Deep Learning Based Side-Channel Attack on Polynomial Multiplication in Post-Quantum Cryptography

Polynomial multiplication, a critical operation in lattice-based post-quantum cryptography, is highly vulnerable to side-channel secret key leak. Recent advancements in deep learning have demonstrated notable effectiveness in side-channel attacks. However, existing deep learning based approaches to attack polynomial multiplication are constrained by several limitations, including the substantial reliance on extensive traces from the target device and the superficial exploration of the effectiveness of diverse deep learning models. In this work, we propose a novel deep learning based side-channel attack on polynomial multiplication, achieving a significant reduction in the number of required traces by fixing the ciphertext and directly employing the key coefficient values as labels. We evaluate the effectiveness of our approach on three key encapsulation mechanisms (KEMs) submitted to the third round of the NIST Post-Quantum Cryptography Standardization Project: NTRU, Saber and Kyber. Each of these KEMs is implemented on an ARM Cortex-M4 embedded processor, utilizing various polynomial multiplication approaches, including schoolbook multiplication, Toom-Cook multiplication, and NTT-based multiplication. We systematically evaluate the performance of four prominent deep learning models: Multi-Layer Perceptron (MLP), Convolutional Neural Network (CNN), Long Short-Term Memory Network (LSTM), and Transformer. Our results indicate that, to fully recover the complete key, CNN and Transformer demonstrate superior performance for NTRU, requiring only 7 traces during the attack stage. For Saber, Transformer exhibits the best performance with 9 traces. For Kyber, MLP outperforms the others with 19 traces. Compared to two recent state-of-the-art side-channel attacks targeting polynomial multiplication, our approach significantly reduces the number of traces required from the target device, with reductions ranging from 62% to 95.5% across different implementations. These results underscore the potential of advanced deep learning techniques in enhancing the efficiency and effectiveness of side-channel attacks on post-quantum cryptographic systems.