Parallel implementation of Wiener's attack on RSA: Algorithm design and performance evaluation
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Bibliographic record
Abstract
The robustness of the RSA cryptosystem is intrinsically tied to the choice of public and private keys. As pinpointed by M. Wiener, should the private decryption exponent, d, be improperly chosen-either disproportionately large or unduly small in relation to the public key n-an adversary could feasibly deduce the private keys within a practical time span. In this paper, the algorithm invented by Wiener is revisited and find a way to parallelize the attacking algorithm by using OpenMP. The algorithm is based on the proof made in Wiener’s article, that if d<1/3 n^(1/4), then the private key d is the denominator of one of the convergent of CF(e/n). Using a constant set of private keys (e,n), an extensive series of simulated attacks employing Wiener’s method was conducted on a laptop to determine the optimal thread count for executing the parallel algorithm. The results indicate that the algorithm’s execution speed can be enhanced by a factor of 1.5607 (rounded to five significant figures). Specifically, while the sequential version of the algorithm averaged a runtime of 3518939.04 nanoseconds, its parallel counterpart averaged 2240493.28 nanoseconds.
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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 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 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