[Resource Topic] 2013/299: Computing class polynomials for abelian surfaces

Welcome to the resource topic for 2013/299

Computing class polynomials for abelian surfaces

Authors: Andres Enge, Emmanuel Thomé


We describe a quasi-linear algorithm for computing Igusa class polynomials of Jacobians of genus 2 curves via complex floating-point approximations of their roots. After providing an explicit treatment of the computations in quartic CM fields and their Galois closures, we pursue an approach due to Dupont for evaluating ϑ-constants in quasi-linear time using Newton iterations on the Borchardt mean. We report on experiments with our implementation and present an example with class number 17608.

ePrint: https://eprint.iacr.org/2013/299

See all topics related to this paper.

Feel free to post resources that are related to this paper below.

Example resources include: implementations, explanation materials, talks, slides, links to previous discussions on other websites.

For more information, see the rules for Resource Topics .