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Algebra Seminar

Monday, December 11, 2006 - 4:00pm

Steven Miller

Rutgers University

Location

University of Pennsylvania

3C4 DRL

Note: Room Change

A famous theorem of Tate asserts that two elliptic curves over the same finite field have the same number of points exactly when they are isogenous. It turns out, however, to be extremely difficult to construct an explicit isogeny; if one could, it would be a powerful tool in elliptic curve cryptography. Instead, we consider the distribution properties of random compositions of low degree isogenies, which can be tackled using Hecke L-functions. As an application, we give a proof that (in most cases) the cryptographic properties of an elliptic curve depend solely on the ground field and point count, but not crucially on the individual curve itself. (Joint work with David Jao, Waterloo, and Ramarathnam Venkatesan, Microsoft Research)