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Computing 2-isogenies between Kummer lines
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Abstract: | 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 formulas, 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 $3M+6S+2m_0$ per bit, compared to $5M+4S+1m_0$ for the standard Montgomery ladder. |
BibTeX
@article{cic-2024-34118, title={Computing 2-isogenies between Kummer lines}, journal={cic}, publisher={International Association for Cryptologic Research}, volume={1, Issue 1}, url={https://cic.iacr.org//p/1/1/26}, doi={10.62056/abvua69p1}, author={Damien Robert and Nicolas Sarkis}, year=2024 }