International Association for Cryptologic Research

International Association
for Cryptologic Research

CryptoDB

Peter Stevenhagen

Publications

Year
Venue
Title
2008
EPRINT
Abelian varieties with prescribed embedding degree
David Freeman Peter Stevenhagen Marco Streng
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 $A$.

Coauthors

David Freeman (1)
Marco Streng (1)