Second generation watermarking schemes differ from first generation 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 an averaging 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. Recently, Furon presented a unified description of second order schemes. Furon showed that O(m2) attacks were required to estimate the quadratic form where m is the spreading period. This presents a significant improvement over O(m) attacks required to estimate the watermarking key in symmetric schemes. In this work, the authors propose an audio watermarking scheme which employs an n-th order detection process. The scheme is based on a generalized differential modulation scheme and provides increased security over second order schemes. The cost of such increased security is a loss of efficiency, so that the watermark must be spread over more content. The paper presents an efficiency and security analysis for the third- and fourth-order scheme.