Computing $2$-isogenies between Kummer lines

Damien Robert; Nicolas Sarkis

Paper 2024/037

Computing -isogenies between Kummer lines

Damien Robert

, Institut de Mathématiques de Bordeaux, Inria Bordeaux - Sud-Ouest Research Centre

Nicolas Sarkis

, Institut de Mathématiques de Bordeaux

Abstract

We use theta groups to study -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 for evaluation. We leverage these translated isogenies to build a hybrid ladder for scalar multiplication on Montgomery curves with rational -torsion, which cost per bit, compared to for the standard Montgomery ladder.

Metadata

Available format(s): PDF
Category: Public-key cryptography
Publication info: Published by the IACR in CIC 2024
DOI: 10.62056/abvua69p1
Keywords: Elliptic curves cryptography Kummer lines Isogenies Scalar multiplication Montgomery ladder
Contact author(s): damien robert @ inria fr
nicolas sarkis @ math u-bordeaux fr
History: 2024-04-18: revised; 2024-01-09: received; See all versions
Short URL: https://ia.cr/2024/037
License: CC BY

BibTeX

@misc{cryptoeprint:2024/037,
      author = {Damien Robert and Nicolas Sarkis},
      title = {Computing $2$-isogenies between Kummer lines},
      howpublished = {Cryptology {ePrint} Archive, Paper 2024/037},
      year = {2024},
      doi = {10.62056/abvua69p1},
      url = {https://eprint.iacr.org/2024/037}
}