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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

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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:
DateEvent
2011Published
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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