Paper 2023/1766

Introducing Clapoti(s): Evaluating the isogeny class group action in polynomial time

Aurel Page, Inria Bordeaux - Sud-Ouest Research Centre, Institut de MathΓ©matiques de Bordeaux
Damien Robert, Inria Bordeaux - Sud-Ouest Research Centre, Institut de MathΓ©matiques de Bordeaux
Abstract

In this short note, we present a simplified (but slower) version Clapoti of Clapotis, whose full description will appear later. Let 𝐸/𝔽_π‘ž be an elliptic curve with an effective primitive orientation by a quadratic imaginary order 𝑅 βŠ‚ End(𝐸). Let π”ž be an invertible ideal in 𝑅. Clapoti is a randomized polynomial time algorithm in 𝑂 ((log Ξ”_𝑅 + log π‘ž)^𝑂(1) ) operations to compute the class group action 𝐸 ↦ 𝐸_π”ž ≃ 𝐸/𝐸[π”ž].

Note: Add a small remark on splittings and pushforwards of isogenies of coprime degrees

Metadata
Available format(s)
PDF
Category
Foundations
Publication info
Preprint.
Keywords
group actionisogeniesorientations
Contact author(s)
aurel page @ inria fr
damien robert @ inria fr
History
2024-03-29: revised
2023-11-15: received
See all versions
Short URL
https://ia.cr/2023/1766
License
Creative Commons Attribution
CC BY

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}
}
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