Part I: Introducing Cryptography

1. Introduction to Cryptography
2. History of Cryptography
   1. Classical Cryptography
   2. Contemporary Cryptography
   3. Cryptography in Popular Culture
   4. Timeline of Notable Events
3. Fundamental Concepts
   1. Goals of Cryptography
   2. Goals of Cryptanalysis
   3. Role of Cryptography in Computer Security
   4. Symmetric Key Ciphers
   5. Asymmetric Key Ciphers
   6. Random Number Generation
   7. Hashes
   8. Key Distribution and Authentication (key management and the web of trust)
   9. Common flaws and weaknesses
   10. Secure Passwords
   11. S-box

Part II: Designing Cryptosystems

1. The Basic Principles
2. Little Secrets Hide Bigger Secrets
3. Open Algorithms and the Value of Peer-Review
4. Think Like a Cryptanalyst
5. Cryptography/Error Correction Systems
6. Mathematical Background
7. Computer Security is More Than Encryption
8. Unbroken is Not Necessarily Unbreakable

Part III: Cryptanalysis

1. The Basic Principles
2. Weaknesses
   1. Proportionality of Secrecy
      1. Length of the key
      2. Quality of Random Source
      3. Plaintext effect on Ciphertext
   2. Statistical Leaking
   3. Faulty Implementation
   4. Inadequate Peer-Review
   5. Social Engineering and Coercion
   6. Leakage and Side Channels
3. Attacks
   1. Brute-Force Attack
      1. Dictionary Attack
   2. Frequency Analysis
   3. Index of Coincidence
   4. Linear Cryptanalysis
   5. Differential Cryptanalysis
   6. Meet in the Middle Attack
   7. Man-in-the-middle attack
4. Breaking Hash Algorithms
   1. Collisions
      1. Generating
      2. Exploiting
   2. Birthday Attack
   3. Joux Attack
   4. Time Memory Trade Off (rainbow tables)
5. How Historical Systems Were Broken
   1. Transposition Ciphers
   2. Caesar Cipher
   3. Enigma Machine
   4. Permutation Cipher
   5. Vigenère Cipher

Part IV: Using Cryptosystems

1. Applying Cryptography
   1. Digital Signatures
      1. Introduction to Digital Signatures
      2. DSA
   2. Database protection
   3. E-Cash
   4. E-Voting
   5. DRM
   6. Biometrics
   7. Anonymity
2. Classical Ciphers
   1. Beale Cipher
   2. Transposition Ciphers
   3. Caesar cipher
   4. Atbash Cipher
   5. Autokey cipher
   6. Playfair Cipher
   7. Polyalphabetic substitution
   8. Scytale
   9. Substitution cipher
   10. nomenclator
   11. Permutation Cipher
   12. Affine cipher
   13. Vigenère cipher
   14. Polybius square
   15. ADFGVX cipher
   16. Fractionation (Polybius square, straddling checkerboard, CT-37c conversion table, etc.)
3. Contemporary Ciphers
   1. Symmetric Ciphers
      1. Enigma Machine
      2. Solitaire cipher
      3. One-Time Pads
      4. Ciphersaber
      5. Data Encryption Standard (DES)
      6. Advanced Encryption Standard
   2. Asymmetric Ciphers
      1. Overview
      2. A Basic Public Key Example
      3. RSA
      4. ElGamal
      5. Elliptic Curve
      6. Blum-Goldwasser
   3. Hashes
      1. MD5
      2. SHA-1
      3. SHA-2
      4. RadioGatún, the direct predecessor of SHA-3
      5. SHA-3
      6. RIPEMD-160
      7. Tiger
      8. message authentication code (often MAC); A MAC algorithm is sometimes called a keyed (cryptographic) hash function.
4. Protocols
   1. Authentication protocols
      1. e.g. Kerberos
   2. Key exchange protocols
      1. Diffie-Hellman
   3. Secure Communications
      1. e.g. SSL, SSH
      2. Generate a keypair using OpenSSL

Part V: Cryptography and Society

1. The Changing Nature of Cryptographic Use
2. Cryptography, Governments and Laws
3. Expectations of Normal Users

Part VI: Miscellaneous

1. Future Possibilities
   1. Quantum Cryptography
   2. Faster, More Parallel Linear Computers
2. Glossary of Terms
3. Further Reading
4. Appendix A: Mathematical background
   1. Number Theory
   2. Group Theory
   3. Computational Complexity
   4. Prime numbers

1. Currently ungrouped content
   1. Tabula Recta
   2. Commitment schemes
   3. Zero-knowledge proofs
   4. Open source implementation of cryptographic algorithms
   5. initialization vector
   6. Linear Cryptanalysis
   7. Differential Cryptanalysis

Pages to be merged into the text.

Cryptography/Prime Curve/Affine Coordinates

Cryptography/Prime Curve/Chudnovsky Coordinates

Cryptography/Prime Curve/Jacobian Coordinates

Cryptography/Prime Curve/Standard Projective Coordinates

Cryptography/Notes