## CryptoDB

### Paper: Abelian varieties with prescribed embedding degree

Authors: David Freeman Peter Stevenhagen Marco Streng URL: http://eprint.iacr.org/2008/061 Search ePrint Search Google 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 $A$.
##### BibTeX
@misc{eprint-2008-17738,
title={Abelian varieties with prescribed embedding degree},
booktitle={IACR Eprint archive},
keywords={public-key cryptography / pairing-friendly curves, embedding degree, abelian varieties, hyperelliptic curves, CM method, complex multiplication},
url={http://eprint.iacr.org/2008/061},
note={ dfreeman@math.berkeley.edu 13913 received 3 Feb 2008},
author={David Freeman and Peter Stevenhagen and Marco Streng},
year=2008
}