International Association for Cryptologic Research

International Association
for Cryptologic Research

CryptoDB

Marco Streng

Publications

Year
Venue
Title
2008
EPRINT
Abelian varieties with prescribed embedding degree
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
CM construction of genus 2 curves with p-rank 1
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 $p$.