A CM construction for curves of genus 2 with p-rank 1
Hitt O'Connor, Laura, McGuire, Gary, Naehrig, Michael and Streng, Marco. (2011) A CM construction for curves of genus 2 with p-rank 1. Journal of Number Theory, Vol.131 (No.5). pp. 920-935. ISSN 0022-314XFull text not available from this repository.
Official URL: http://dx.doi.org/10.1016/j.jnt.2010.05.002
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.
|Item Type:||Journal Article|
|Divisions:||Faculty of Science > Mathematics|
|Journal or Publication Title:||Journal of Number Theory|
|Page Range:||pp. 920-935|
|Access rights to Published version:||Restricted or Subscription Access|
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