Improved CRT Algorithm for Class Polynomials in Genus 2

Kristin Lauter and Damien Robert

2012

We present a generalization to genus 2 of the probabilistic algorithm in Sutherland for computing Hilbert class polynomials. The improvement over the algorithm presented in [BGL] for the genus 2 case, is that we do not need to find a curve in the isogeny class with endomorphism ring which is the maximal order: rather we present a probabilistic algorithm for “going up” to a maximal curve (a curve with maximal endomorphism ring), once we find any curve in the right isogeny class. Then we use the structure of the Shimura class group and the computation of isogenies to compute all isogenous maximal curves from an initial one.

Publication type | Article |

Published in | Algorithmic Number Theory Symposium |

URL | http://eprint.iacr.org/2012/443 |

Volume | 2012 |

Publisher | Mathematical Science Publishers |

- Affine Pairings on ARM
- Constructing elliptic curves with a given number of points over a finite field
- Group Law Computations on Jacobians of Hyperelliptic Curves

> Publications > Improved CRT Algorithm for Class Polynomials in Genus 2