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 Mathรฉmatiques de Bordeaux
Damien Robert, Inria Bordeaux - Sud-Ouest Research Centre, Institut de Mathรฉmatiques de Bordeaux
Abstract

In this short note, we present a simplified (but slower) version Clapoti of Clapotis, whose full description will appear later. Let ๐ธ/๐”ฝ_๐‘ž be an elliptic curve with an effective primitive orientation by a quadratic imaginary order ๐‘… โŠ‚ End(๐ธ). Let ๐”ž be an invertible ideal in ๐‘…. Clapoti is a randomized polynomial time algorithm in ๐‘‚ ((log ฮ”_๐‘… + log ๐‘ž)^๐‘‚(1) ) operations to compute the class group action ๐ธ โ†ฆ ๐ธ_๐”ž โ‰ƒ ๐ธ/๐ธ[๐”ž].

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
2023-11-17: approved
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},
      note = {\url{https://eprint.iacr.org/2023/1766}},
      url = {https://eprint.iacr.org/2023/1766}
}
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