Robustness and Efficiency of Non-linear Side-Informed Watermarking Gu´ enol´ e C.M. Silvestre 1 , Neil J. Hurley 1 , and Teddy Furon 2 1 University College Dublin, Belfield, Dublin 4, Ireland {guenole.silvestre,neil.hurley}@ucd.ie 2 IRISA, INRIA, Rennes, France teddy.furon@ieee.org Abstract. A number of new non-linear watermark detectors have been proposed recently [1, 2, 3] in which the watermark detection statistic is an n th order polynomial function of the extracted vector. Coupled with a side-informed watermark embedding scheme that selects a watermark to maximise the detection output, it has been shown that hypothesis tests using such detectors are highly efficient. This paper presents fur- ther analysis of these non-linear schemes, focusing in particular on the robustness of the schemes in the presence of noise and the use of periodic filtering functions in order to reduce interference from the host signal. 1 Introduction Watermark embedding in multimedia contents proceeds by extracting a vector of features r from the original content and mixing that vector with a watermark signal w, to produce a watermarked vector r w . The watermarked vector is em- bedded back into the contents by inverting the extraction process. The object of watermark detection is to reliably detect the presence of the watermark signal in watermarked contents. Most state-of-the-art watermarking schemes are blind and symmetric . In blind schemes, decoding is achieved without recourse to the original signal. In symmetric schemes, the embedding of watermark information depends on a private key which is also available at the detector. Spread-spectrum watermarking [4, 5] is the most common form of blind, symmetric watermarking. A pseudo-random signal, z, is modulated on the original contents and detection relies on an hypothesis test based on the correlation of the received signal with z. Hence, the signal z can be considered as a private key, which must be available to both the embedder and detector. It was widely believed that, with the assumption that the original vectors are Gaussian, the optimum scheme was spread spectrum (SS) with a correlation detector. However, in [1] it was shown that this is not the case and a new class of watermarking schemes was proposed that use side-information to maximise the power of the detector. Recent work has focused on the development of asymmetric watermarking schemes (e.g. [6, 7]) in which detection does not rely on the same private keys F.A.P. Petitcolas (Ed.): IH 2002, LNCS 2578, pp. 106–119, 2003. c  Springer-Verlag Berlin Heidelberg 2003