Supersingular isogeny search
Construct an explicit isogeny between two supersingular elliptic curves.
General curves · classical · unconditional
Any explicit isogeny between supersingular elliptic curves; unconditional asymptotic analysis
Results
| # | PUBLICATION / AUTHORS | DATE | TIME BOUND | SPACE BOUND | EVIDENCE |
|---|---|---|---|---|---|
| 1 | The Supersingular Isogeny Problem in Time and Memory $p^{1/3+o(1)}$, UnconditionallyarXiv 2609.22018SourceBibTeX / detailsclassical supersingular isogenies unconditional claim preprint | 18 Sept 2026 | p1/3 exp(O(sqrt(log p log log p))) = p1/3+o(1) expected time | p1/3+o(1) expected memory | PreprintSource checked |
| 1 | Smoothness of Shortest Isogenies to Frobenius ConjugatesarXiv 2610.21488SourceBibTeX / detailsclassical supersingular isogenies unconditional claim preprint | 15 Oct 2026 | p1/3+o(1) | Memory of the referenced Wesolowski algorithm; not independently re-derived here | PreprintSource checked |
| 3 | Solving the supersingular isogeny problem in time $p^{2/5+o(1)}$ using bivariate multipoint evaluationePrint 2026/1575SourceBibTeX / details | 3 Aug 2026 | p2/5+o(1) | p2/5+o(1) | PreprintSource checked |
Comparison definition & assumptions
- Regime
- Any explicit isogeny between supersingular elliptic curves; unconditional asymptotic analysis
- Computation
- Classical
- Rigor
- Provable
- Instances
- Supersingular curves over F_{p^2}
- Cost scale
- p^{c+o(1)}
- Parameter
- p
- Description
- Any explicit isogeny between supersingular elliptic curves; unconditional asymptotic analysis
- Comparison rules
- Include only bounds established without a smoothness heuristic or GRH. Theoretical multipoint-evaluation bounds need not imply a practical cryptanalytic improvement.
- Tags
- general supersingular curves, unconditional