Novel Formulations of M-Term Overlap-Free Karatsuba Binary Polynomial Multipliers and Their Hardware Implementations
Bibliographic record
Abstract
Novel binary polynomial multipliers have been designed using M-term overlap-free Karatsuba multiplication (OFKM), where$M$is 5–8. The proposed designs were realized in digital hardware and implemented on field-programmable gate array (FPGA) and the best value of$M$was selected and presented for common National Institute of Standards and Technology (NIST) operand sizes from 64 to 571 bits. The implemented hardware designs use a hybrid approach that combines a given M-term overlap-free Karatsuba multipliers with two-term splitting to reduce the need for zero-padding in the final recurrent stages. Compared to the traditional M-term Karatsuba multipliers, the proposed overlap-free implementations offer reductions in delay and area-delay product (ADP). The proposed designs also compare favorably to previous implementations of binary polynomial multipliers. Their favorable characteristics make the proposed overlap-free Karatsuba polynomial multipliers viable options for use in cryptographic systems where speed is a significant consideration and hardware resource consumption must be limited.
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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 | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.005 | 0.001 |
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".