Ordinary isogeny search
Construct an isogeny between ordinary curves with the same endomorphism ring.
Classical · horizontal isogenies
Two ordinary curves over F_q with the same cardinality and endomorphism ring
Results
| # | PUBLICATION / AUTHORS | DATE | TIME BOUND | SPACE BOUND | EVIDENCE |
|---|---|---|---|---|---|
| 1 | Improved Algorithm for the Isogeny Problem for Ordinary Elliptic CurvesApplicable Algebra in Engineering, Communication and Computing 2013SourceBibTeX / details | 31 May 2011 | O~(q1/4) | Not stated in the checked source | PublishedSource checked |
Comparison definition & assumptions
- Regime
- Two ordinary curves over F_q with the same cardinality and endomorphism ring
- Computation
- Classical
- Rigor
- Heuristic
- Instances
- Same endomorphism ring
- Cost scale
- q^{c+o(1)}
- Parameter
- q
- Description
- Two ordinary curves over F_q with the same cardinality and endomorphism ring
- Comparison rules
- Specify the common order/discriminant and allowed isogeny representation. Random-walk heuristics and practical constant-factor improvements remain explicit.
- Tags
- ordinary curves, horizontal isogenies, random walks