Implementing the Castryck-Decru attack on SIDH with general primes
Bibliographic record
Abstract
With the rapid progress of quantum computers in recent years, efforts have been made to standardize new public-key cryptographic protocols which would be secure against them. One of the schemes in contention was Supersingular Isogeny Diffie-Hellman (SIDH). This scheme relied on the assumed hardness of the isogeny problem on supersingular elliptic curves. However, in the SIDH protocol extra information on the secret isogenies is transmitted. In July 2022, Castryck and Decru found a way to exploit this information to completely break the scheme. They gave an implementation of their attack which allows to recover Bob’s secret key in a few seconds on a laptop. Usually, Alice and Bob’s secret isogenies are taken to have degree 2^a and 3^b respectively. This thesis gives a more general implementation of the attack in Magma which works even if Alice and Bob’s secret isogenies have degrees lA^a and lB^b for more general primes lA and lB.
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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 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.003 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.004 | 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".