Bit-Serial and Bit-Parallel Montgomery Multiplication and Squaring over GF(2^m)
Bibliographic record
Abstract
Multiplication and squaring are main finite field operations in cryptographic computations and designing efficient multipliers and squarers affect the performance of cryptosystems. In this paper, we consider the Montgomery multiplication in the binary extension fields and study different structures of bit-serial and bit-parallel multipliers. For each of these structures, we study the role of the Montgomery factor, and then by using appropriate factors, propose new architectures. Specifically, we propose two bit-serial multipliers for general irreducible polynomials, and then derive bit-parallel Montgomery multipliers for two important classes of irreducible polynomials. In this regard, first we consider trinomials and provide a way for finding efficient Montgomery factors which results in a low time complexity. Then, we consider type-II irreducible pentanomials and design two bit-parallel multipliers which are comparable to the best finite field multipliers reported in the literature. Moreover, we consider squaring using this family of irreducible polynomials and show that this operation can be performed very fast with the time complexity of two XOR gates.
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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) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.004 | 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".