The supersingular isogeny problem in time and memory $p^{1/3+o(1)}$

Benjamin Wesolowski

ePrint 2026/1486

Time bound

p^1/3+o(1)

Space bound

p^1/3+o(1)

Source / version date

23 Jul 2026

Comparison variant

General curves · classical · heuristic

Cost scale

p^c+o(1)

assumption

Smoothness heuristic

source-chronology

Received 20 July; approved 23 July 2026

Assumptions and source notes

The time and memory bound assumes smoothness of certain random integers. The source notes a superpolynomial overhead hidden in o(1) and substantial memory requirements; concrete impact is not established.

Source location

Abstract; approved 2026-07-23
Version: Checked 2026-11-08; see linked source version/date

Primary source ↗

@misc{wesolowski26-isogeny,
  author = {Benjamin Wesolowski},
  title = {{The supersingular isogeny problem in time and memory $p^{1/3+o(1)}$}},
  year = {2026},
  url = {https://eprint.iacr.org/2026/1486},
  keywords = {supersingular isogenies, smoothness heuristic, endomorphism rings},
  cr_date = {2026-07-23},
  cr_date_precision = {day},
  cr_status = {preprint},
  cr_venue = {Cryptology ePrint Archive 2026/1486},
  cr_author_ids = {benjamin-wesolowski}
}