Paper 2026/1575
Solving the supersingular isogeny problem in time $p^{2/5+o(1)}$ using bivariate multipoint evaluation
, University of LuxembourgAbstract
This note presents a new unconditional attack on the supersingular isogeny problem, with time and memory complexity $p^{2/5+o(1)}$. It builds on the approach by Eisenträger-Hallgren-Leonardi-Morrison-Park (2020) and Fuselier-Iezzi-Kozek-Morrison-Namoijam (2025), and is related to the recent heuristic attack with complexity $p^{1/3+o(1)}$ by Wesolowski (ePrint 2026/1486): all of these search for a separable isogeny from a curve to its Galois conjugate to form a non-scalar endomorphism. Our attack is based on highly theoretical multivariate multipoint evaluation algorithms from Kedlaya-Umans (2008, 2011), Bhargava-Ghosh-Guo-Kumar-Umans (2022), and Ghosh-Harsha-Herdade-Kumar-Saptharishi (2023), and therefore does not threaten isogeny cryptosystems in practice; it is of theoretical interest.
Metadata
- Available format(s)
-
PDF
- Category
- Attacks and cryptanalysis
- Publication info
- Preprint.
- Keywords
- IsogeniesElliptic curvesOneEndCryptanalysis
- Contact author(s)
- aleksei @ affine group
- History
- 2026-08-03: approved
- 2026-07-31: received
- See all versions
- Short URL
- https://ia.cr/2026/1575
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2026/1575,
author = {Aleksei Udovenko},
title = {Solving the supersingular isogeny problem in time $p^{2/5+o(1)}$ using bivariate multipoint evaluation},
howpublished = {Cryptology {ePrint} Archive, Paper 2026/1575},
year = {2026},
url = {https://eprint.iacr.org/2026/1575}
}
