Cryptography

• Required text:
  • Title: An Introduction to Cryptography
  • Author: Richard A Mollin
  • ISBN: 1584881275
  • Publisher: Chapman & Hall / CRC
• Recommended reading:
  • Title: Cryptonomicon
  • Author: Neal Stephenson
  • Amazon page for ordering the paperback
  • This is a novel about cryptography by the author of the cult sci-fi classics "Snow Crash" and "The Diamond Age". It features excellent (and well-researched) accounts of cryptography in the Second World War and a clever cryptosystem that only requires a deck of playing cards.
  • Cryptonomicon Home Page

Look up your grades

1. Install Mozilla from Page for obtaining the Mozilla browser
   It will also be necessary to install math fonts for this browser. Information on how to install these can be found on
   The MathML Fonts Page
   For linux users, the necessary fonts can be found in: mozilla-math.tar.gz (these should be installed in X windows).

Note: Other web pages for this course will not necessarily even show up in other browsers! Once you have installed Mozilla and the fonts, you can check your installation by viewing:

Online Homework

Note: You need Mozilla to access this, and you need to run Mozilla from the Program menu (if you're using Windoze).

Online Homework

The MathML Start Page

Use this to check whether MathML is working properly on your web browser. Unfortunately, the Windows version of Mozilla seems to have a bug that will cause it to complain about missing fonts even though the fonts are there (and Mozilla is using them correctly).

Topics covered

1. Origins, Computer arithmetic, and Complexity
   • History
   • A history of factoring and primality testing
2. Symmetric-key cryptosystems
   • An introduction to congruences
     Equation for Fibonnaci numbers
   • Block ciphers
   • DES cryptanalysis and its successor AES
   • Stream ciphers
3. Public-key cryptosystems
   • Exponentiation, discrete logarithms and protocols
   • Public-key cryptography
   • Authentication
   • Knapsack
4. Primality testing
   • Primitive roots
   • True primality tests
   • Probabilistic primality tests
5. Elliptic curve cryptography
6. Zero-knowledge
7. Quantum cryptography

Sign up sheet for presentations (Graduate students only)

Links

• Frequency table for English (used in decrypting simple-substitution)
• National Security Agency
  This is the Federal agency responsible for developing US cryptosystems.
• Crypto-Gram Home Page
  This is a monthly newsletter on cryptography
• Number Stations 1
• Number Stations 2
• Vigenère Cipher Home Page
• Rijndael Cipher Home Page
• Block Cipher Home Page
• Applied Abstract Algebra Home Page
• Pari Home Page
  Pari is a free computer algebra system specialized for doing number theoretic computations

Exam Schedule

1. Exam 1, Week 3
2. Exam 2, Week 6
   Answers to exam 2
3. Exam 3, Week 9

Homework

1. Due 1/12/2004
   • p. 15, 1.5
   • p. 16, 1.7
     The ciphers in the two problems above were the main ciphers in use in the first World War.
   • p. 17, 1.9 (this is simple substitution, use the frequency table for English letters)
2. Due 1/21/2004: p. 72, 2.6; p. 73, 2.14

Lecture Notes

Note: you may have to zoom on these images to see them clearly

1. 1-7-2004
2. 1-9-2004
3. 1-12-2004
4. 1-14-2004
5. 1-16-2004
6. 1-21-2004
7. 1-26-2004
8. 1-28-2004
9. 1-30-2004
10. 2-2-2004
11. 2-6-2004
12. 2-9-2004
13. 2-11-2004
14. 2-18-2004
15. 2-20-2004
16. 2-23-2004
17. 2-25-2004
18. 2-27-2004