Tate pairing computation on the divisors of hyperelliptic curves for cryptosystems.
Bibliographic record
Abstract
In recent papers [4], [9] they worked on hyperelliptic curves H b defined by y +y = x +x +b over a finite field F2 n with b = 0 or 1 for a secure and e#cient pairing-based cryptosystems. We find a completely general method for computing the Tate-pairings over divisor class groups of the curves H b in a very explicit way. In fact, Tate-pairing is defined over the entire divisor class group of a curve, not only over the points on a curve. So far only pointwise approach has been made in [4], [9] for the Tate-pairing computation on the hyperelliptic curves H b over F2 n . Furthermore, we obtain a very e#cient algorithm for the Tate pairing computation over divisors by reducing the cost of computing. We also find a necessary condition for hyperelliptic curve to have a significant reduction of the loop cost in the Tate pairing computation. Keywords- Tate pairing computation, hyperelliptic curve, cryptosystem, divisors 1
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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 | 0.002 |
| Science and technology studies | 0.002 | 0.002 |
| Scholarly communication | 0.003 | 0.006 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.010 | 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".