Efficient architectures for modular exponentiation using Montgomery powering ladder
Bibliographic record
Abstract
Side channel attacks have been considered as serious threats to certain public-key cryptosystems, such like RSA and elliptic curve system. For modular exponentiation for RSA and scalar multiplication for elliptic curve cryptosystems, Montgomery powering ladder has been shown to be a good choice for counter-measures against side-channel attacks. In this paper, two efficient architectures for modular exponentiation respectively using Montgomery powering ladder algorithm and m-ary powering ladder method are proposed. The first one is a straightforward and efficient implementation of the Montgomery powering ladder algorithm, in which the multiplication and squaring are performed in parallel during each clock cycle. A novel-designed two-by-two cross-point switch is used to select each ladder step. By parallelizing the Montgomery powering ladder using loop unrolling technique so that the number of loops is reduced by half, a second efficient architecture is proposed that requires only half number of clock cycles compared to the first one. The second proposed architecture realizes the m-ary Montgomery powering ladder for the case that the radix equals to 4.
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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 | 0.000 |
| 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 | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| 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".