A GPU implementation of the Montgomery multiplication algorithm for elliptic curve cryptography
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Bibliographic record
Abstract
This work presents a GPU implementation of the Montgomery multiplication algorithm that is heavily optimized for the GPU's SEVID architecture, as well as the field sizes and constraints required for elliptic curve cryptography. We present and compare the throughput results of our proposed algorithm for 10 commonly used field sizes from 112 to 521 bits. When executed by our NVIDIA GTX-480 GPU device, the proposed algorithm's measured throughput in multiplication operations per second is 1.24 to 1.72 times greater than the next fastest GPU-based algorithm running on the same device, and is significantly greater than all other published CPU and GPU-based implementations. The proposed work could be used as a component of an elliptic curve cryptography acceleration appliance, or for cryptanalysis.
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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 | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 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 it