We find mathematically optimal side-channel distinguishers by looking at the side-channel as a communication channel. Our methodology can be adapted to any given scenario (device, signal-to-noise ratio, noise distribution, leakage model, etc.). When the model is known and the noise is Gaussian, the optimal distinguisher outperforms CPA and covariance. However, we show that CPA is optimal when the model is only known on a proportional scale. For non-Gaussian noise, we obtain different optimal distinguishers, one for each noise distribution. When the model is imperfectly known, we consider the scenario of a weighted sum of the sensitive variable bits where the weights are unknown and drawn from a normal law. In this case, our optimal distinguisher performs better than the classical linear regression analysis.