Finite-field discrete logarithms
Compute discrete logarithms in multiplicative groups of finite fields, separating prime fields, characteristic growth and extension structure.
Special prime fields · classical heuristic
p = r^e − s with r and s small; exploitable representation supplied
Results
| # | PUBLICATION / AUTHORS | DATE | TIME BOUND | SPACE BOUND | EVIDENCE |
|---|---|---|---|---|---|
| 1 | The Special Function Field SieveSIAM Journal on Discrete Mathematics 2002SourceBibTeX / details | 2002 | Lp[1/3, (32/9)1/3] | Not extracted from the source | PublishedSource checked |
Comparison definition & assumptions
- Regime
- p = r^e − s with r and s small; exploitable representation supplied
- Computation
- Classical
- Rigor
- Heuristic
- Instances
- special-form prime fields F_p
- Cost scale
- L_p[1/3,c]
- Parameter
- p
- Description
- Special-prime DLP with an essential representation restriction. Here L_X[α,c] = exp((c+o(1))(ln X)^α(ln ln X)^(1−α)); all logarithms in this definition are natural.
- Comparison rules
- Special-prime DLP with an essential representation restriction. Here L_X[α,c] = exp((c+o(1))(ln X)^α(ln ln X)^(1−α)); all logarithms in this definition are natural. 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
- special number field sieve, special primes, heuristic