This paper addresses the problem of detecting the presence of data hidden in digital media by the Least Significant Bit (LSB) matching scheme. In a theoretical context of known digital medium parameters, two important results are presented. First, the use of hypothesis testing theory allows the design of the Most Powerful (MP) test. Second, a study of the MP test provides the opportunity to analytically calculate its statistical properties in order to warrant a given probability of false-alarm. In practice when detecting LSB matching, the unknown medium parameters have to be estimated. Based on a local model of medium content, two different estimations which lead to two different tests are present. A numerical comparison with state-of-the-art detectors shows the good performance of the proposed tests and highlights the relevance of the proposed methodology.