| Examples for Chapter 2 | |
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| Examples for Chapter 3 | |
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| Examples for Chapter 6 | |
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| Examples for Chapter 8 | |
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| Examples for Chapter 12 | |
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| Examples for Chapter 13 | |
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| Examples for Chapter 16 | |
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| Suggestions for Further Reading | |
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| Bibliography | |
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| Index | |