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A CM construction for curves of genus 2 with p-rank 1
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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. doi:10.1016/j.jnt.2010.05.002
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Official URL: http://dx.doi.org/10.1016/j.jnt.2010.05.002
Abstract
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 | ||||
| Publisher: | Academic Press | ||||
| ISSN: | 0022-314X | ||||
| Official Date: | 2011 | ||||
| Dates: |
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| Volume: | Vol.131 | ||||
| Number: | No.5 | ||||
| Page Range: | pp. 920-935 | ||||
| DOI: | 10.1016/j.jnt.2010.05.002 | ||||
| Status: | Peer Reviewed | ||||
| Publication Status: | Published | ||||
| Access rights to Published version: | Restricted or Subscription Access |
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