# Capstone

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

Recommended text: A. McAndrew, "Introduction to Cryptography with open-source software", CRC Press, 2011

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:

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

## Computational Fourier Transforms course webpage

Policy on grading and syllabus for SM472
Spriing 2006-2007

Text: James Walker, 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:
1. Each student produces a written report resulting from several iterations of review and editing.
2. Each student gives several oral presentations.
This course will require a 15 page (typed) paper, completed homework assignments, and several presentations. The paper must be clearly and carefully written, containing precise definitions, theorems and rigorous proofs.
• 6 week grade: This will be based on
• homework done,
• a 5 page outline of your paper (some examples: Culver, Hess, Nelan and Tyler are good ones to try to base yours on), and
• one 10-15 minute presentation (here is an example - a powerpoint presentation converted to pdf).
• 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.
Possible topics:
1. DCT and DST
2. Applications of FTs to DEs
3. Convolution and applications
4. Shannon's sampling theorem
5. Parseval's identity and Poisson's summation formula
6. Filters and FTs
7. FFTs
8. DWTs and wavelets.
9. Statistics (based on the extra credit exercises from ch 5).
Syllabus and hmwk:
• 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
class notes (pdf), class notes (html)

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

SAGE examples