Computing class polynomials for abelian surfaces
| hal.structure.identifier | Lithe and fast algorithmic number theory [LFANT] | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | ENGE, Andreas | |
| hal.structure.identifier | Cryptology, Arithmetic: Hardware and Software [CARAMEL] | |
| dc.contributor.author | THOMÉ, Emmanuel | |
| dc.date.accessioned | 2024-04-04T02:20:45Z | |
| dc.date.available | 2024-04-04T02:20:45Z | |
| dc.date.created | 2013 | |
| dc.date.issued | 2014 | |
| dc.identifier.issn | 1058-6458 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/189518 | |
| dc.description.abstractEn | 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 20016. | |
| dc.language.iso | en | |
| dc.publisher | Taylor & Francis | |
| dc.subject.en | Number theory | |
| dc.subject.en | Complex Multiplication | |
| dc.subject.en | Theta functions | |
| dc.title.en | Computing class polynomials for abelian surfaces | |
| dc.type | Article de revue | |
| dc.identifier.doi | 10.1080/10586458.2013.878675 | |
| dc.subject.hal | Informatique [cs]/Cryptographie et sécurité [cs.CR] | |
| dc.subject.hal | Mathématiques [math]/Théorie des nombres [math.NT] | |
| dc.identifier.arxiv | 1305.4330 | |
| dc.description.sponsorshipEurope | Algorithmic Number Theory in Computer Science | |
| bordeaux.journal | Experimental Mathematics | |
| bordeaux.page | 129-145 | |
| bordeaux.volume | 23 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.issue | 2 | |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-00823745 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-00823745v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Experimental%20Mathematics&rft.date=2014&rft.volume=23&rft.issue=2&rft.spage=129-145&rft.epage=129-145&rft.eissn=1058-6458&rft.issn=1058-6458&rft.au=ENGE,%20Andreas&THOM%C3%89,%20Emmanuel&rft.genre=article |
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