Defeating Lattice-Based Data Hiding Code Via Decoding Security Hole

Lattice code has been widely used for data hiding. It can provide security for data hiding by randomly translating its codebook with a secret dither. However, besides the secret dither, there are an infinite amount of points that are near the secret dither and can also be used for perfect decoding in the noiseless scenario. This means that lattice-based data hiding has a serious security hole, named decoding security hole (DSH) in this paper. After a theoretical analysis of DSH, we find that these points form a convex polytope and the centroid of this convex polytope is the secret dither. Based on this finding, a simple yet effective attack method is presented to estimate the secret dither of lattice-based data hiding. Extensive experimental results show that the proposed method significantly outperforms state-of-the-art attack methods, especially when the number of observations is small or the document-to-watermark ratio changes over a wide range.