Math/CMSC 456, Cryptology, Spring 2012, TuTh 9:30-10:45


Course Location: BPS 1236

Lecturer: Larry Washington (For email address, hold cursor here and look at the bottom of the page)
Office: Math 1106, Phone: 301-405-5059
Office Hours: Monday 10:30am-11:30am, Thursday 11:00am-12:00m .
Book: Introduction to Cryptography, by W. Trappe and L. Washington, 2nd edition (the 2nd edition differs substantially from the first edition)

Course Description:

Cryptology is the study of the design and analysis of various encryption schemes, and related topics. The plan is to study the basics of the subject and then touch on several recent developments.

Grading: Homework 15%, Two midterms: 25% each, Final: 35%

The final exam will be on Monday, May 14, 8:00-10:00 am.

Homework is due by 11:59:59pm on the due date. Late homework will be accepted; however, the score will be reduced by a factor of 50%.

Approximate syllabus: (subject to adjustment):

1. Construction and analysis of simple cryptosystems (affine, substitution, Vigenere, linear feedback shift registers)

2. Public key cryptography (RSA, finding large primes, factoring techniques, ElGamal systems)

3. The Data Encryption Standard and the Advanced Encryption Standard

4. Signature schemes (how to sign an electronic message)

5. Key distribution

6. Secret sharing schemes (design a system that can be activated by any 5 people in a group, but never by 4)

7. Hash functions

8. Zero-knowledge proofs (prove that you have some information without revealing the information)

9. Elliptic curves

Course Related Links

Computer Programs (borrowed from Jonathan Rosenberg's website):

The web page for the text has some sample programs you can use for working on the homework. Also, if you are using matlab, you probably don't want to have to download all the M-files one at a time. So here are versions with the matlab files bundled together:

  1. Mathematica notebook for Mathematica 6 or 7. A tutorial on how to use Mathematica is available here. For the problems in Ch. 16 on plotting elliptic curves, use ContourPlot in place of ImplicitPlot, which is now obsolete.
  2. zip archive of M-files for MATLAB. If you have the symbolic toolbox with the Mupad engine, which is now the default (as opposed to the Maple engine, which has to be explicitly substituted if you want it), use ciphertexts_mupad.m in place of ciphertexts_maple.m. Also note that there was a bug in the old version of addell.m (used for Ch. 16), which has been fixed in this archive.
  3. Mupad notebook and transcript thereof illustrating calculations related to RSA, etc.
  4. Mupad notebook and transcript thereof illustrating the "low exponent attack on RSA" (using continued fractions), section 6.2.1.
  5. Mupad notebook and transcript thereof illustrating the "p - 1 factoring method", section 6.4.
  6. Mathematica notebook illustrating the "p - 1 factoring method", section 6.4.
  7. Mupad notebook and transcript thereof illustrating the "universal exponent method" of factoring, section 6.4.2.
  8. Mupad notebook and transcript thereof illustrating Diffie-Hellman key exchange and various attacks on discrete log cryptosystems.
  9. Mupad notebook and transcript thereof illustrating various algorithms for computing discrete logs.
  10. Another Mupad notebook and transcript thereof illustrating various algorithms for computing discrete logs.
  11. Mupad notebook and transcript thereof illustrating the "baby step, giant step" algorithm for computing discrete logs.
  12. Mupad notebook and transcript thereof illustrating addition in elliptic curves mod n and applications to factoring.
  13. Mupad notebook and transcript thereof illustrating doubling in an elliptic curve over Q.