ON CURVES OVER FINITE FIELDS WITH JACOBIANS OF SMALL EXPONENT

On Curves over Finite Fields with Jacobians of Small Exponent

We show that finite fields over which there is a curve of a given genus g ≥ 1 with its Jacobian having a small exponent, are very rare. This extends a recent result of W. Duke in the case g = 1. We also show when g = 1 or g = 2 that our bounds are best possible.

Curves and Jacobians over function fields

On maximal curves over finite fields of small order

On counting and generating curves over small finite fields

We consider curves defined over small finite fields with points of large prime order over an extension field. Such curves are often referred to as Koblitz curves and are of considerable cryptographic interest. An interesting question is whether such curves are easy to construct as the target point order grows asymptotically. We show that under certain number theoretic conjecture, if q is a prim...

Abelian Surfaces over Finite Fields as Jacobians