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REVIEW 4 major objections 8 minor 43 references

Early Detection of Hardware Trojans Using Neural Controlled Differential Equations and Analysis of Power Traces

T0 review · 4 major / 8 minor · reviewed 2026-07-30 · grok-4.5

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Pith's one-line read An NCDE trained only on clean power traces can flag dormant hardware Trojans once their power footprint exceeds about 3% of peak amplitude.

desk verdict Solid NCDE-on-power application with real active-Trojan results, but the headline dormant/three-state claim was never measured on the real dormant traces the authors already had. read the letter →

arxiv 2607.23417 v1 pith:RJFIGPOQ submitted 2026-07-26 cs.CR

Hasala Senevirathne , Rahul Vishwakarma , Amin Rezaei This is my paper · ORCID
classification cs.CR
keywords HardwareTrojanDetectionNeuralControlledDifferentialEquationsPowerSide-ChannelAnalysisDormantPredictionSlidingWindowLinearDiscriminant
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

Hardware Trojans can sit quietly inside a chip and only activate under rare conditions, so most detectors catch them only after damage is already possible. This paper shows that a neural controlled differential equation, trained solely on Trojan-free power measurements, can learn the chip’s normal continuous-time power behavior. When new traces are fed through a sliding window, the model’s next-sample prediction error rises if a Trojan is present, even while dormant. A simple linear classifier then sorts each window into three states: clean, dormant Trojan, or active Trojan. On standard FPGA power-trace benchmarks the method matches or beats prior machine-learning detectors on active Trojans and, above a roughly 3% peak-power sensitivity floor, also reports the dormant state that earlier methods leave unlabeled.

What carries the argument

Neural Controlled Differential Equation (NCDE) next-sample predictor: a continuous-time model of nominal power dynamics whose sliding-window mean-squared prediction error becomes the sole feature for an LDA three-way threshold.

What would settle it

Measure real dormant-Trojan power traces (with known trigger timestamps) on the same Sakura-G setup; if the NCDE-plus-LDA pipeline cannot separate them from clean traces at the claimed 3% threshold, or if structured non-Gaussian residuals collapse the three-state accuracy, the central claim fails.

Watch

Extended reading notes

Core claim

An NCDE trained exclusively on Trojan-free power traces, combined with LDA on sliding-window next-sample MSE, can perform three-state classification (no Trojan / dormant Trojan / active Trojan) and detect dormant Trojans once their power deviation exceeds roughly 3% of peak amplitude, with active-Trojan accuracy at or above prior ML methods on the TrustHub/Sakura-G benchmarks.

Load-bearing premise

That the power signature of a real dormant Trojan looks enough like simple random noise added at a few percent of peak amplitude for the reported sensitivity curve to transfer to actual chips.

Editorial extensions

If this is right

  • Security monitors can raise an early warning while a Trojan is still dormant, shrinking the window between insertion and first activation.
  • Three-state labels give operators a graded risk signal instead of a binary clean/infected decision.
  • The same NCDE residual pipeline can be reused for other continuous side-channel tasks such as aging or fault detection without retraining the dynamics model on malicious data.
  • Once multi-modal side-channels are fused, the 3% sensitivity floor may drop, extending coverage to stealthier Trojans.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Because the NCDE never sees Trojan examples during training, the approach is closer to one-class anomaly detection than to supervised malware classifiers, which may ease deployment when golden Trojan-infected chips are scarce.
  • If richer latent-state features replace scalar MSE, the same continuous-time backbone could separate process variation from Trojan footprints more cleanly than noise-injection tests allow.
  • The sliding-window formulation suggests a natural online monitor that could run on edge hardware with modest buffer memory.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 8 minor

