A Concrete Introduction to Higher Algebra, 2nd Edition

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Unformatted text preview: CS 276 Projects CS 276 Projects General Your term project should address some research issue in cryptography. There are two categories of projects: Study projects involve the survey of a series of research papers on a particular subject. The outcome of the project is a report describing the general problem, the solutions provided in the various papers, and the conceptual and technical contributions of each paper. One or more key results should be stated and proved in the report, possibly filling any gap in the original presentation (see below). A clear description of how the presented result fits into the general picture should also be given. There is no page limit (either minimum or maximum), and reports will be evaluated on technical content (not on length), but we expect that a typical report would be about 5 to 10 pages long, be written in latex, and have an extensive bibliography. Every study project should contain "something old" and "something new". The "something old" is the survey of the research papers, and is the main focus of the project. As for the "something new", the intention is that every project should at least a little bit of new technical material. For instance, you could take a claim or lemma that is not proven in the paper (or whose proof is only sketched) and give the full proof. Or, in the case of a theorem stated in asymptotic terms (e.g., "if X has superpolynomial security, then so does Y"), you could translate it into concrete security terms (give the exact form of the reduction: e.g., "if X is (t,q,e)-secure, then Y is (t/2,sqrt(q),10e)- secure"). Or, you could take any security result and say something about how tight it is (e.g., if X is claimed to be (t,q,e)-secure, can you find an attack that (t,q,e/2)-breaks it? what is the best attack you can find against a scheme satisfying the premises of the theorem?). Or, if there is a theorem with a complicated proof, you could take some easier special case and give a simpler proof for that special case. Feel free to be creative in your choice of what you will do. You must state in your proposal what new technical item you will provide. Research projects are of theoretical nature, and are directed to prove a certain result (not previously known). Topics should be chosen so that proofs should not be very hard, and that the final result should be interesting. Since theoretical research is intrinsically inpredictable, it is possible that one month (or twenty years, for that matter) might not be enough to come up with a solution. Partial solutions will be accepted. In case of no results, the project can be turned into a study project on the same topic. If you're at a loss for a project topic, we have prepared a list of possible project topics that you can peruse as examples of how to a pick a suitable project. See below. But don't feel limited to these suggestions! They are intended only as examples....
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