Computing $2$-isogenies between Kummer lines
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| hal.structure.identifier | Analyse cryptographique et arithmétique [CANARI] | |
| dc.contributor.author | ROBERT, Damien | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| hal.structure.identifier | Analyse cryptographique et arithmétique [CANARI] | |
| dc.contributor.author | SARKIS, Nicolas | |
| dc.date.accessioned | 2024-04-04T02:31:27Z | |
| dc.date.available | 2024-04-04T02:31:27Z | |
| dc.date.issued | 2024-01-09 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/190309 | |
| dc.description.abstractEn | We use theta groups to study $2$-isogenies between Kummer lines, with a particular focus on the Montgomery model. This allows us to recover known formula, along with more efficient forms for translated isogenies, which require only $2S+2m_0$ for evaluation. We leverage these translated isogenies to build a hybrid ladder for scalar multiplication on Montgomery curves with rational $2$-torsion which cost $3M+6S+2m_0$ by bits, compared to $5M+4S+1m_0$ for the standard Montgomery ladder. | |
| dc.language.iso | en | |
| dc.subject.en | Elliptic curves cryptography | |
| dc.subject.en | Kummer lines | |
| dc.subject.en | Isogenies | |
| dc.subject.en | Scalar multiplication | |
| dc.subject.en | Montgomery ladder | |
| dc.title.en | Computing $2$-isogenies between Kummer lines | |
| dc.type | Document de travail - Pré-publication | |
| dc.subject.hal | Mathématiques [math]/Théorie des nombres [math.NT] | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| hal.identifier | hal-04382643 | |
| hal.version | 1 | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-04382643v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.date=2024-01-09&rft.au=ROBERT,%20Damien&SARKIS,%20Nicolas&rft.genre=preprint |
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