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Computing 2-isogenies between Kummer lines

Authors:
Damien Robert , Univ. Bordeaux, CNRS, INRIA, Bordeaux INP
Nicolas Sarkis , Univ. Bordeaux, CNRS, INRIA, Bordeaux INP
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DOI: 10.62056/abvua69p1
URL: https://cic.iacr.org//p/1/1/26
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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
}