We construct Weil numbers corresponding to genus-2 curves with p-rank 1 over the finite field F_{p^2} of p^2 elements. The corresponding curves can be constructed using explicit CM constructions. In one of our algorithms, the group of F_{p^2}-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 F_{p^2} out of necessity: we show that curves of p-rank 1 over F_p for large p cannot be efficiently constructed using explicit CM constructions.

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In  Journal of Number Theory

Publisher  Elsevier
Copyright © 2007 Elsevier B.V. All rights reserved.

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