A bootstrap attack on digital watermarks in the frequency domain

Abstract

In this paper, we propose five simple algorithms to execute a collusion attack given several watermarked documents. Each document considered is a picture represented as a matrix of two dimensional Discrete Cosine Transform (DCT2) coefficients. Our algorithm is independent of media type. Bootstrap methods are used to construct confidence intervals for each DCT2 coefficient and determine its uncertainty. Using simulation studies we show that Bootstrap procedures are highly efficient with respect to the number of iterations and sample size per iteration while maintaining stellar probabilistic coverage, providing results at least as good as averaging or taking the median of signals. Most importantly, a set of simulation studies suggest that the precision of our heuristic methodology increases quickly when the number of watermarked copies are increased, but good probabilistic coverage is achieved with a low number of independently watermarked copies. We conjecture that the Bootstrap methodology will be highly effective in reconstructing the original signal for documents with high redundancy. © 2008 Springer Berlin Heidelberg.