Computing $2$-isogenies between Kummer lines

Damien Robert; Nicolas Sarkis

Paper 2024/037

Computing $2$-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 $2$-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.

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},
      note = {\url{https://eprint.iacr.org/2024/037}},
      url = {https://eprint.iacr.org/2024/037}
}