Chapter 1: A History of Cryptography

• Codes
• Monoalphabetic Substitution
• Ciphers
• Frequency Analysis on Caesar Ciphers
• Frequency Analysis on Monoalphabetic Substitution Ciphers
• Polyalphabetic Substitution Ciphers
• The Vigenere Cipher and Code Wheels
• Breaking Simple Vigenere Ciphers
• The Kaisiski Method of Determining Key Length
• The Full Vigenere Cipher
• The Auto-Key Vigenere Cipher
• The Running Key Vigenere Cipher
• Breaking Auto Key and Running Key Vigenere Ciphers
• The One-Time Pad
• Transposition Ciphers
• Polygram Substitution Ciphers
• The Playfair Cipher
• Breaking Simple Polygram Ciphers
• The Jefferson Cylinder
• Homophonic Substitution Ciphers
• Combination Substitution/Transposition Ciphers
• Exercises 

Chapter 2: Large Integer Computing 

• Constructors
• Comparison Methods
• Arithmetic Methods
• The Java BigInteger Class
• Constructors
• Methods
• Exercises 

Chapter 3: The Integers

• The Division Algorithm
• The Euclidean Algorithm
• Fundamental Theorem of Arithmetic
• Exercises 

Chapter 4: Linear Diophantine Equations & Linear Congruences

• Linear Diophantine Equations
• Linear Congruences
• Modular Inverses
• Exercises 

Chapter 5: Linear Ciphers

• The Caesar Cipher
• Weaknesses of the Caesar Cipher
• Affine Transformation Ciphers
• Weaknesses of Affine Transformation Ciphers
• The Vigenere Cipher
• Block Affine Ciphers
• Weaknesses of the Block Affine Cipher-Known Plaintext Attack
• Padding Methods
• Exercises 

Chapter 6: Systems of Linear Congruences-Single Modulus 

• Modular Matrices
• Modular Matrix Inverses
• Exercises 

Chapter 7: Matrix Ciphers 

• Weaknesses of Matrix Cryptosystems
• Transposition Ciphers
• Combination Substitution/Transposition Ciphers
• Exercises 

Chapter 8: Systems of Linear Congruences-Multiple Moduli

• The Chinese Remainder Theorem
• Exercises 

Chapter 9: Quadratic Congruences 

• Quadratic Congruences Modulo a Prime
• Fermat’s Little Theorem
• Quadratic Congruences Modulo a Composite
• Exercises 

Chapter 10: Quadratic Ciphers 

• The Rabin Cipher
• Weaknesses of the Rabin Cipher
• Strong Primes
• Salt
• Cipher Block Chaining-CBC
• Blum-Goldwasser Probabilistic Cipher
• Weaknesses of the Blum-Goldwasser Probabilistic Cipher
• Exercises 

Chapter 11: Primality Testing

• Miller’s Test The Rabin-Miller Test
• Exercises 

Chapter 12: Factorization Techniques 

• Fermat Factorization
• Monte Carlo Factorization
• The Pollard p-1 Method of Factorization
• Exercises 

Chapter 13: Exponential Congruences

• Order of an Integer
• Generators
• Generator Selection
• Calculating Discrete Logarithms
• Exercises 

Chapter 14: Exponential Ciphers 

• Diffie-Hellman Key Exchange
• Weaknesses of Diffie-Hellman
• The Pohlig-Hellman Exponentiation Cipher
• Weaknesses of the Pohlig-Hellman Cipher
• Cipher Feedback Mode-CFB
• The ElGamal Cipher Weaknesses of ElGamal
• The RSA Cipher
• Weaknesses of RSA
• Exercises 

Chapter 15: Establishing Keys and Message Exchange

• Establishing Keys
• Diffie-Hellman Key Exchange Application
• Message Exchange
• Cipher Chat Application
• Exercises 

Chapter 16: Cryptographic Applications 

• Shadows
• Database Encryption
• Large Integer Arithmetic
• Random Number Generation
• Signing Messages
• Message Digests
• Signing with ElGamal
• Attacks on Digest Functions
• Zero Knowledge Identification
• Exercises 

Appendix: List of Propositions

Appendix II:   Information Theory 

• Entropy of a Message
• Rate of a Language
• Cryptographic Techniques
• Confusion
• Diffusion
• Compression 

Recommended Reading
Index