Supersingular isogeny search
Construct an explicit isogeny between two supersingular elliptic curves.
F_p-rational curves · classical · heuristic
Find an isogeny between F_p-rational supersingular curves using small-degree isogenies
Results
| # | PUBLICATION / AUTHORS | DATE | TIME BOUND | SPACE BOUND | EVIDENCE |
|---|---|---|---|---|---|
| 1 | Computing isogenies between supersingular elliptic curves over F_pDesigns, Codes and Cryptography 2016SourceBibTeX / details | 29 Oct 2013 | O~(p1/4) | Not stated in the checked source | PublishedSource checked |
Comparison definition & assumptions
- Regime
- Find an isogeny between F_p-rational supersingular curves using small-degree isogenies
- Computation
- Classical
- Rigor
- Heuristic
- Instances
- Both curves defined over F_p
- Cost scale
- p^{c+o(1)}
- Parameter
- p
- Description
- Find an isogeny between F_p-rational supersingular curves using small-degree isogenies
- Comparison rules
- The number of F_p-rational vertices is about p^{1/2}, unlike the full F_{p^2} graph. Keep the source random-walk assumptions and GRH connectivity condition; do not mix this easier input restriction with general supersingular curves.
- Tags
- F_p rational, random walks, GRH