This paper investigates the detection of information hidden in digital media by the least significant bit (LSB) matching scheme. In a theoretical context of known medium parameters, two important results are presented. First, based on the likelihood ratio test, we present a test that asymptotically maximizes the detection power whatever the embedding rate might be. Second, the statistical properties of this test are analytically calculated; it is particularly shown that the decision threshold which warrants a given probability of false-alarm is independent of inspected medium parameters. This provides an asymptotic upper-bound for the detection power of any test that aims at detecting data hidden with the LSB matching method. In practice, when detecting LSB matching, the unknown medium parameters have to be estimated. Based on a local model of digital media, a generalized likelihood ratio test is presented by replacing the unknown parameters by their estimation. Numerical results on large databases highlight the relevance of the proposed methodology and comparison with state-of-the-art detectors shows that the proposed tests perform well.