Exp-HE: a family of fast exponentiation algorithms resistant to SPA, fault, and combined attacks
Bibliographic record
Abstract
Security and privacy are growing concerns in modern embedded software, given the increasing level of connectivity as well as complexity and features in embedded devices. Use of cryptographic techniques is often a requirement on which the security of the device relies. However, important challenges arise when potential attackers have physical access to the device. Side-channel analysis, including simple power analysis (SPA), is a class of powerful non-intrusive attacks that are suitable for adversaries with physical access to the device. Countermeasures exist, but they typically involve a considerable performance penalty, and some of them in turn introduce a vulnerability to induced fault attacks. In this work, we present several new efficient cryptographic exponentiation algorithms that work by splitting the exponent in two halves for simultaneous processing while using special representations derived from signed-digit encoding that improve computational efficiency. A key detail in the design of these algorithms is that they are compatible with the idea of buffering the operations to provide resistance to SPA. Experimental results are presented, including implementations of the proposed methods with both modular integer exponentiation and elliptic curve (ECC) scalar multiplication. We also performed statistical analysis of the traces, showing that trace segments for different exponent bits are statistically indistinguishable. Our proposed techniques also exhibit better resistance against fault attacks and combined fault and side-channel attacks, compared to previous SPA-resistant techniques.
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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 | 0.002 | 0.007 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.003 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.003 | 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".