Danger of low-dimensional watermarking subspaces

The security issue has been neglected for a long time in digital watermarking. Recent results for video watermarking have pointed out that existing watermarking schemes are not secure, i.e., a hostile intelligence succeeds in removing the hidden watermarks. In particular, for a given secret key, many watermarking schemes embed watermarks which lie in the same low-dimensional subspace whatever the host data is. We show that this subspace can be quite easily estimated with an efficient principal component analysis (PCA). For storage convenience, an online expectation-maximization (EM) algorithm is considered. Once this watermarking subspace has been estimated, an attacker only has to project incoming data onto the orthogonal of this subspace to remove the watermark.