Summary. The manuscript proposes HOODOO, a hardware-Trojan detection pipeline in which a Neural Controlled Differential Equation (NCDE) model is trained one-class on Trojan-free power traces to predict the next sample within a sliding window; the resulting next-sample MSE is thresholded by an LDA-calibrated boundary b_LDA (clean vs. infected) and a second threshold T_triggered (dormant vs. active), yielding a three-state classifier. Experiments use the Sakura-G/TrustHub power side-channel dataset [42] (AES and RS232 bases, six Trojan variants, 10,000 traces per category). The active-Trojan detection results are plausible: prediction error elevates markedly under triggered Trojans (Fig. 2c) and the reported active accuracies (92–100%, Table III) are competitive with prior ML detectors. The paper's novelty claim, however, is dormant-Trojan detection and three-state classification, and this is where the evidence thins: the dormant-detection numbers in Table III and the ~3% sensitivity floor in Fig. 3 come entirely from injecting i.i.d. Gaussian noise into Trojan-free traces, and T_triggered is never calibrated (authors state trigger timestamps are unavailable). The NCDE application to side-channel traces is genuinely novel as far as I know, the one-class training protocol is clean and non-circular, and §V.F is unusually candid about limitations.

Significance. If the dormant-detection claim were validated on real dormant traces, this would be a notable advance: most ML-based HT detectors operate post-activation, and a golden-model-free, one-class NCDE pipeline with a three-state output would address a genuine gap. The strengths that survive scrutiny are the sound active-Trojan results on physical hardware measurements, the honest sensitivity floor analysis in Fig. 3, and the explicit limitation discussion in §V.F. However, because the central dormant/three-state claims currently rest on a synthetic noise proxy despite real dormant data being in hand, the significance of the work as written is considerably lower than the abstract suggests. The gap is closable within the manuscript's existing scope and dataset, which is why I do not recommend rejection.

