Paper 2026/2677
Smoothness of Shortest Isogenies to Frobenius Conjugatess
, University of Science and Technology of China, Hefei National Laboratory, University of Science and Technology of China, Hefei National LaboratoryAbstract
Let \(E\) be chosen uniformly from the geometric isomorphism classes of supersingular elliptic curves over \(\overline{\mathbb{F}}_p\) and \(\delta_E\) be the minimum degree of isogenies from \(E\) to its Frobenius conjugate \(E^{(p)}\). We establish bounds for the smoothness probability of $\delta_E$ and hence affirm Wesolowski's \(p^{1/3+o(1)}\) attack on the supersingular endomorphism ring problem is unconditional. We also establish a uniform asymptotic formula, with a main term expressed in terms of Dirichlet \(L\)-values, for the probability that a connection isogeny of degree $n$ exists between $E$ and $E^{(p)}$.
Metadata
- Available format(s)
-
PDF
- Category
- Attacks and cryptanalysis
- Publication info
- Preprint.
- Keywords
- Supersingular elliptic curvesleast isgeny degreesmooth numberBrandt operatorWesolowski’s p1/3-attack.
- Contact author(s)
-
yiouyang @ ustc edu cn
veivei @ mail ustc edu cn
xuzheng1 @ mail ustc edu cn - History
- 2026-10-31: approved
- 2026-10-29: received
- See all versions
- Short URL
- https://ia.cr/2026/2677
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2026/2677,
author = {Yi Ouyang and Wei Wei and Zheng Xu},
title = {Smoothness of Shortest Isogenies to Frobenius Conjugatess},
howpublished = {Cryptology {ePrint} Archive, Paper 2026/2677},
year = {2026},
url = {https://eprint.iacr.org/2026/2677}
}
