Résumé : This paper considers watermarking detection, also known as zero-bit watermarking. A watermark, carrying no hidden message, is inserted in content. The watermark detector checks for the presence of this particular weak signal in content. The paper aims at looking to this problem from a classical detection theory point of view, but with side information enabled at the embedding side. This means that the watermarking signal is a function of the host content. Our study is twofold. The first issue is to design the best embedding function for a given detection function (a Neyman-Pearson detector structure is assumed). The second issue is to find the best detection function for a given embedding function. This yields two conditions, which are mixed into one ‘fundamental' differential equation. Solutions to this equation are optimal in these two senses. Interestingly, there are other solutions than the regular quantization index modulation scheme. The JANIS scheme, for instance, invented in a heuristic manner several years ago, is justified as it is one of these solutions.