### 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.

Available format(s)
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
See all versions
Short URL
https://ia.cr/2008/491

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},
note = {\url{https://eprint.iacr.org/2008/491}},
url = {https://eprint.iacr.org/2008/491}
}

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