Fast computation of Tate pairing on general divisors of genus 3 hyperelliptic curves.
Bibliographic record
Abstract
For the Tate pairing computation over hyperelliptic curves, there are developments by DuursmaLee and Barreto et al., and those computations are focused on degenerate divisors. As divisors are not degenerate form in general, it is necessary to find algorithms on general divisors for the Tate pairing computation. In this paper, we present two e#cient methods for computing the Tate pairing over divisor class groups of the hyperelliptic curves y of genus 3. First, we provide the pointwise method, which is a generalization of the previous developments by Duursma-Lee and Barreto et al. In the second method, we use the resultant for the Tate pairing computation. According to our theoretical analysis of the complexity, the resultant method is 48.5% faster than the pointwise method in the best case and 15.3% faster in the worst case, and our implementation result shows that the resultant method is much faster than the pointwise method. These two methods are completely general in the sense that they work for general divisors with Mumford representation, and they provide very explicit algorithms.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.004 |
| Open science | 0.001 | 0.003 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.008 | 0.002 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".