Laura Hitt O'Connor, Gary McGuire, Michael Naehrig, and Marco Streng
We construct Weil numbers corresponding to genus-2 curves with p-rank 1 over the finite field Fp2 of p2 elements. The corresponding curves can be constructed using explicit CM constructions. In one of our algorithms, the group of Fp2-valued points of the Jacobian has prime order, while another allows for a prescribed embedding degree with respect to a subgroup of prescribed order. The curves are defined over Fp2 out of necessity: we show that curves of p-rank 1 over Fp for large p cannot be efficiently constructed using explicit CM constructions.
|Published in||Journal of Number Theory|
Copyright © 2007 Elsevier B.V. All rights reserved.