A performance comparison of elliptic curve scalar multiplication algorithms on smartphones
Bibliographic record
Abstract
This work presents an evaluation of different software implementations of algorithms to compute the most demanding operation in cryptographic schemes based on Elliptic Curve Cryptography (ECC), the scalar multiplication. Five different methods were studied, including traditional and more sophisticated methods for elliptic curve cryptography defined over prime and binary fields. For evaluation, the key generation algorithm in ECC consisting on a single scalar multiplication was implemented on a P500h LG smarthphone, which includes an ARM processor running at 600MHz. Both execution time and memory usage was evaluated. It was found that in general, scalar multiplication runs 8 times faster for ECC defined over prime fields, being the NAF the best performer method. For ECC over binary fields, the best performer method was wNAF. The results presented in this work could help a designer to select the most appropriate method when implementing ECC-based cryptographic schemes such as encryption or digital signatures on mobile devices like smartphones, meeting implementation requirements in terms of execution time and memory usage.
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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 | 0.001 | 0.004 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 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) | 0.003 | 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".