Paper 2024/037 Original: eprint.iacr.org/2024/037 ↗
Computing $2$-isogenies between Kummer lines
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
- Preprint.
- History
- 2024-04-18: last updated
- 2024-01-09: published
- Short URL
- https://ia.cr/2024/037
- License
- https://creativecommons.org/licenses/by/4.0/
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},
url = {https://eprint.iacr.org/2024/037}
}