Computing $2$-isogenies between Kummer lines - Archive ouverte HAL
Pré-Publication, Document De Travail Année : 2024

Computing $2$-isogenies between Kummer lines

Résumé

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.
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Dates et versions

hal-04382643 , version 1 (09-01-2024)
hal-04382643 , version 2 (18-04-2024)

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  • HAL Id : hal-04382643 , version 1

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Damien Robert, Nicolas Sarkis. Computing $2$-isogenies between Kummer lines. 2024. ⟨hal-04382643v1⟩
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