Paper 2008/491
A CM construction for curves of genus 2 with p-rank 1
Laura Hitt O'Connor, Gary McGuire, Michael Naehrig, and Marco Streng
Abstract
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.
Metadata
- Available format(s)
-
PDF
- Category
- Foundations
- Publication info
- Published elsewhere. Unknown where it was published
- Keywords
- hyperelliptic curve cryptography
- Contact author(s)
- gary mcguire @ ucd ie
- History
- 2010-05-11: last of 2 revisions
- 2008-11-24: received
- See all versions
- Short URL
- https://ia.cr/2008/491
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2008/491,
author = {Laura Hitt O'Connor and Gary McGuire and Michael Naehrig and Marco Streng},
title = {A {CM} construction for curves of genus 2 with p-rank 1},
howpublished = {Cryptology {ePrint} Archive, Paper 2008/491},
year = {2008},
url = {https://eprint.iacr.org/2008/491}
}
