Information and Resources for the Final Project
Schedule of Presentations
Read this article on "how to give a good math talk" by Professor Joseph Gallian, a renowned mathematician and good speaker.
Time Line
1. Preliminary Outline: Due date Thursday, Nov 9. First choose a topic in Coding Theory or Cryptography. Below are some suggestions (and resources) about possible topics, but you may choose a different topic. This one-page outline should include what you want to cover, and what sources you will be using.
2. Detailed Outline: Due date: Thursday Nov 30 . This should probably be 3 pages or so, and should include precise statements of theorems, sketches of proofs, and summaries of contextual or historical material.
3. In-class presentations. Last day of the class, Tuesday, Dec 12. You can have up to 50 minutes to present your project.
4. The final paper: Due Saturday, Dec 16, 6:30 pm
Ideas About Possible Topics
Here is a list of some possible topics, with references as a starting point. You can also find a lot of resources on the internet.Your topic does not have to be one of these, you can choose a different topic. Some of these topics are covered in our textbook. If you choose a topic that is in the textbook, you must use other resources as well. In general, you should use several different sources. Accuracy and correctness are crucial. Give complete and careful references, do not plagiarize. The numbers for references refer to the list of resources at the end of the course syllabus. (More references have been added to the list after it was distributed at the beginning of the semester. Please refer to the updated version available on the course web page). The material we are planning to cover from our textbook for the rest of the semester is as follows: Finish Chp 4, 10.1, 10.2, 11.1, Most of Chp 12, and if time permits Chp 5 (or parts of it). (This list and references may change/grow in the next couple of weeks)
The list below is in no particular order.
Coding Theory
1. Weight Enumerators and MacWilliam's identity. This is a well-known and fundamental theorem in coding theory relating weight enumerator of a code to its dual. Can be found in most coding theory books but there is a more accessible proof in [14]. You may include material on self-dual codes.
2. BCH Codes and their decodings. Can be found in most coding theory books.
3. Reed Solomon Codes and their decodings. Can be found in most coding theory books.
4. Codes and Designs (combinatorial designs). Start with [3] and [6].
5. Codes over Z_4. [3], [6], [9].
6. Convolutional Codes. [9], [6],[13],[15],[21]
7. Low Density Parity Check (LDPC) Codes. [13]
8. Quadratic Residue Codes: [3],[6], [9],[10],[14].
9. Games and Codes, Lexicodes: [3],[22], and this paper. This project may involve a programming part to generate lexicodes.
10. You can find ideas about computational/programming projects in [24] (for both coding theory and cryptography).
11. Also see these web pages for [22] for more ideas and tips for Mapla/Magma programming: 1, 2, 3
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Cryptography
1. Secret Sharing Schemes. [1] and first edition of (1995) [11].
2. Cryptographic Hash Functions. [5],[11], [16],[17] http://csrc.nist.gov/CryptoToolkit/tkhash.html
3. Integer Factoring Algorithms: [1],[5],[11], [16].
4. Primality Tests and Prime Number Generation: [5], [11],[16],[17].
5. Elliptic Curve Cryptography: [1],[5]
6. Pseudo-Random Number Generation: First edition of (1995) [11], [16]
7. Computational Complexity: [16],[18]
8. Quantum Computation and (Quantum Error-Correcting Codes or Quantum Cryptography): [1], [19],[23], [25].
9. NTRU: http://www.ntru.com
10. Knapsack Cryptosystems
11. History of Cryptography (be sure to include sufficient mathematical content). See the relevant articles on this page. There is also more there.
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Database
Search the Ohio Link for additional resources (or locating the resources listed above).
Use the search engine of MathSciNet to find articles on particular topics, or particular articles referenced in other articles.
Journals
Designs, Codes and Cryptography
An important journal for coding theory is IEEE Transactions on Information Theory. You don't have access to it. If you need any articles from that journal, let me know.