Breaking the challenge

To defeat this watermarking scheme, all we had to do was to recreate the mark that was inserted and to substract it.

The first step was to recover the mark. This was done by renormalizing $D=AM-A$ on periods of $147$ samples and averaging the result on periods of $1470$ samples.

Then, we could ``unwatermark'' the second song $BM$ by remultiplying the extracted mark by the corresponding norm in $BM$ and then performing a simple substraction of $BM$ and the newly created mark.

Our results are illustrated by the figures in the appendix. They represent the outputs of our detection algorithm, for the first forty seconds of the songs. The $x$-axis always represents seconds. Correlations are made on periods of either one second (figures 4, 5) or of fifteen seconds (figure 6).

It should be noted that the knowledge of $\beta$ allows the real detector to perform better than ours, and that the results of the real detector may vary from ours. It is also possible that some elements, like, for example, the inner structure of the mark, allows the construction of a more accurate detector. However, the results of our detector are similar for the two marked songs on the one hand, and for all unmarked song and our newly created one on the other. This lead us to think that our technique allows to remove a proportion of the initial which is enough to make detection fail.

It should also be noted that our newly created song is much closer from the original than the marked version. Consequently, we cannot have any quality problems, and testing the quality of the final result is not required.