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Side-channel analysis is a non-invasive form of attack that reveals the secret key of the cryptographic circuit by analyzing the leaked physical information. The traditional brute-force and cryptanalysis attacks target the weakness in the encryption algorithm, whereas side-channel attacks use statistical models such as differential analysis and correlation analysis on the leaked information gained from the cryptographic device during the run-time. As a non-invasive and passive attack, the side-channel attack brings a lot of difficulties for detection and defense. In this work, we propose a key update scheme as a countermeasure for power and electromagnetic analysis-based attacks on the cryptographic device. The proposed countermeasure utilizes a secure coprocessor to provide secure key generation and storage in a trusted environment. The experimental results show that the proposed key update scheme can mitigate side-channel attacks significantly.