Frobenius Maps of Abelian Varieties and Finding Roots of Unity in Finite Fields
Frobenius Maps of Abelian Varieties and Finding Roots of Unity in Finite Fields
We give a generalization to Abelian varieties over finite fields of the algorithm of Schoof for elliptic curves. Schoof showed that for an elliptic curve E over ${{\mathbf {F}}_q}$, given by a Weierstrass equation, one can compute the number of ${{\mathbf {F}}_q}$-rational points of E in time $O({(\log q)^9})$. Our …