A deep learning (DL)-assisted and combined side-channel attack (SCA) is exploited to disclose the secret key of an advanced encryption standard (AES) cryptographic circuit with a countermeasure. Different physical leakages of the protected AES cryptographic circuit such as power dissipation and electromagnetic (EM) emission are captured together at first. Then the deep neural networks are utilised to model the relationship between the power noise and the EM noise by analysing the captured power dissipation and EM emission profiles. Ultimately, a special power attack is performed on the protected AES cryptographic circuit to leak the secret key efficiently through using the EM noise to filter the power noise. As demonstrated in the results, for the conventional SCAs, the secret key of the protected AES cryptographic circuit is undisclosed to the adversary even if 1 million plaintexts are enabled. By contrast, only analysing 32,500 number of plaintexts are sufficient to leak the secret key if the DL-assisted and combined SCA is executed.