Tuesday, October 22, 14:00, 7.527.

Frauke Bleher (University of Iowa)
Cup products on elliptic curves over finite fields I, II.

Abstract:
This is joint work with Ted Chinburg.
Let E be an elliptic curve over a finite field k, and let n be a positive integer not divisible by the characteristic of k. Suppose \bar{k} is an algebraic closure of k, and let \bar{E} be the base change of E to \bar{k}. Miller's algorithm gives an efficient way to compute cup products of normalized classes of \bar{E} with coefficients in Z/n or mu_n. This algorithm is an essential tool for key sharing in cryptography. In this talk, we will discuss a recent extension of Miller's algorithm to the cup products of normalized classes of E. This result cannot be generalized to higher genus curves.