2007-05-16
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1. Turn in graded homework.

2. Reminder: second drafts of projects are due Friday (!)  You want to 
   do a good job on these, since they are the last freebie. 

3. New homework assignment. 

4. Elliptic curves (short lecture):
    (a) defn over QQ
    (b) geometric description of group law
    (c) defn over Z/pZ
    (d) algebraic description of group law -- makes sense mod p.
    (e) we will use elliptic curves for: 
           -- deeper understanding of problems in number theory
           -- attacking cryptosystems by factoring integers 
                (Lenstra's ECM method)
           -- building cryptosystems

  Next time -- elliptic curve factorization

4. Projects -- everyone say your name and a 2-sentence description of
   your project.