Paper 2008/061
Abelian varieties with prescribed embedding degree
David Freeman, Peter Stevenhagen, and Marco Streng
Abstract
We present an algorithm that, on input of a CM-field $K$, an integer $k \ge 1$, and a prime $r \equiv 1 \bmod k$, constructs a $q$-Weil number $\pi \in \O_K$ corresponding to an ordinary, simple abelian variety $A$ over the field $\F$ of $q$ elements that has an $\F$-rational point of order $r$ and embedding degree $k$ with respect to $r$. We then discuss how CM-methods over $K$ can be used to explicitly construct $A$.
Metadata
- Available format(s)
-
PDF
- Category
- Public-key cryptography
- Publication info
- Published elsewhere. Unknown where it was published
- Keywords
- pairing-friendly curvesembedding degreeabelian varietieshyperelliptic curvesCM methodcomplex multiplication
- Contact author(s)
- dfreeman @ math berkeley edu
- History
- 2008-02-11: received
- Short URL
- https://ia.cr/2008/061
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2008/061,
author = {David Freeman and Peter Stevenhagen and Marco Streng},
title = {Abelian varieties with prescribed embedding degree},
howpublished = {Cryptology {ePrint} Archive, Paper 2008/061},
year = {2008},
url = {https://eprint.iacr.org/2008/061}
}
