x-only point addition formula and faster compressed SIKE
Bibliographic record
Abstract
The optimization of the main key compression bottlenecks of the supersingular isogeny key encapsulation mechanism (SIKE) has been a target of research in the last few years. Significant improvements were introduced in the recent works of Costello et al. (EUROCRYPT’2017) and Zanon et al. (PQCrypto’2018; IEEE ToC’2018). The combination of the techniques in Zanon et al. (PQCrypto’2018; IEEE ToC’2018) reduced the running time of binary torsion basis generation in decompression by a factor of 29 compared to previous work. On the other hand, generating such a basis still takes almost a million cycles on an Intel Core i5-6267U Skylake. In this paper, we continue the work of Zanon et al. (IEEE ToC’2018) and introduce a technique that drops the complexity of binary torsion basis generation by a factor $$\log p$$ in the number of underlying field multiplications. In particular, our experimental results show that a basis can be generated in about 1300 cycles, attaining an improvement by a factor more than 600. Although this result eliminates one of the key compression bottlenecks, many other bottlenecks remain. In addition, we give further improvements for the ternary torsion generation with significant impact on the related decompression procedure. Moreover, a new trade-off between ciphertext sizes versus decapsulation speed and storage is introduced and achieves a 1.7 times faster decapsulation.
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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 | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.005 |
| 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".