Paper 2023/1747 Original: eprint.iacr.org/2023/1747 ↗
An Algorithmic Approach to $(2,2)$-isogenies in the Theta Model and Applications to Isogeny-based Cryptography
Abstract
In this paper, we describe an algorithm to compute chains of $(2,2)$-isogenies between products of elliptic curves in the theta model. The description of the algorithm is split into various subroutines to allow for a precise field operation counting. We present a constant time implementation of our algorithm in Rust and an alternative implementation in SageMath. Our work in SageMath runs ten times faster than a comparable implementation of an isogeny chain using the Richelot correspondence. The Rust implementation runs up to forty times faster than the equivalent isogeny in SageMath and has been designed to be portable for future research in higher-dimensional isogeny-based cryptography.
Metadata
- Available format(s)
PDF- Category
- Applications
- Publication info
- Preprint.
- History
- 2024-12-19: last updated
- 2023-11-11: published
- Short URL
- https://ia.cr/2023/1747
- License
- https://creativecommons.org/licenses/by/4.0/
BibTeX
@misc{cryptoeprint:2023/1747,
author = {Pierrick Dartois and Luciano Maino and Giacomo Pope and Damien Robert},
title = {An Algorithmic Approach to $(2,2)$-isogenies in the Theta Model and Applications to Isogeny-based Cryptography},
howpublished = {Cryptology {ePrint} Archive, Paper 2023/1747},
year = {2023},
url = {https://eprint.iacr.org/2023/1747}
}