A New Multiplicative Inverse Architecture in Normal Basis Using Novel Concurrent Serial Squaring and Multiplication
Bibliographic record
Abstract
Itoh and Tsujii proposed a fast algorithm for computing multiplicative inverses (inversions) over GF(2m) using normal bases by iterating single multiplications and cyclic shifts. Recently, the Itoh-Tsujii algorithm (ITA) has been modified to use two digit-level single multiplications. The improvements of the modified Itoh-Tsujii and its variant algorithms are based on reducing the computational latency at the expense of more area requirements. In this paper, we propose a new inversion architecture based on the classical IT algorithm (or improved one) utilizing a novel interleaved computations of two single multiplications and squarings at the digit-level. The new inverter outperforms previous modified Itoh-Tsujii algorithms (such as the Ternary Itoh-Tsujii and optimal 3-chain algorithms) in terms of its lower latency, higher throughput, and improved hardware efficiency. The efficiency of the proposed field inverter is demonstrated by comparisons based on application specific integrated circuits (ASIC) implementations results using the standard 65nm CMOS technology libraries.
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How this classification was reachedexpand
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 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".