Communications in Cryptology IACR CiC

Computing 2-isogenies between Kummer lines

Authors

Damien Robert, Nicolas Sarkis
Damien Robert ORCID
Univ. Bordeaux, CNRS, INRIA, Bordeaux INP, Talence, France
damien dot robert at inria dot fr
Nicolas Sarkis ORCID
Univ. Bordeaux, CNRS, INRIA, Bordeaux INP, Talence, France
nicolas dot sarkis at math dot u-bordeaux dot fr
Keywords: Elliptic curve cryptography Kummer lines Isogenies Scalar multiplication Montgomery ladder

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.

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DOI: https://doi.org/10.62056/abvua69p1
History
Submitted: 2024-01-09
Accepted: 2024-03-05
Published: 2024-04-09
How to cite

Damien Robert and Nicolas Sarkis, Computing 2-isogenies between Kummer lines. IACR Communications in Cryptology, vol. 1, no. 1, Apr 09, 2024, doi: 10.62056/abvua69p1.

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