Fast Bit Parallel-Shifted Polynomial Basis Multipliers in <formula formulatype="inline"><tex>$GF(2^{n})$</tex></formula>
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Bibliographic record
Abstract
A new nonpipelined bit-parallel-shifted polynomial basis multiplier for GF(2n) is presented. For some irreducible trinomials, the space complexity of the multiplier matches the best results available in the literature, and its gate delay is equal to T A+lceillog2nrceilTX, where TA and TX are the delay of one two-input and and xor gates, respectively. To the best of our knowledge, this is the first time that the gate delay bound TA+lceillog2nrceilTX is reached. For some irreducible pentanomials, its gate delay is equal to TA +(1+lceillog2nrceil)TX. NIST has recommended five binary fields for the elliptic curve digital signature algorithm applications: GF(2163), GF(2233), GF(2 283), GF(2409), and GF(2571), but no irreducible trinomials exist for three degrees, viz., 163, 283 and 571. For the three corresponding binary fields, we show that the gate delay of the proposed multiplier is TA+(1+lceillog2nrceil)TX. This result outperforms the previously known results
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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 | 0.002 | 0.000 |
| Meta-epidemiology (narrow) | 0.002 | 0.002 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.002 | 0.003 |
| Science and technology studies | 0.003 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.002 | 0.000 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 0.001 |
Machine scores (provisional)
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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