A Faster Hardware Implementation of the AES S-box
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Bibliographic record
Abstract
In this paper, we propose a very fast, yet compact, AES S-box, by applying two techniques to a composite field <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$GF((2^{4})^{2})$</tex> fast AES S-box. The composite field fast S-box has three main components, namely the input transformation matrix, the inversion circuit, and the output transformation matrix. The core inversion circuit computes the multiplicative inverse over the composite field <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$GF((2^{4})^{2})$</tex> and consists of three arithmetic blocks over subfield <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$GF(2^{{4}})$</tex> , namely exponentiation, subfield inverter, and output multipliers. For the first technique, we consider multiplication of the input of the composite field fast S-box by 255 nonzero 8-bit binary field elements. The multiplication constant increases the variety of the input and output transformation matrices of the S-box by a factor of 255, hence increasing the search space of the logic minimization algorithm correspondingly. For the second technique, we reduce the delay of the composite field fast S-box, by combining the output multipliers and the output transformation matrix. Moreover, we modify the architecture of the input transformation matrix and re-design the exponentiation block and the subfield inverter for lower delay and area. We find that 8 unique binary transformation matrices could be used to change from the binary field <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$GF(2^{8})$</tex> to the composite field <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$GF(({2}^{{4}})^{2})$</tex> at the input of the composite field S-box. We use Matla <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathbf{b}$</tex> ® to derive all <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$(255\times 8=2040)$</tex> new input transformation matrices. We search the matrices for the fastest and lowest complexity implementation and the minimal one is selected for the proposed fast S-box. The proposed fast S-box is 24% faster (with 5% increase in area) than the composite field fast design and 10% faster (with about 1% increase in area) than the fastest S-box available in the literature, to the best of our knowledge.
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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 | 0.000 |
| 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 it