Elliptic-curve discrete logarithms
Compute discrete logarithms in elliptic-curve groups; distinguish ordinary cryptographic curves from anomalous or other exceptional families.
Anomalous prime-field curves
Trace one; p-adic lift techniques
Results
| # | PUBLICATION / AUTHORS | DATE | TIME BOUND | SPACE BOUND | EVIDENCE |
|---|---|---|---|---|---|
| — | The Discrete Logarithm Problem on Elliptic Curves of Trace OneJournal of Cryptology 1999SourceBibTeX / detailsanomalous curves p-adic logarithm | Oct 1997 | Polynomial time in log p for trace-one curves | Not extracted from the source | PublishedSource checked |
Comparison definition & assumptions
- Regime
- Trace one; p-adic lift techniques
- Computation
- Classical
- Rigor
- Provable
- Instances
- curves E/F_p with #E(F_p)=p
- Cost scale
- Expression only
- Parameter
- log₂ p
- Description
- Exceptional curve family admitting polynomial-time attacks; this does not apply to ordinary cryptographic prime-order curves.
- Comparison rules
- Exceptional curve family admitting polynomial-time attacks; this does not apply to ordinary cryptographic prime-order curves. Only compare entries with this cost scale, input domain and computational model. Polynomial and quasi-polynomial expressions without an extracted scalar are not ranked.
- Tags
- anomalous curves, trace one, p-adic logarithm