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

Aurel Page; Damien Robert

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 Mathématiques de Bordeaux

Damien Robert, Inria Bordeaux - Sud-Ouest Research Centre, Institut de Mathématiques 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_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].

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 action isogenies orientations
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: 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},
      note = {\url{https://eprint.iacr.org/2023/1766}},
      url = {https://eprint.iacr.org/2023/1766}
}