major comments (4)
  1. [§V.D, Table III] The headline contribution — three-state classification with dormant-Trojan detection — is never evaluated on actual dormant-Trojan traces, even though §V.A states the dataset [42] contains 10,000 'HT inactive (dormant)' traces per benchmark alongside the active and Trojan-free categories. Instead, §V.D and the dormant-accuracy column of Table III are built entirely on i.i.d. Gaussian noise injected into Trojan-free traces at 1–5% of peak amplitude. Real dormant TrustHub Trojans contribute only static/leakage current and routing overhead (AES-T500 is 0.29% of base area), a footprint plausibly below the 3% floor the paper itself identifies in §V.F, and almost certainly not white Gaussian. The authors already possess the data needed to close this gap: report per-benchmark detection rates on the real HT-inactive traces. Until then, the claim of 'handling dormant Trojans above a sensitivity t
  2. [§IV.C, Eq. (5), Algorithm 3] The paper presents a three-state classifier (Algorithm 3, Eq. (5)) but states that T_triggered 'requires labeled traces with known trigger timestamps, which are unavailable in the current benchmark' and is therefore never calibrated. What is actually evaluated is (a) binary clean-vs-infected detection via b_LDA and (b) a synthetic noise sensitivity curve. No three-state confusion matrix, no dormant-vs-active error rate, and no evidence that a single monotone MSE axis can support two thresholds simultaneously (a dormant trace with large leakage could exceed a small active Trojan's MSE). Either the three-state claim should be demonstrated on the benchmark's active/dormant split (e.g., calibrating T_triggered on active-trace MSE distributions even without timestamps), or the contribution should be reframed as binary detection plus sensitivity analysis.
  3. [Table III, §V.E] Table III reports single dormant/active accuracy numbers aggregated across six benchmarks whose Trojans span 0.29%–4.46% of base area — an order-of-magnitude spread that almost certainly produces large per-benchmark variance in detectability. No per-benchmark breakdown, no window-level vs trace-level accuracy definition, and no variance over splits or seeds are given. Additionally, the 'Active Acc.' column is indexed by noise-injection level ('1% Thr: 92.4 ... 5% Thr: 100.0'), which is ambiguous: active-Trojan accuracy should be measured on the real HT-activated traces, not as a function of injected noise. As tabulated, it is unclear what quantity each cell reports. This needs a precise metric definition and a per-benchmark table before the comparison to prior work can be interpreted.
  4. [§V.B.3, §IV.C] The calibration protocol for b_LDA is underspecified in a load-bearing way. §V.B.3 says LDA is trained 'on MSE values from both Trojan-free and Trojan-infected traces,' but does not state whether 'infected' means active traces, dormant traces, or both. If b_LDA is calibrated on active traces (the natural reading), dormant traces with subtler deviations would systematically fall below the boundary, and the dormant column of Table III would then reflect only the synthetic experiment. This interacts with major comment 1 and must be clarified. Relatedly, the pipeline is described as 'trained exclusively on Trojan-free data,' but the LDA stage requires labeled infected traces; the framing in the Abstract and §IV should state this dependence on labeled Trojan hardware explicitly, since it is a meaningful deployment assumption.
minor comments (8)
  1. [Fig. 2, §V.C] Fig. 2 presents qualitative predicted-vs-actual traces for the three conditions but no quantitative baseline (MSE values, R², or residual distributions) for the Trojan-free model. A histogram of MSE for the three classes on real data would substantially strengthen the paper and is cheap to add.
  2. [Table I, §IV.A] Table I lists RK4 step size 0.2 while windows are mapped to t ∈ [0,1] (§IV.A.2), implying only ~5 solver steps per 50-sample window. Please clarify whether this is intentional, and whether accuracy is sensitive to step size, W, hidden channels, and stride — an ablation over W and step size is warranted given the sensitivity claims.
  3. [Table III, §V.E] Table III compares against MLNN [32] (gate-level netlists) and GPT-4 [35] (RTL/netlist) — different input modalities and threat assumptions. A note that these are not like-for-like comparisons, and ideally a comparison against power-trace baselines (LSTM [33], HTM [34]) re-run on the same dataset splits, would make the 'superior accuracy' claim defensible.
  4. [§V.E, ref [33]] Reference [33] is titled 'A Siamese deep learning framework...' but is described in §V.E as 'LSTM'. Please reconcile the label with the cited method.
  5. [Algorithm 1] Algorithm 1 concatenates a vector of ones of dimension 'input dim' with h; the role and naming of x here is confusing since x elsewhere denotes the power trace. Rename (e.g., bias term) and explain.
  6. [§V.A] No runtime/latency measurements are reported despite the run-time detection motivation (§I). With W=50, stride 1, and RK4 integration per window, per-window inference cost on the A16 and on CPU should be reported to support deployability claims.
  7. [Abstract, §VI] The abstract and §VI claim 'superior performance relative to conventional machine learning techniques,' but Table III shows HTM [34] at 92.2% active accuracy, which overlaps the paper's own 92.4–100% range depending on the row interpretation. Please temper or precisely support the superiority wording.
  8. [§V.A] Process variation is mentioned only as having been 'addressed in the original dataset by collecting traces from two separate Sakura-G boards' (§V.A). It is unclear whether training and testing traces come from the same or different boards; cross-board evaluation would speak directly to the masking concern raised in §III.B.

Circularity Check

1 steps flagged · score 2.0 of 10

Standard one-class NCDE+LDA pipeline; only mild circularity is presenting noise-injection sensitivity curves as dormant-Trojan accuracy.

  1. fitted input called prediction [§V.D, Fig. 3, Table III (dormant Acc. column)]
    "To evaluate detection sensitivity, we injected normally distributed noise at varying levels (1–5% of peak power trace amplitude) into Trojan-free traces, simulating the subtle power deviations that stealthy hardware Trojans introduce... As shown in Fig. 3, our NCDE-based method successfully detected Trojans at noise levels ≥3% of peak power value. ... NCDE (Ours) ... 1% Thr: 55.7 ... 3% Thr: 80.2 ... 5% Thr: 92.2"

