💻 computer science

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

This paper proposes a novel hardware Trojan detection framework that utilizes Neural Controlled Differential Equations (NCDEs) to model nominal power traces and a Linear Discriminant Analysis (LDA) classifier to identify and distinguish between dormant and active Trojans, achieving superior accuracy and early detection capabilities compared to traditional machine learning methods.

Original authors: Hasala Senevirathne, Rahul Vishwakarma, Amin Rezaei

Published 2026-07-28

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CC BY 4.0

Original authors: Hasala Senevirathne, Rahul Vishwakarma, Amin Rezaei

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine the world of computer chips as a bustling, high-tech city built inside a tiny silicon neighborhood. Every day, billions of tiny workers (transistors) follow strict instructions to keep your phone, car, or laptop running smoothly. But what if a few of these workers were secretly hired by a villain? These aren't just lazy workers; they are "Hardware Trojans." They are sneaky, hidden modifications planted inside the chip's design. Most of the time, they sit perfectly still, pretending to be normal, waiting for a secret signal to wake up and cause chaos—like stealing your passwords or shutting down a system. The scary part is that once they wake up, it's often too late to stop them.

For years, security experts have tried to catch these digital spies, but it's like looking for a ghost in a crowded room. Traditional methods try to inspect the blueprints (the design) or test the workers one by one, but these spies are too good at hiding. They only show up when they want to, or they hide so well that standard tests miss them completely. This is where a new kind of detective comes in, one that doesn't just look at the workers, but listens to the "heartbeat" of the city. By watching how much electricity the chip uses (its power trace), experts can hear the faint, irregular thumping of a hidden spy. However, these signals are messy and change constantly, making them hard to read with old-school tools.

Enter the researchers from California State University, Long Beach, who have built a new kind of digital detective called HOODOO. Think of HOODOO as a super-smart, continuous-time listener that doesn't just take snapshots of the chip's energy use, but watches the flow of electricity like a river. Instead of checking the water level every second (which might miss a tiny ripple), HOODOO uses a mathematical tool called Neural Controlled Differential Equations (NCDEs). You can imagine NCDEs as a magical lens that turns a jagged, choppy line of data into a smooth, flowing story. This allows the system to learn exactly what a "healthy" chip sounds like when it's doing its normal job.

The genius of this paper lies in how HOODOO spots the trouble. The system is trained only on chips that are known to be clean. It learns the perfect rhythm of a Trojan-free chip. Then, when it listens to a new chip, it tries to predict the next beat of the rhythm. If the chip is clean, the prediction is perfect. But if a Trojan is hiding—even if it's still asleep (dormant)—it creates a tiny, almost invisible wobble in the rhythm. Because HOODOO is so sensitive to the flow of time, it notices these tiny deviations that other methods miss. The paper shows that this approach can successfully distinguish between three scenarios: a chip with no spy, a chip with a sleeping spy, and a chip where the spy has already woken up and is causing trouble.

In their experiments, the team tested this method on standard hardware benchmarks, including chips designed to do encryption and serial communication. They found that HOODOO could reliably detect these hidden threats. Specifically, the system was able to spot a "sleeping" Trojan when the power deviation was at least 3% of the peak power value. Below that 3% threshold, the signal became too quiet to distinguish from normal background noise, suggesting a limit to how small a spy can be before it remains invisible to this specific method. However, for anything larger than that, the method proved highly effective, outperforming older machine learning techniques like LSTMs and Multi-Layer Neural Networks, which often struggle with the messy, irregular nature of real-world power data.

The paper doesn't claim to have solved the problem of hardware security forever, nor does it suggest that HOODOO can catch every single possible spy. The authors are careful to note that their method relies on the Trojan leaving a measurable "footprint" in the power usage. If a spy is designed to be perfectly silent or if the noise in the environment is too high, detection becomes harder. Furthermore, while the system is excellent at telling the difference between "clean" and "infected," telling the difference between a "sleeping" and an "active" Trojan required some extra steps involving noise injection in their tests, as the standard datasets didn't provide exact timestamps for when the spies woke up.

Ultimately, this research suggests that by treating power traces as a continuous, flowing story rather than a series of disconnected dots, we can catch hardware spies much earlier. The HOODOO framework offers a promising new way to keep our digital cities safe, not just by waiting for the alarm to ring, but by listening for the faintest whisper of a secret plan before it ever begins.

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

Problem Statement

Evolving Hardware Trojans (HTs) pose a critical threat to modern digital systems by stealthily altering Integrated Circuits (ICs) to cause unauthorized access, data leakage, or system failure. Traditional detection methods face significant limitations:

Static methods (e.g., logic testing, static analysis) struggle with scalability and fail to identify Trojans with rare activation triggers.
Dynamic methods using standard neural networks (e.g., RNNs, LSTMs) often require substantial computational resources and may fail to capture the irregular, high-dimensional nature of side-channel signals like power consumption.
The Dormant Gap: Most existing approaches focus solely on detecting active Trojans. They lack the capability to identify Trojans that are physically present but currently dormant (not yet triggered), leaving a critical window for security breaches before the malicious payload executes.

