Abstract—This paper presents a method for accelerating side-channel attacks on the Rivest-Shamir-Adleman (RSA) algorithm implemented in the GnuPG software by jointly analyzing acoustic and Electromagnetic (EM) emissions. A hardware-software experimental setup was developed to investigate the interaction between these two physical leakage channels during RSA-4096 decryption. The study proposes a signal correction technique based on weighted combination of acoustic and EM signals, enhancing the quality of leaked data and reducing the number of iterations required to recover the private key bits. Experimental results obtained under controlled laboratory conditions demonstrate a statistically significant reduction in the average attack time compared to acoustic-only attacks. The results confirm the feasibility of improving side-channel attacks through multimodal signal analysis and highlight the importance of such techniques in evaluating the practical security of cryptographic implementations.