The widespread use of public key cryptographic algorithms in embedded devices has made them a primary target for side-channel analysis. Clustering-based Simple Power Analysis (SPA) poses a significant threat to public key implementations by inferring secret keys through the identification of distinguishable patterns in side-channel information. However, traditional clustering-based SPA methods are highly sensitive—even to non-key-dependent patterns—thereby limiting their robustness and practical applicability. To address these limitations, this paper proposes a double clustering method that enhances the flexibility, accuracy, and robustness of clustering-based SPA. By progressively adjusting the the number of clusters, the method adaptively identifies optimal clustering configurations, mitigating the need for fixed assumptions and improving resistance to noise and other interfering factors. Experiments covering multiple cryptographic algorithms, hardware platforms, and countermeasure settings demonstrate that the proposed method consistently outperforms traditional clustering-based SPA methods.

Side-channel analysis (SCA) based on machine learning, particularly neural networks, has gained considerable attention in recent years. However, previous works predominantly focus on establishing connections between labels and related profiled traces. These approaches primarily capture label-related features and often overlook the connections between traces of the same label, resulting in the loss of some valuable information. Besides, the attack traces also contain valuable information that can be used in the training process to assist model learning. In this paper, we propose a profiled SCA approach based on contrastive learning named CL-SCA to address these issues. This approach extracts features by emphasizing the similarities among traces, thereby improving the effectiveness of key recovery while maintaining the advantages of the original SCA approach. Through experiments of different datasets from different platforms, we demonstrate that CL-SCA significantly outperforms other approaches. Moreover, by incorporating attack traces into the training process using our approach, we can further enhance its performance. This extension can improve the effectiveness of key recovery, which is fully verified through experiments on different datasets.

The module-lattice-based digital signature standard, formerly known as CRYSTALS-DILITHIUM, is a lattice-based post-quantum cryptographic scheme. In August 2024, the National Institute of Standards and Technology officially standardized ML-DSA under FIPS 204. ML-DSA generates one valid signature and multiple rejected signatures during a single signing process. Most side-channel attacks targeting ML-DSA have focused solely on the valid signature, while largely neglecting the hints contained in rejected signatures. Building on prior SASCA frameworks originally proposed for ML-DSA, in this paper we present an efficient and fully practical instantiation of a private-key recovery attack on ML-DSA that jointly exploits side-channel leakages from both valid and rejected signatures within a unified factor graph. This concrete instantiation maximizes the information extracted from a single signing attempt and minimizes the number of required traces for full key recovery. We conducted a proof-of-concept experiment with both reference and ASM-optimized implementations on a Cortex-M4 core chip, where the results demonstrate that incorporating rejected signatures reduces the required number of traces by at least 50.0% for full key recovery. Moreover, we show that using only rejected signatures suffices to recover the key with fewer than 30 traces under our setup. Our findings highlight that protecting rejected signatures is crucial, as their leakage provides valuable side-channel information. We strongly recommend implementing countermeasures for rejected signatures during the signing process to mitigate potential threats.