Radical Vélu Isogeny Formulae

Thomas Decru

Paper 2024/878

Radical Vélu Isogeny Formulae

Thomas Decru

, Université Libre de Bruxelles

Abstract

We provide explicit radical -isogeny formulae for all odd integers . The formulae are compact closed-form expressions which require one th root computation and basic field operations. The formulae are highly efficient to compute a long chain of -isogenies, and have the potential to be extremely beneficial for speeding up certain cryptographic protocols such as CSIDH. Unfortunately, the formulae are conjectured, but we provide ample supporting evidence which strongly suggests their correctness. For CSIDH-512, we notice an additional 35% speed-up when using radical isogenies up to , compared to the work by Castryck, Decru, Houben and Vercauteren, which uses radical isogenies up to only. The addition of our radical isogenies also speeds up the computation of larger class group actions in a comparable fashion.

Metadata

Available format(s): PDF
Category: Public-key cryptography
Publication info: Published by the IACR in CRYPTO 2024
Keywords: Post-quantum cryptography isogeny-based cryptography radical isogenies CSIDH
Contact author(s): thomas decru @ ulb be
History: 2024-06-05: approved; 2024-06-02: received; See all versions
Short URL: https://ia.cr/2024/878
License: CC BY

BibTeX

@misc{cryptoeprint:2024/878,
      author = {Thomas Decru},
      title = {Radical Vélu Isogeny Formulae},
      howpublished = {Cryptology {ePrint} Archive, Paper 2024/878},
      year = {2024},
      url = {https://eprint.iacr.org/2024/878}
}