What if the best way to improve an AES side-channel attack is not a new attack at all, but a smarter way to clean the measurements first? This paper uses singular value decomposition to keep useful leakage while suppressing noise. The traces used in side-channel analysis are essential to breaking the key of encryption, and signal quality greatly affects the correct rate of key guessing.

The collected signal is often mixed with strong internal circuit noise, external environmental noise, and other factors, so preprocessing becomes important. The proposed framework targets very low signal-to-noise ratio traces by using singular value decomposition and low-rank matrix approximation theory.

It combines hard thresholding from truncated singular value decomposition with soft threshold singular value shrinkage damping, and evaluates raw traces from DPA contest V2 and AES HD. Collected side-channel information includes physical leakage from encryption and decryption operations, but also unrelated operations and interference from complex environments.

These disturbances are usually treated as noise, so the signal acquisition process is strongly interfered with by noise and trace preprocessing is essential. Side-channel preprocessing can remove noise interference and enhance signal characteristics, reducing the computational complexity of side-channel distinguishers and improving attack efficiency.

Extracting feature information from the side-channel signal is therefore central to improving signal-to-noise ratio and attack success rate. A traditional approach can average traces for noise reduction, but it often requires a massive number of traces; other approaches reduce traces or noise but can remain computationally large or complex.

Earlier work explored fourth-order cumulants, Kalman filtering, wavelet analysis, empirical mode decomposition, singular spectrum analysis, and improved singular value decomposition. Singular value decomposition can extract different characteristic components of the traces, but only one is selected as the signal component, so the others are discarded.

An improved wavelet-transform method using singular spectrum analysis and detrended fluctuation analysis addresses some wavelet-denoising problems, but detrended fluctuation can lose some signal features. The hybrid method follows a relatively complex sequence: Butterworth low-pass filtering, empirical mode decomposition, and wavelet denoising of high-frequency noise.

The method uses the low-rank property of a matrix to distinguish a signal matrix from a noise matrix, treating low-rank Hankel matrix approximation as a way to separate signal and noise. A trace is embedded into a Hankel matrix, and truncated singular value decomposition decomposes that matrix into a low-rank signal matrix and a sparse noise matrix.

The difficulty is that, when noise is high, the signal subspace can still contain residual noise. To address that residual noise, the framework refines three Schatten norm-based hard thresholding truncation methods and introduces two soft threshold shrinkage damping methods.

The paper refines three hard threshold calculation methods for truncated singular value decomposition based on the Schatten norm. The three methods are normalized singular value threshold, norm ratio singular value threshold, and contribution rate singular value threshold.

The framework introduces two kinds of singular value soft threshold operations to shrink and damp singular vectors, respectively. Figure 2 maps the hybrid threshold denoising framework from input to output: standardization, window-length calculation, Hankel matrix construction, and singular value decomposition come first.

The singular values then pass through hard-threshold options—normalized, non-ratio, or contribution-based—followed by soft thresholding through threshold shrinkage and threshold damping. Finally, the method reconstructs the matrix, averages anti-diagonals, and applies inverse standardization, showing how each ordered step contributes to producing the denoised trace.

The trace is normalized first to ensure consistency in scale, and the optimal window length is then determined. A Hankel delay matrix is constructed from that window length, and singular value decomposition obtains the singular values of the trace. Hard thresholding is followed by soft thresholding, which shrinks and damps the truncated singular value sequence before matrix reconstruction.

Because the reconstructed matrix is not Hankel structured, anti-diagonal averaging is performed, and inverse normalization produces the final trace. Truncated singular value decomposition determines an effective rank with a predetermined hard threshold, selects the larger singular values for signal reconstruction, and sets the smaller values to zero.

This requires a hard threshold parameter to be defined in advance empirically, so the paper refines normalized threshold, norm ratio threshold, and contribution threshold truncation. Singular value thresholding uses a soft threshold to shrink singular values while recovering a low-rank matrix through a convex optimization method that minimizes the nuclear norm.

With an appropriate threshold, part of the singular values can be contracted to zero to realize a low-rank approximation. Singular value decomposition is performed on the Hankelized traces, and only singular values satisfying the hard threshold condition are retained.

The retained singular values are contracted by soft threshold shrinkage, while the left and right singular vector matrices remain unchanged and only singular value magnitude changes. After the hybrid threshold method selects singular value components, the selected components are used for matrix reconstruction.

The reconstructed matrix does not conform to the Hankel matrix structure, so diagonal averaging is necessary. That diagonal averaging produces the reconstructed processed side-channel trace as a time series. The evaluation analyzes original and preprocessed traces with non-profiled side-channel analysis, including Correlation Power Analysis with a max discriminant and Mutual Information Analysis with a cumulative sum discriminant.

