The Supersingular Isogeny Problem in Time and Memory $p^{1/3+o(1)}$, Unconditionally

José Luis Delgado

arXiv 2609.22018

Time bound

p^1/3 exp(O(sqrt(log p log log p))) = p^1/3+o(1) expected time

Space bound

p^1/3+o(1) expected memory

Source / version date

18 Sept 2026

Comparison variant

General curves · classical · unconditional

Cost scale

p^c+o(1)

model

Classical Las Vegas; expected time and memory

reduction

OneEnd to EndRing and Isogeny; see also arXiv:2502.17010

source-chronology

arXiv v1 submitted 18 September 2026

Assumptions and source notes

The source abstract claims a Las Vegas OneEnd algorithm analyzed without a smoothness heuristic, with the displayed expected time and memory. Known unconditional reductions transfer OneEnd to the supersingular endomorphism-ring and isogeny problems. This is a preprint claim checked against the primary arXiv abstract; the full proof was not independently audited. The p exponent remains exponential in log p and is not a concrete parameter-set break.

Source location

Abstract
Version: arXiv:2609.22018v1

Primary source ↗

@misc{delgado26-unconditional-isogeny,
  author = {José Luis Delgado},
  title = {{The Supersingular Isogeny Problem in Time and Memory $p^{1/3+o(1)}$, Unconditionally}},
  year = {2026},
  url = {https://arxiv.org/abs/2609.22018},
  keywords = {supersingular isogenies, unconditional, OneEnd, Las Vegas},
  cr_date = {2026-09-18},
  cr_date_precision = {day},
  cr_status = {preprint},
  cr_venue = {arXiv:2609.22018},
  cr_author_ids = {jose-luis-delgado},
  archiveprefix = {arXiv},
  eprint = {2609.22018},
  primaryclass = {cs.CR}
}