    The reported “dormant Acc. (%)” figures are detection rates on synthetic traces the authors constructed by adding exactly k% peak-amplitude Gaussian noise to clean data, then tabulated under the same k% labels. The quantity is therefore the classifier’s sensitivity to a known injected perturbation, not an independent prediction about real dormant HTs. Presenting that sensitivity curve as dormant-Trojan accuracy renames a fitted/controlled experimental condition as the claimed three-state capability. (Active-Trojan and clean evaluations on real traces are not affected.)

full rationale

The core derivation is not circular. The NCDE is trained solely on Trojan-free traces to minimize next-sample MSE (Eq. 2), a conventional one-class residual model; higher MSE on held-out traces is an independent empirical signal, not forced by definition. LDA’s boundary b_LDA is ordinary supervised calibration on labeled clean vs. infected MSE values and does not make the detection claim tautological. Active-Trojan numbers in Table III are evaluated against real TrustHub/Sakura-G activated traces and are therefore externally falsifiable. Self-citations ([11],[14],[15],[19]) appear only as related-work context and do not underwrite the NCDE construction or the decision rule. The sole mild circularity is presentational: §V.D and Table III’s “dormant Acc.” column report detection rates on Trojan-free traces into which the authors themselves injected Gaussian noise at 1–5% of peak amplitude, then index those rates by the same injection levels. That quantity is by construction a noise-sensitivity curve, not a measurement on the benchmark’s actual HT-inactive traces (which the dataset description says exist). This is a renaming of a controlled sensitivity experiment as “dormant Trojan accuracy,” not a load-bearing self-definitional collapse of the method. Score 2 reflects that single minor step; the central NCDE residual + LDA claim remains independently contentful.

Assumptions & free parameters 7 free parameters · 5 assumptions · 1 invented entities

The central claim rests on standard NCDE mathematics, the domain premise that dormant HTs leave a power footprint, several hand-chosen architectural and threshold parameters, and the experimental proxy that Gaussian noise stands in for dormant Trojan leakage. No new physical entity is postulated; HOODOO is a named pipeline. The free parameters that most affect the headline dormant accuracies are the noise amplitude levels and the LDA/MSE thresholds.

free parameters (7)
  • sliding_window_W = 50
    Window length fixed at 50 samples; directly controls temporal context and MSE aggregation. Chosen by authors, not derived.
  • NCDE_hidden_channels = 64
    Hidden state width of the CDE; capacity hyperparameter affecting residual magnitude.
  • b_LDA = fitted on calibration set (value not reported)
    LDA decision boundary on MSE separating clean vs Trojan-infected; fit on labeled calibration MSEs.
  • T_triggered = not calibrated; proxied by 1–5% noise levels
    Second threshold intended to separate dormant from active; authors state it cannot be calibrated from the benchmark and substitute noise intensity instead.
  • noise_amplitude_percent_of_peak = 1%, 2%, 3%, 4%, 5%
    1–5% Gaussian noise levels used both to define and to score dormant detection sensitivity; headline 3% floor depends on this choice.
  • RK4_step_size = 0.2
    Numerical solver step for CDE integration; affects prediction fidelity.
  • AdamW_LR_and_WD = LR 1e-3, WD 1e-4
    Optimization hyperparameters for NCDE training.
assumptions (5)
  • domain assumption Neural Controlled Differential Equations (Kidger et al.) correctly model continuous-time dynamics of irregular or noisy power side-channel traces for next-sample prediction.
    Invoked throughout §III.C and §IV.B as the reason NCDEs outperform discrete RNNs on this signal class.
  • domain assumption A dormant (untriggered) hardware Trojan still produces a measurable deviation in power consumption relative to a golden Trojan-free trace.
    Stated in §III.A and required for any pre-activation detection; limitations §V.F note failure below ~3% peak.
  • ad hoc to paper Mean squared next-sample prediction error aggregated over sliding windows is a sufficient statistic for LDA separation of clean vs infected traces.
    Core of Algorithms 3 and Eq. (3)–(5); authors themselves note richer latent residuals might be better (§V.F).
  • ad hoc to paper Additive white Gaussian noise at a few percent of peak amplitude is a valid experimental proxy for stealthy dormant-Trojan power leakage.
    §V.D sensitivity study and Table III dormant columns rest on this; contradicted in spirit by the limitation that real signatures may be structured/non-Gaussian (§V.F).
  • standard math Cubic spline / Hermite interpolation of discrete power samples yields a control path X(t) adequate for CDE integration in this application.
    Standard NCDE practice cited via Kidger/Morrill; used in §IV.A–B and Algorithm 2.
invented entities (1)
  • HOODOO framework
    purpose: Named end-to-end pipeline combining NCDE next-step model, sliding windows, MSE residuals, and LDA three-state rules for HT detection/prediction.
    Branding of the method in §IV and Fig. 1; not a new physical or mathematical object beyond the composition of existing parts.

