Low complexity sequential normal basis multipliers over GF(2/sup m/)
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Bibliographic record
Abstract
For efficient hardware implementation of finite field arithmetic units, the use of a normal basis is advantageous. Two architectures for multipliers over the finite field GF(2/sup m/) are proposed. Both of these multipliers are of sequential type - after receiving the coordinates of the two input field elements, they go through m iterations (or clock cycles) to finally yield all the coordinates of the product in parallel. These multipliers are highly area efficient and require fewer number of logic gates even when compared with the most area efficient multiplier available in the open literature. This makes the proposed multipliers suitable for applications where the value of m is large but space is of concern, e.g., resource constrained cryptographic systems. Additionally, the AND gate count for one of the multipliers is /spl lfloor/m/2/spl rfloor/+1 only. This implies that if the multiplication over GF(2/sup m/) is performed using a suitable subfield GF(2/sup n/), where n>1 and n|m, then the corresponding multiplier architecture will yield a highly efficient digit or word serial multiplier.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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 it