As a post-quantum digital signature scheme, Dilithium was specifically designed to withstand known quantum algorithm attacks, and its side-channel resistance has garnered significant research attention. However, current side-channel attacks against Dilithium exhibit several limitations: (1) failure to leverage low-correlation characteristics in power traces, (2) loss functions limited to categorical information extraction from power traces, (3) dependency on specific coefficient recovery conditions while neglecting inter-coefficient statistical dependencies, (4) requirement for separate profiling models per intermediate value, resulting in substantial information loss. To address these limitations, we propose an enhanced template attack framework integrating deep learning with classical template attack methodology. Our approach employs a dual-loss similarity learning mechanism for feature extraction from high-dimensional power traces, enabling the construction of more discriminative templates while preserving weakly correlated features. Through assembly-level analysis of the y polynomial generation routine, we reveal inherent correlations among coefficientsyk0,yk1,yk2,yk3. Building on this discovery, our dual-loss similarity learning framework is designed to capture these inter-coefficient relationships, preserving their intrinsic dependencies while achieving effective inter-class separation and intra-class aggregation properties, which significantly enhances the effectiveness of subsequent template attacks. Experimental results on Cortex-M4 power traces demonstrate our method achieves 32.94% polynomial coefficient recovery accuracy for polynomial coefficients y, outperforming conventional SOD-based (83% improvement), T-Test-based (97%), and PCA-based template attacks (197% enhancement). Furthermore, complete private key recovery is achieved with merely 14 power traces under specific conditions. This DL-enhanced template attack framework demonstrates superior side-channel leakage exploitation, yielding substantial performance enhancements over conventional approaches.

In recent years, the security of Dilithium against side-channel attacks (SCA) has attracted great attentions from the cryptographic engineering community. However, existing power analysis attacks cannot fully utilize the side-channel leakages of the Dilithium reference implementation to efficiently recover the private key. In light of this, a screening least square technique assisted multivariate template attack (SLST assisted MTA) is proposed in this paper. In SLST assisted MTA, side-channel leakages of coefficient$y_{i}$of random polynomial y, unsigned number$x_{i}$and random byte string$a_{i^{\prime }}$can be utilized simultaneously to recover coefficient$y_{i}$of random polynomial y with MTA. Then, one can build error-tolerant equations, and the private key$\mathbf {s_{1}}$can be solved with SLST efficiently. We evaluate the private key recovery efficiency of SLST assisted MTA with real traces measured from the Cortex-M4 processor based Dilithium reference implementation, and the evaluation results show that with MTA, 19.41%, 15.70% and 16.88% of the coefficients of y can be accurately recovered in cases of Dilithium 2, 3 and 5. Besides, using SLST, after five times screening, only 38, 40 and 39 power traces are enough to recover private key$\mathbf {s_{1}}$of Dilithium 2, 3 and 5 with 100% of success rate.