Supersingular isogeny search
Construct an explicit isogeny between two supersingular elliptic curves.
General curves · classical · heuristic
Any explicit isogeny between two supersingular elliptic curves; p→∞
Results
| # | PUBLICATION / AUTHORS | DATE | TIME BOUND | SPACE BOUND | EVIDENCE |
|---|---|---|---|---|---|
| 1 | The supersingular isogeny problem in time and memory $p^{1/3+o(1)}$ePrint 2026/1486SourceBibTeX / details | 23 Jul 2026 | p1/3+o(1) | p1/3+o(1) | PreprintSource checked |
| 2 | Computing isogenies between supersingular elliptic curves over F_pDesigns, Codes and Cryptography 2016SourceBibTeX / details | 29 Oct 2013 | O~(p1/2) | Not stated in the checked source | PublishedSource checked |
Comparison definition & assumptions
- Regime
- Any explicit isogeny between two supersingular elliptic curves; p→∞
- Computation
- Classical
- Rigor
- Heuristic
- Instances
- Supersingular curves over F_{p^2}
- Cost scale
- p^{c+o(1)}
- Parameter
- p
- Description
- Any explicit isogeny between two supersingular elliptic curves; p→∞
- Comparison rules
- The output may be a compact chain of isogenies of varying degrees. A fixed-degree or short-path problem is different. Keep smoothness/random-walk assumptions and memory costs explicit. A p exponent is not a base-2 dimension exponent.
- Tags
- general supersingular curves, heuristic