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Cite this review

Pith. "Pith review of Early Detection of Hardware Trojans Using Neural Controlled Differential Equations and Analysis of Power Traces." pith.science (2026). https://pith.science/paper/RJFIGPOQ

@misc{pith2026260723417,
  author       = {Pith},
  title        = {Pith review of: Early Detection of Hardware Trojans Using Neural Controlled Differential Equations and Analysis of Power Traces},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/RJFIGPOQ}},
  note         = {Machine review of arXiv:2607.23417}
}
read the original abstract

Evolving Hardware Trojans pose a serious threat to modern digital systems by evading traditional detection through stealthy, adaptive behavior. Even recent methods that leverage advances in machine learning can only detect them after activation, leaving a critical window for potential security breaches. To address this gap, we propose a novel approach for hardware Trojan detection and prediction using Neural Controlled Differential Equations (NCDEs) and analysis of power traces. Our method leverages an NCDE model trained exclusively on Trojan-free data to learn nominal power behavior, combined with a Linear Discriminant Analysis (LDA) classifier calibrated on labeled data, to distinguish between three scenarios: no Trojan, dormant Trojan, and active Trojan. Our method uses a sliding window to process side-channel measurements, enabling detection of subtle power consumption deviations that indicate Trojan presence, even when dormant. Experimental results demonstrate that the proposed NCDE-based method achieves superior accuracy compared to traditional machine learning approaches, with the additional advantage of handling dormant Trojans above a sensitivity threshold. We validate our approach on standard hardware Trojan benchmarks, showing robust detection and prediction performance.

Figures

Figures reproduced from arXiv: 2607.23417 by the authors.

Figure 1
Figure 1. HOODOO: NCDE-based Hardware Trojan Detection and Prediction Framework traces, though they require extensive training data and may not capture continuous-time dynamics. A brain-inspired model known as Hierarchical Temporal Memory (HTM) is proposed for HT detection and is designed to be resilient to natural variations in side-channel measurements [34]. Recently, the application of Large Language Models (LLMs) to hardw… view at source ↗
Figure 3
Figure 3. Detection Sensitivity Thresholds of HTs TABLE III: Comparison of HOODOO with Existing Methods Method 3-State Class? Dormant Acc. (%) Active Acc. (%) MLNN [32] No N/A 85.0 LSTM [33] No N/A 86.8 HTM [34] No N/A 92.2 LLM (GPT-4) [35] No N/A Context-Free: 81.0 Contextual: 91.7 NCDE (Ours) Yes 1% Thr: 55.7 1% Thr: 92.4 2% Thr: 62.5 2% Thr: 94.6 3% Thr: 80.2 3% Thr: 95.4 4% Thr: 88.3 4% Thr: 99.3 5% Thr: 92.2 5% Thr: 100.… view at source ↗
Figure 2
Figure 2. NCDE Predictions under Different HT conditions [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗

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Reference graph

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Pith tools

Reviewed July 30, 2026 · model on record in the stance chip above.