Towards constant-time probabilistic root finding for code-based cryptography
Bibliographic record
Abstract
In code-based cryptography, deterministic algorithms are used in the root-finding step of the decryption process. However, probabilistic algorithms are more time efficient than deterministic ones for large fields. These algorithms can be useful for long-term security where larger parameters are relevant. Still, current probabilistic root-finding algorithms suffer from time variations making them susceptible to timing side-channel attacks. To prevent these attacks, we propose a countermeasure to a probabilistic root-finding algorithm so that its execution time does not depend on the degree of the input polynomial but on the cryptosystem parameters. We compare the performance of our proposed algorithm to other root-finding algorithms already used in code-based cryptography. In general, our method is faster than the straightforward algorithm in Classic McEliece. The results also show the range of degrees in larger finite fields where our proposed algorithm is faster than the Additive Fast Fourier Transform algorithm.
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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 | 0.003 | 0.017 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.003 | 0.005 |
| Open science | 0.002 | 0.003 |
| Research integrity | 0.002 | 0.004 |
| Insufficient payload (model declined to judge) | 0.003 | 0.002 |
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".