## CryptoDB

### Marco Streng

#### Publications

Year
Venue
Title
2008
EPRINT
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 $A$.
2008
EPRINT
We present an algorithm for constructing cryptographic hyperelliptic curves of genus $2$ and $p$-rank $1$, using the CM method. We also present an algorithm for constructing such curves that, in addition, have a prescribed small embedding degree. We describe the algorithms in detail, and discuss other aspects of $p$-rank 1 curves too, including the reduction of the class polynomials modulo $p$.

#### Coauthors

David Freeman (1)
Gary McGuire (1)
Michael Naehrig (1)
Laura Hitt O'Connor (1)
Peter Stevenhagen (1)