Most recent watermarking schemes differ from symmetric schemes in that the detection process does not require the use of the same private key in both the embedder and the detector. An advantage of such schemes is that estimation of the watermark by collusion attack is rendered impossible, so that the overall system is more secure. Almost all second generation schemes to date are also second-order; that is, they are based on the computation of a quadratic form in the detector. In this work, the authors propose a new class of watermarking schemes which employ an nth-order detection process. The scheme is based on a generalised differential modulation scheme. We address the question of how to choose the watermark signal in order to optimise the output of the detection and examine the efficiency and security of this new class of schemes.