A CM construction for curves of genus 2 with p-rank 1

3Citations
Citations of this article
14Readers
Mendeley users who have this article in their library.

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. © 2010 Elsevier Inc.

Cite

CITATION STYLE

APA

Hitt O’Connor, L., McGuire, G., Naehrig, M., & Streng, M. (2011). A CM construction for curves of genus 2 with p-rank 1. Journal of Number Theory, 131(5), 920–935. https://doi.org/10.1016/j.jnt.2010.05.002

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Save time finding and organizing research with Mendeley

Sign up for free