Mixed Boolean-Arithmetic (MBA) Obfuscation Using Permutation Polynomials on Modular Lipschitz Integers
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Bibliographic record
Abstract
In 2007 Zhou et al. introduced a powerful software obfuscation technique using Mixed Boolean-Arithmetic (MBA) expressions and a special family of permutation polynomials on the modular integer ring ${{\mathbb{Z}}_{{2^n}}}$ (integers modulo 2<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sup> or unsigned integers of n-bit width). Since then MBA-based software obfuscation has attracted considerable interest in industry and the scientific research community. In this paper, we introduce new families of permutation polynomials by extending Zhou’s techniques to the non-commutative ring of modular Lipschitz integers ${{\mathbb{L}}_{{2^n}}}$. Permutation polynomials on the non-commutative ring ${{\mathbb{L}}_{{2^n}}}$ can be interpreted as invertible multivariate transformations on the modular integer ring ${{\mathbb{Z}}_{{2^n}}}$ and therefore the newly introduced permutation polynomials of this paper greatly expand the variety of invertible polynomial transformations on ${{\mathbb{Z}}_{{2^n}}}$ that can be used for MBA-based software obfuscation and potentially other applications such as whitebox cryptography.
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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 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| 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 it