Paper 2023/1766 Original: eprint.iacr.org/2023/1766 ↗
Introducing Clapoti(s): Evaluating the isogeny class group action in polynomial time
Abstract
In this short note, we present a simplified (but slower) version Clapoti of Clapotis, whose full description will appear later. Let 𝐸/𝔽_𝑞 be an elliptic curve with an effective primitive orientation by a quadratic imaginary order 𝑅 ⊂ End(𝐸). Let 𝔞 be an invertible ideal in 𝑅. Clapoti is a randomized polynomial time algorithm in 𝑂 ((log Δ_𝑅 + log 𝑞)^𝑂(1) ) operations to compute the class group action 𝐸 ↦ 𝐸_𝔞 ≃ 𝐸/𝐸[𝔞].
Metadata
- Available format(s)
PDF- Category
- Foundations
- Publication info
- Preprint.
- History
- 2024-03-29: last updated
- 2023-11-15: published
- Short URL
- https://ia.cr/2023/1766
- License
- https://creativecommons.org/licenses/by/4.0/
BibTeX
@misc{cryptoeprint:2023/1766,
author = {Aurel Page and Damien Robert},
title = {Introducing Clapoti(s): Evaluating the isogeny class group action in polynomial time},
howpublished = {Cryptology {ePrint} Archive, Paper 2023/1766},
year = {2023},
url = {https://eprint.iacr.org/2023/1766}
}