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Side-channel attacks (SCAs), which infer secret information (for example secret keys) by exploiting information that leaks from the implementation (such as power consumption), have been shown to be a non-negligible threat to modern cryptographic implementations and devices in recent years. Hence, how to prevent side-channel attacks on cryptographic devices has become an important problem. One of the widely used countermeasures to against power SCAs is the injection of random noise sequences into the raw leakage traces. However, the indiscriminate injection of random noise can lead to significant increases in energy consumption in device, and ways must be found to reduce the amount of energy in noise generation while keeping the side-channel invisible. In this paper, we propose an optimal energy-efficient design for artificial noise generation to prevent side-channel attacks. This approach exploits the sparsity among the leakage traces. We model the side-channel as a communication channel, which allows us to use channel capacity to measure the mutual information between the secret and the leakage traces. For a given energy budget in the noise generation, we obtain the optimal design of the artificial noise injection by solving the side-channel's channel capacity minimization problem. The experimental results also validate the effectiveness of our proposed scheme.