Highly nonlinear s-boxes with reduced bound on maximum correlation (extended abstract)
Bibliographic record
Abstract
In this paper, we consider S-boxes with n (odd) input bits and m ≥ 2 output bits as combiners in stream cipher systems. We construct two classes of balanced S-boxes with nonlinearity 2 n−1 − 2 (n−1)/2 for protection against correlation and linear approximation attacks. However, having a high nonlinearity may not be sufficient for security. Zhang and Chan [3] considered a more general correlation attack by using a nonlinear function of output bits. In this case, we will require the maximum correlation coefficients to be low in order to protect against their attack. They proved an upper bound for maximum correlation that is low for functions with high nonlinearity. We improve their result for our S-boxes by reducing their upper bound by a factor of √ 2. Thus, our S-boxes are more secure against general correlation attacks. Besides
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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) | 0.000 | 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 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".