A generalisation of Miller's algorithm and applications to pairing computations on abelian varieties
| hal.structure.identifier | Institut de Recherche Mathématique de Rennes [IRMAR] | |
| dc.contributor.author | LUBICZ, David | |
| hal.structure.identifier | Lithe and fast algorithmic number theory [LFANT] | |
| hal.structure.identifier | Laboratoire International de Recherche en Informatique et Mathématiques Appliquées [LIRIMA] | |
| dc.contributor.author | ROBERT, Damien | |
| dc.date.accessioned | 2024-04-04T02:22:20Z | |
| dc.date.available | 2024-04-04T02:22:20Z | |
| dc.date.created | 2013-03-28 | |
| dc.date.issued | 2015 | |
| dc.identifier.issn | 0747-7171 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/189644 | |
| dc.description.abstractEn | In this paper, we use the theory of theta functions to generalize to all abelian varieties the usual Miller's algorithm to compute a function associated to a principal divisor. We also explain how to use the Frobenius morphism on abelian varieties defined over a finite field in order to shorten the loop of the Weil and Tate pairings algorithms. This extend preceding results about ate and twisted ate pairings to all abelian varieties. Then building upon the two preceding ingredients, we obtain a variant of optimal pairings on abelian varieties. Finally, by introducing new addition formulas, we explain how to compute optimal pairings on Kummer varieties. We compare in term of performance the resulting algorithms to the algorithms already known in the genus one and two case. | |
| dc.description.sponsorship | Espaces de paramètres pour une arithmétique efficace et une évaluation de la sécurité des courbes - ANR-12-BS01-0010 | |
| dc.description.sponsorship | SIM et théorie des couplages pour la sécurité de l'information et des communications - ANR-12-INSE-0014 | |
| dc.description.sponsorship | Centre de Mathématiques Henri Lebesgue : fondements, interactions, applications et Formation - ANR-11-LABX-0020 | |
| dc.language.iso | en | |
| dc.publisher | Elsevier | |
| dc.subject.en | Pairings | |
| dc.subject.en | Abelian varieties | |
| dc.subject.en | Cryptography | |
| dc.title.en | A generalisation of Miller's algorithm and applications to pairing computations on abelian varieties | |
| dc.type | Article de revue | |
| dc.identifier.doi | 10.1016/j.jsc.2014.08.001 | |
| dc.subject.hal | Mathématiques [math]/Théorie des nombres [math.NT] | |
| dc.description.sponsorshipEurope | Algorithmic Number Theory in Computer Science | |
| bordeaux.journal | Journal of Symbolic Computation | |
| bordeaux.page | 68-92 | |
| bordeaux.volume | 67 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-00806923 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-00806923v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Journal%20of%20Symbolic%20Computation&rft.date=2015&rft.volume=67&rft.spage=68-92&rft.epage=68-92&rft.eissn=0747-7171&rft.issn=0747-7171&rft.au=LUBICZ,%20David&ROBERT,%20Damien&rft.genre=article |
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