Computing cup products on elliptic curves over finite fields
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Frauke Bleher(University of Iowa)
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Europe/Paris
Salle Pellos (1R2)
Salle Pellos
1R2
Description
Let be an elliptic curve over a finite field , and let be a positive integer not divisible by the characteristic of . Suppose is an algebraic closure of , and . Miller's algorithm gives an efficient way to compute cup products of normalized classes of with coefficients in or . 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 . This result cannot be generalized to higher genus curves. This is joint work with Ted Chinburg.