# Capstone

**SM473, Projects in Cryptography, Codes, and Informtion Security, Spring 2011-2012**: A capstone course on cryptography

- policy statement.
- tentative syllabus.
- local Sage server (ask in class for URL, and please use your email login also as the Sage login).
- Sage server at the University of Washington.
- Some of the capstone papers (posted by permission): John Nash's letters to NSA

Working Groups: The class is divided into two-member working groups. Each group will work on the homework together. Also, there will be class group activities such as groups solving each other's ciphers.

Quizzes: There are several quizzes (open notes, but are taken individually not in groups).

There will be hour exams and a final project. The final project is an *individual* project.

Software: Using Sage (as in the textbook) will make the homework a lot easier and our cryptology calculations less trivial and more interesting. http://www.sagemath.org/

Topics the course should cover:

- Classical ciphers (Vigenere Cipher, Hill Cipher ...)
- Information theory concepts (Perfect Secrecy, Entropy ...)
- Number Theory basics Public Key cryptosystems (RSA, Rabin, ...)
- Modern Symmetric Ciphers
- Discrete Logarithm Problem and related ciphers (ElGamal, Diffie-Hellman ...)
- Stream Ciphers
- Error Correcting Codes and Stegonagraphy
- Digital Signatures

- Interesting papers in Frode Weierud's cryptocellar
- W. Stein and others,
**Sage**- a mathematical software system,

http://www.sagemath.org/ - T. Brock,
**Linear Feedback Shift Registers and Cyclic Codes in Sage**, Rose-Hulman Undergraduate Mathematics Journal, vol. 7, 2006. http://www.rose-hulman.edu/mathjournal/v7n2.php, or

brock - M. Hogan,
**The Blum-Goldwasser cryptosystem**, hogan - K. Tucker-Davis,
**An analysis of the F5 steganographic system**, tucker-davis - O. Pell's well-wriiten mathematics essay on Cryptology,
- NY Times article on GCHQ's online crypto puzzle,
- Cryptography videos:
- Peter Rowlett lecture: Substitution ciphers: Ancient - Renaissance (recorded 2009)
- Diffie Hellman talk: Information Security—Before & After Public-Key Cryptography (recorded 2005)
- Short documentary, mostly on WWII ciphers: The Innovation of Cryptology: An Enigma of History (recorded date unknown)
- Steve Weis (on Google's Applied Security team) talk Theory and Practice of Cryptography (recorded 2007)
- Prof Ronald Rivest talk The Growth of Cryptography (recorded 2011)

## Computational Fourier Transforms course webpage

Policy on grading and syllabus for SM472

Spriing 2006-2007

**Fast Fourier Transforms, 2nd edition**, CRC Press, 1996. This course is designed to cap, complete and finish the major. Specific requirements for the course are:

- Each student produces a written report resulting from several iterations of review and editing.
- Each student gives several oral presentations.

- 6 week grade: This will be based on
- 12 week grade: This will be based on homework done, a 10 page outline of your paper (some examples: Culver, Eubanks, Nelan, Tyler), and one 20-30 minute presentation.
- 16 week grade: This will be based on homework done, the 15 page final version of your paper, and the final presentation. Attendence and presentation at the SASMC conference may replace the class presentation, if the student wishes.

- DCT and DST
- Applications of FTs to DEs
- Convolution and applications
- Shannon's sampling theorem
- Parseval's identity and Poisson's summation formula
- Filters and FTs
- FFTs
- DWTs and wavelets.
- Statistics (based on the extra credit exercises from ch 5).

- chapter 1: exercises: 1-4, 6-7, 9-12, 14-15, 21, 23-27
- chapter 2: exercises 1-3, 6, 8-9
- chapter 3: extra credit exercises: 1-3
- chapter 5: exercises: 1, 7, 16, 23, 49-50

extra credit: 39-48, 62-63

Additional resource: Articles on Fourier series. (If this is dead, here is the local version, posted here by permission: Articles on Fourier series.)