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Paper 2008/491

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

Laura Hitt O'Connor and Gary McGuire and 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
Creative Commons Attribution
CC BY
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