Smoothness of Shortest Isogenies to Frobenius Conjugates

Yi Ouyang · Wei Wei · Zheng Xu

arXiv 2610.21488

Time bound

p^1/3+o(1)

Space bound

Memory of the referenced Wesolowski algorithm; not independently re-derived here

Source / version date

15 Oct 2026

Comparison variant

General curves · classical · unconditional

Cost scale

p^c+o(1)

model

Classical; unconditional-analysis claim for the referenced algorithm

distribution

Uniform geometric supersingular isomorphism classes in the smoothness theorem

related-algorithm

Wesolowski, ePrint 2026/1486

reduction

Unconditional equivalence/random self-reduction: arXiv:2502.17010

source-chronology

arXiv v1 submitted 15 October 2026; ePrint 29 October

Assumptions and source notes

The source studies the minimum degree of an isogeny to the Frobenius conjugate for a uniformly random supersingular geometric isomorphism class. Its abstract claims smoothness bounds making Wesolowski’s p^{1/3+o(1)} endomorphism-ring attack unconditional. The known reductions and random self-reducibility connect this with general supersingular isogeny search. This is a supporting-analysis record, not a further time-exponent improvement over Delgado 2026. Preprint/source-attributed claim; full proof and reduction details were not independently audited. ePrint 2026/2677 was posted later, on 29 October; chronology follows the first arXiv submission.

Source location

Abstract
Version: arXiv:2610.21488; first version 15 October 2026; revised 25 October 2026

Primary source ↗

@misc{ouyang-wei-xu26-frobenius-smoothness,
  author = {Yi Ouyang and Wei Wei and Zheng Xu},
  title = {{Smoothness of Shortest Isogenies to Frobenius Conjugates}},
  year = {2026},
  url = {https://arxiv.org/abs/2610.21488},
  keywords = {supersingular isogenies, Frobenius conjugates, smoothness, unconditional},
  cr_date = {2026-10-15},
  cr_date_precision = {day},
  cr_status = {preprint},
  cr_venue = {arXiv:2610.21488; Cryptology ePrint Archive 2026/2677},
  cr_author_ids = {yi-ouyang; wei-wei; zheng-xu},
  archiveprefix = {arXiv},
  eprint = {2610.21488},
  primaryclass = {math.NT}
}