Cryptology ePrint Archive: Report 2013/299

Computing class polynomials for abelian surfaces

Andres Enge and Emmanuel Thomé

Abstract: 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.

Category / Keywords: public-key cryptography / number theory

Date: received 19 May 2013

Contact author: Emmanuel Thome at gmail com

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Version: 20130525:134609 (All versions of this report)

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