Signal-to-noise ratio and attack success rate are the primary evaluation metrics, with maximum correlation value and minimum traces used to demonstrate the preprocessing framework. The experiments use part of the DPA contest V2 public database and AES HD dataset, with traces captured from a noisy FPGA.

The paper uses the Hamming weight model to represent leakage information and sets four experiment parameters to zero point one, zero point nine nine seven, zero point nine, and three, respectively. The comparison includes the best-performing wavelet denoising method because other cited methods did not perform well on these datasets or were computationally complex and time-consuming.

Figure three shows one power trace from each dataset, with the area of interest highlighted: yellow for DPA v2 and pink for AES HD. The DPA v2 trace spans roughly three thousand two hundred fifty-three sample points, consistent with measurements covering ten AES rounds, while the AES HD trace comes from an unprotected AES-128 FPGA implementation.

These highlighted regions identify where later preprocessing and side-channel analysis focus on extracting key-related information. For DPA v2, hybrid threshold denoising increased the signal-to-noise ratio for every last-round key byte except the fourth, and the thirteenth byte reached the maximum value.

For DPA v2, the hybrid threshold denoising framework using SVD increased SNR for most last-round-key bytes, except the fourth, with the thirteenth reaching the maximum. The listed average SNR increases for all last-round-key bytes were nineteen point seventy, seventeen point zero one, seventeen point twenty-one, twenty-three point sixteen, twenty-two point thirty-nine, and twenty-three point twenty-six percent, compared with twelve point twenty-nine percent for wavelet denoising.

For AES HD, the signal-to-noise ratio increased for every byte except the fifth, ninth, and fourteenth, and the twelfth byte reached the maximum value. For AES HD, the proposed preprocessing produced average SNR increases of three point sixty-eight, four point eighty-seven, five point eighty-three, eleven point zero one, eleven point zero one, and ten point ninety-three percent, outperforming wavelet denoising by zero point ninety-seven percent.

Table 2 compares the maximum correlation for the correct guess of byte sixteen in the AES-128 last-round key, using traces from DPA v2 and AES HD after different preprocessing methods. Relative to the original baselines of zero point zero four nine and zero point zero four eight, the listed methods report higher correlation values and corresponding improvements, with NTD-SVD, NRTD-SVD, and CTD-SVD each reporting zero point zero seven nine for AES HD.

This matters because correlation is used here as an indicator of how clearly the correct key guess can be distinguished. Figure four compares correlation-coefficient curves for the correct guess of the sixteenth byte of the AES-128 last-round key under several preprocessing methods, in DPA version two and AES HD.

In both panels, the correct-key curves form visible peaks that can be distinguished from the gray wrong-guess traces, while preprocessing changes the curve shapes and peak separation. This matters because correlation coefficient is positively related to signal-to-noise ratio and provides an efficiency indicator for side-channel attacks.

The success-rate evaluation applies CPA and MIA to original traces and traces preprocessed by the proposed framework, relating attack success on the AES-128 last-round key to the number of traces. Using the same number of traces, the proposed preprocessing gives a higher attack success rate than the original traces, and about four thousand traces are needed to reach the original-trace success rate for DPA v2.

Overall, the preprocessing improves attack efficiency and is better than wavelet denoising, but on the AES dataset the CPA success rate is only slightly better than baseline and wavelet denoising. On the AES dataset, MIA after the proposed preprocessing is better than baseline and wavelet denoising.

Figure five compares attack success rate against the number of traces for CPA and MIA, using original traces and several SVD-based preprocessing methods. The four panels cover DPA v2 and AES HD, with success rates for recovering the AES-128 last-round key shown across increasing trace counts.

This matters because success rate is a direct measure of side-channel attack efficiency, allowing the authors to evaluate how preprocessing affects both attack methods and datasets. Table 3 reports the CPA and MIA attack results for the sixteenth byte of the last-round AES-128 key, using traces from DPA v2 and AES HD after different preprocessing methods.

It includes the original baseline alongside NTS-SVD, NRTS-SVD, CTS-SVD, NTD-SVD, NRTD-SVD, and CTD-SVD, with each entry giving the measured number of traces to disclosure. This matters because MTD is used to evaluate preprocessing efficiency in side-channel analysis, making the table a direct comparison of attack effort across datasets and methods.

The preprocessing shows similar or superior performance compared with the baseline. The performance gain is more prominent for CPA, where the minimum traces to disclosure is reduced by almost fifty percent. For MIA, the minimum traces to disclosure reduction is only around ten percent, while CPA attack efficiency is much higher than MIA.

The hybrid threshold framework generally improves signal-to-noise ratio and attack efficiency on DPA v2 and AES HD, although the gains vary by dataset and attack method. That makes preprocessing a practical lever for side-channel analysis.