Séminaire de Théorie des Nombres

Computing cup products on elliptic curves over finite fields

par Frauke Bleher (University of Iowa)

Europe/Paris
Salle Pellos (1R2)

Salle Pellos

1R2

Description

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 k¯ is an algebraic closure of k, and E¯=k¯kE. Miller's algorithm gives an efficient way to compute cup products of normalized classes of E¯ with coefficients in Z/n or μn. 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. This is joint work with Ted Chinburg.