Two mathematical security aspects of the RSA cryptosystem : signature padding schemes and key generation with a backdoor
Bibliographic record
Abstract
This work presents mathematical properties of the RSA cryptosystem. The topics of backdoors and padding algorithm are developped. For padding schemes, we give a practical instantiation with a security reduction. It is based on the compression function of SHA-1 without any chaining function. Our solution has the advantage over the previous one of removing the relation of the output length of the compression function to the length of the RSA modulus. For backdoors, improvements on definitions, existing algorithms as well as extensions of existing theorems are shown. The definitions pertaining to backdoored key generators are improved as to make their analysis uniform and comparable. New algorithms are presented and compared to existing ones as to show improvements mainly on their running time, the indistinguishability of the keys produced, and that some of these new algorithms are, for all practical purposes, the best that may be called asymmetric. Our theorem on the correctness (or completeness) of one of our better backdoored key generators is a generalization of a theorem of Boneh, Durfee and Frankel's on partial information on the decryption exponent.
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How this classification was reachedexpand
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 | 0.001 | 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 | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".