Tripling on Hessian curves via isogeny decomposition

Thomas Decru; Sabrina Kunzweiler

Paper 2026/334

Tripling on Hessian curves via isogeny decomposition

Thomas Decru

, KU Leuven

Sabrina Kunzweiler

, Inria Bordeaux - Sud-Ouest Research Centre

Abstract

We provide a new interpretation of the arithmetic on Hessian Kummer lines using level-3 theta structures. This allows us to break the record for tripling on elliptic curves and their Kummer lines, requiring only 4 multiplications and 4 squarings per tripling for well-chosen curve parameters.

Metadata

Available format(s): PDF
Category: Public-key cryptography
Publication info: Preprint.
Keywords: Elliptic curves Hessian curves Kummer line Tripling formulas Isogenies Theta structures
Contact author(s): thomas decru @ kuleuven be
sabrina kunzweiler @ math u-bordeaux fr
History: 2026-04-10: revised; 2026-02-20: received; See all versions
Short URL: https://ia.cr/2026/334
License: CC BY

BibTeX

@misc{cryptoeprint:2026/334,
      author = {Thomas Decru and Sabrina Kunzweiler},
      title = {Tripling on Hessian curves via isogeny decomposition},
      howpublished = {Cryptology {ePrint} Archive, Paper 2026/334},
      year = {2026},
      url = {https://eprint.iacr.org/2026/334}
}