Methodology: The HOODOO Framework

The authors propose HOODOO (Hardware TrOjan deTectiOn and preDictiOn framewOrk), a novel approach combining Neural Controlled Differential Equations (NCDEs) with power side-channel analysis. The framework operates through four main stages:

1. Data Acquisition and Preprocessing

Input: High-resolution power consumption traces from hardware platforms (specifically using TrustHub benchmarks on FPGA boards).
Sliding Window: Traces are segmented into windows of $W=50$ samples.
Processing: Each window undergoes normalization (zero mean, unit variance) and is converted into a continuous path using cubic spline or Hermite cubic interpolation. This allows the model to handle irregular sampling and noise.

2. NCDE Model Architecture and Training

Core Concept: Unlike discrete-time RNNs, NCDEs model hidden state evolution as a continuous-time process controlled by the input data. The model is defined by the differential equation:
$h(t) = h(t_0) + \int_{t_0}^{t} f_\theta(h(s)) dX(s)$
where $X(t)$ is the interpolated input path and $f_\theta$ is a neural network governing dynamics.
Training Strategy: The NCDE model is trained exclusively on Trojan-free data. Its objective is to learn the "nominal" power behavior of the circuit and predict the next power sample given a window of preceding samples.
Optimization: The model minimizes the Mean Squared Error (MSE) between predicted and actual power values using the AdamW optimizer and OneCycleLR scheduler.

3. Prediction and Anomaly Detection

Inference: During testing, the trained NCDE model processes new power traces. It predicts the next sample for each sliding window.
Error Aggregation: The squared prediction error is computed for each window. These errors are aggregated across the trace to calculate a global MSE.
Logic: A Trojan-infected circuit deviates from the learned nominal behavior, resulting in a higher MSE compared to a clean circuit.

4. Three-Way Classification

The system employs a Linear Discriminant Analysis (LDA) classifier to categorize the device into three distinct states based on the MSE:

No Trojan: $MSE \leq b_{LDA}$ (where $b_{LDA}$ is the optimal boundary derived from LDA).
Dormant Trojan: $b_{LDA} < MSE \leq T_{triggered}$ (Subtle deviations indicating presence without activation).
Active Trojan: $MSE > T_{triggered}$ (Pronounced deviations indicating payload execution).

Note: While $T_{triggered}$ is defined conceptually, the experimental validation for the dormant-vs-active distinction relies on noise injection levels due to the lack of explicit trigger timestamps in the benchmark dataset.

Key Contributions

Novel Three-Way Classification: The paper introduces a classification scheme that distinguishes between "No Trojan," "Dormant Trojan," and "Active Trojan," moving beyond traditional binary detection.
NCDE Application to Side-Channels: It adapts NCDEs to model the continuous-time dynamics of power traces, effectively handling irregular sampling and capturing subtle temporal dependencies that discrete models might miss.
Dormant Detection Threshold: The work explores the sensitivity threshold at which the model can reliably detect the presence of a Trojan while it remains dormant, identifying a critical boundary for detection capability.
Efficient Sliding Window Implementation: The framework utilizes a systematic sliding window approach to process power traces without requiring hardware modifications.

Experimental Results

The authors validated HOODOO using the TrustHub dataset (AES-128 and RS232 circuits with various Trojan variants) on an NVIDIA A16 GPU.

Baseline Performance: The NCDE model demonstrated strong capability in predicting nominal circuit behavior (Trojan-free) and exhibited clear deviations when Trojans were present.
Detection Sensitivity:
- The method successfully detected Trojans when noise/perturbation levels were $\geq 3\%$ of the peak power trace amplitude.
- Below the 3% threshold, the ability to distinguish dormant Trojans from normal behavior degraded, indicating a current limitation in sensitivity for extremely stealthy Trojans.
Comparison with State-of-the-Art:
- Compared against MLNN, LSTM, HTM, and LLM-based methods, HOODOO achieved competitive or superior accuracy for active Trojan detection (e.g., 95.4% accuracy at 3% noise threshold).
- Crucially, HOODOO is the only method in the comparison that offers dormant detection capability (Three-State Classification), whereas others are limited to binary (Clean vs. Infected) or active-only detection.

Significance and Claims

The paper claims that HOODOO provides a significant advancement in hardware security by enabling proactive measures. By detecting Trojans in their dormant state, security teams can identify malicious hardware before it is triggered and causes system failure or data leakage.

The authors emphasize that their approach:

Does not require hardware modifications.
Leverages the continuous-time modeling of NCDEs to handle the inherent irregularity and noise of side-channel signals.
Offers a more nuanced view of system security than binary classification.

Limitations Acknowledged:
The paper modestly notes that detection assumes dormant Trojans produce a measurable side-channel footprint; Trojans inducing variations below 3% of peak amplitude may currently evade detection. Additionally, the sensitivity analysis uses Gaussian noise as a proxy, whereas real-world dormant Trojans may exhibit structured, non-Gaussian signatures. The authors suggest future work should explore richer anomaly features from NCDE latent states and multi-modal side-channel data to improve sensitivity.