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Advancements in quantum computing present a security threat to classical cryptography algorithms. Lattice-based key exchange protocols show strong promise due to their resistance to theoretical quantum-cryptanalysis and low implementation overhead. By contrast, their physical implementations have shown vulnerability against side-channel attacks (SCAs) even with a single power measurement. The state-of-the-art SCAs are, however, limited to simple, sequentialized executions of post-quantum key-exchange (PQKE) protocols, leaving the vulnerability of complex, parallelized architectures unknown. This article proposes 2Deep—a deep-learning (DL)-based SCA—targeting parallelized implementations of PQKE protocols, namely, Frodo and NewHope with data augmentation techniques. Specifically, we explore approaches that convert 1-D time-series power measurement data into 2-D images to formulate SCA an image recognition task. The results show our attack’s superiority over conventional techniques including horizontal differential power analysis (DPA), template attacks (TAs), and straightforward DL approaches. We demonstrate improvements up to 1.5 × to recover a 100% success rate compared to DL with 1-D input data while using fewer data. We furthermore show that machine learning improves the results up to 1.25 × compared to TAs. Furthermore, we perform cross-device attacks that obtain profiles from a single device, which has never been explored. Our 2-D approach is especially favored in this setting, improving the success rate of attacking Frodo from 20% to 99% compared to the 1-D approach. Our work thus urges countermeasures even on parallel architectures and single-trace attacks. [ABSTRACT FROM AUTHOR]